Sudah siap hadapi UTBK tahun 2022 nanti? Yuk, tingkatkan persiapanmu dengan latihan soal UTBK 2022 Matematika Saintek beserta pembahasannya di bawah ini. Selamat mengerjakan!
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Subtopik : Latihan Soal Barisan dan Deret
1. Diketahui menyatakan suku ke-n suatu barisan aritmetika. Jika , maka nilai dari adalah ….
- -689
- -637
- -585
- 585
- 689
Jawaban: C
Pembahasan:
Dari persamaan , apabila dilakukan substitusi , didapat perhitungan sebagai berikut.
Kemudian, apabila dilakukan substitusi dan gunakan pula nilai didapat perhitungan sebagai berikut.
Selanjutnya, beda dari barisan aritmetika tersebut dapat dihitung sebagai berikut.
Dengan demikian, nilai dari dapat dihitung sebagai berikut.
Jadi, jawaban yang tepat adalah C.
Subtopik : Limit Fungsi Aljabar & Sifat Limit
2. Diketahui dengan . Hasil dari adalah ….
Jawaban: E
Pembahasan:
Akan dihitung nilai dari terlebih dahulu.
Didapat hasil dengan penyebutnya bernilai nol. Namun, diketahui nilai limitnya ada. Oleh karena itu, pembilangnya haruslah bernilai nol sehingga didapat nilai sebagai berikut.
Substitusi sehingga didapat perhitungan sebagai berikut.
Oleh karena itu, nilai dari dapat dihitung sebagai berikut.
Kemudian, ingat bahwa dengan k adalah suatu konstanta.
Akibatnya, didapat hasil perhitungan sebagai berikut.
Dengan demikian, hasil dari adalah
Jadi, jawaban yang tepat adalah E.
Topik: Geometri Saintek
Subtopik: Dimensi Tiga
3. Diketahui kubus ABCD.EFGH memiliki panjang rusuk 3 cm. Jika titik O terletak di tengah diagonal FH dan titik S berada di ruas garis AE sedemikian sehingga AS : ES = 1 : 2, jarak titik E ke bidang FHS adalah … cm.
Jawaban: E
Pembahasan:
Dapat diperhatikan bahwa gambar kubus yang dimaksud pada soal adalah sebagai berikut.
Dapat diperhatikan bahwa SF dan SH akan memiliki panjang yang sama sehingga proyeksi titik E pada bidang SFH akan berada pada garis OS.
Dalam hal ini, jarak titik E ke bidang FHS adalah panjang EP, dengan P adalah titik yang terletak di ruas garis OS sedemikian sehingga EP tegak lurus dengan OS.
Kemudian, perhatikan segitiga siku-siku SEO berikut ini!
Panjang SO dapat dihitung menggunakan Teorema Pythagoras sebagai berikut.
Oleh karena itu, akan dicari panjang ES dan panjang EO terlebih dahulu.
Panjang EO sama dengan setengah dari diagonal bidang EG. Ingat bahwa panjang diagonal bidang suatu kubus sama dengan , dengan s merupakan panjang rusuk kubus. Akibatnya, panjang EO adalah sebagai berikut.
Kemudian, panjang ES didapat dari perbandingan AS : ES = 1 : 2. Akibatnya, panjang ES dapat dihitung sebagai berikut.
Oleh karena itu, panjang SO adalah sebagai berikut.
Akibatnya, panjang EP dapat dihitung sebagai berikut.
Dengan demikian, jarak titik E ke bidang FHS adalah
Jadi, jawaban yang tepat adalah E.
Subtopik : Fungsi Trigonometri
4. Diketahui Jika maka titik potong grafik fungsi terhadap sumbu –y adalah ….
- (0, 2)
- (0, 3)
- (0, 6)
- (0, 9)
- (0, 11)
Jawaban: E
Pembahasan:
Perhatikan perhitungan dari bentuk pertidaksamaan berikut.
Diketahui bahwa . Oleh karena itu, didapat dua persamaan sebagai berikut.
Eliminasi persamaan (1) dan (2), sehingga diperoleh nilai sebagai berikut.
Diperoleh nilai q = 2.
Substitusi nilai q ke persamaan (2), sehingga diperoleh nilai p sebagai berikut.
Diketahui bahwa p,q > 0 sehingga didapat p = 3.
Dengan demikian, fungsi adalah sebagai berikut.
Titik potong fungsi terhadap sumbu-y dapat ditentukan pada saat nilai x = 0.
Dengan demikian, titik potong fungsi terhadap sumbu-y adalah (0, 11).
Jadi, jawaban yang tepat adalah E.
Subtopik : Kaidah Pencacahan
5. Sebanyak 5 siswa berprestasi yang terdiri dari 2 pria dan 3 wanita akan melakukan sesi foto. Banyak susunan berfoto berjajar untuk kelima siswa tersebut dengan 2 siswa pria tidak boleh berdekatan adalah ….
- 36
- 48
- 60
- 72
- 90
Jawaban: D
Pembahasan:
Banyak susunan berfoto untuk kelima siswa tersebut tanpa syarat adalah sebagai berikut.
Untuk menentukan banyak susunan berfoto dengan 2 siswa pria selalu berdekatan adalah dengan menganggap 2 siswa pria tersebut menjadi 1 unsur sehingga banyak unsur yang disusun adalah 4 dan banyak susunan dari 2 pria yang berdekatan adalah 2! = 2.
Akibatnya, banyak susunan berfoto jika 2 pria harus berdekatan adalah sebagai berikut.
Dengan demikian, banyak susunan berfoto berjajar untuk kelima siswa tersebut dengan 2 siswa pria tidak boleh berdekatan adalah 120 – 48 = 72.
Jadi, jawaban yang tepat adalah D.
Topik: Turunan II
SUBTOPIK : Turunan Fungsi Trigonometri
6. Jika , maka
JAWABAN : C
PEMBAHASAN :
Perhatikan bahwa
Misalkan dan , maka
Perhatikan bahwa
Perhatikan pula bahwa
dan
Sehingga
Topik: Integral
SUBTOPIK : Integral Aljabar
7. Suatu fungsi memenuhi Diketahui
Maka nilai dari adalah ….
JAWABAN : B
PEMBAHASAN :
Diketahui
Perhatikan bahwa
Perhatikan bentuk integral berikut
Misalkan , maka .
Untuk batasnya, jika x=0, maka w=0 dan jika x=-3a, maka w=a.
Sehingga
Selanjutnya perhatikan bentuk integral berikut
Misalkan x=2w, maka dx=2dw.
Untuk batasnya, jika x=0, maka w=0 dan jika x=2a, maka w=a.
Sehingga
Selanjutnya perhatikan bahwa
Sehingga
Topik: Teori Peluang
SUBTOPIK : Aturan Perkalian, Kombinasi
8. Banyak bilangan berbentuk dengan adalah ….
- 372
- 420
- 444
- 462
- 504
JAWABAN : D
PEMBAHASAN :
Perhatikan bahwa a,b,c,d,e, dan f dapat ditempati oleh bilangan berapapun dari 0 sampai 9. Namun angka pertama tidak boleh ditempati dengan 0. Sehingga a>0.
Maka .
Hal ini berarti a,b,c,d,e, dan f hanya dapat ditempati oleh bilangan dari 1 sampai 9.
Perhatikan bahwa terdapat empat kondisi yang dapat terjadi, yaitu
Untuk kondisi pertama, berarti sama saja dengan memilih 6 angka berbeda dari 9 angka yang tersedia yang dapat dihitung sebagai
Untuk kondisi kedua, berarti sama saja dengan memilih 5 angka berbeda dari 9 angka yang tersedia yang dapat dihitung sebagai
Untuk kondisi ketiga, berarti sama saja dengan memilih 5 angka berbeda dari 9 angka yang tersedia yang dapat dihitung sebagai
Untuk kondisi keempat, berarti sama saja dengan memilih 4 angka berbeda dari 9 angka yang tersedia yang dapat dihitung sebagai
Sehingga banyaknya bilangan yang terbentuk adalah
Topik: Trigonometri
SUBTOPIK : Jumlah Selisih Sudut, Sudut Rangkap
9. Jika maka ….
JAWABAN : C
PEMBAHASAN :
Dari didapat bahwa
Sehingga
Dan
Perhatikan bahwa
Topik: Limit
SUBTOPIK : Limit Fungsi Aljabar
10. Jika adalah fungsi kontinu dengan maka ….
JAWABAN : D
PEMBAHASAN :
Karena adalah fungsi kontinu dengan maka
Sehingga perhatikan bahwa
Topik: Polinomial
SUBTOPIK : Pembagian Polinomial, Teorema Sisa
11. Sisa pembagian oleh adalah Nilai dari
JAWABAN : E
PEMBAHASAN :
Perhatikan bahwa jika dibagi oleh dan bersisa dapat ditulis sebagai berikut
dengan adalah hasil baginya.
Sehingga
Misalkan maka
Selanjutnya misalkan , maka
Perhatikan bahwa
Sehingga perhatikan bahwa
Topik: Bidang Ruang: Jarak
SUBTOPIK : Jarak Titik ke Titik
12. Diketahui balok ABCD.EFGH dengan panjang, lebar, dan tinggi yang berbeda. Jika diketahui panjang, lebar, dan tingginya dipilih dari himpunan {3 cm, 4 cm, 12 cm} dan panjang AF < AH < AC, maka luas persegi panjang BDHF adalah ….
JAWABAN : B
PEMBAHASAN :
Perhatikan sketsa balok ABCD.EFGH sebagai berikut
Misalkan AB = p, BC = l, CG = t dan dengan p, l, dan t dipilih dari panjang sisi-sisi yang telah diketahui yaitu 3 cm, 4 cm, dan 12 cm.
Sehingga
Perhatikan bahwa
Perhatikan bahwa karena panjang p, l, dan t adalah bilangan positif, maka
Kemudian
Sehingga didapatkan bahwa
Karena panjang sisi-sisi yang telah diketahui yaitu 3 cm, 4 cm, dan 12 cm, maka
Maka luas persegi panjang BDHF adalah
Topik: Lingkaran
SUBTOPIK : Persamaan Lingkaran
13. Lingkaran memiliki jari-jari Jari-jari dari lingkaran adalah ….
JAWABAN : E
PEMBAHASAN :
Perhatikan bahwa jari-jari dari lingkaran adalah
Karena lingkaran memiliki jari-jari maka
Selanjutnya, jari-jari dari lingkaran yaitu
Topik: Vektor
SUBTOPIK : Vektor Posisi dan Komponen, Perkalian Vektor
14. Diketahui dan adalah dua buah vektor yang saling tegak lurus dengan dan . Maka
JAWABAN : B
PEMBAHASAN :
Karenadan adalah dua buah vektor yang saling tegak lurus, maka
Perhatikan bahwa
Maka
Topik: Barisan dan Deret
SUBTOPIK : Barisan & Deret Aritmetika, Barisan & Deret Geometri
15. Diketahui bilangan-bilangan p, q, r, s, dan t membentuk barisan aritmetika dengan rata-rata 45. Jika p, q, dan s membentuk barisan geometri dengan rasio , maka beda barisan aritmetika tersebut adalah ….
JAWABAN : E
PEMBAHASAN :
Misalkan barisan aritmetika tersebut memiliki beda b.
Dengan acuan bilangan r, maka didapat
Karena rata-ratanya adalah 45, maka
Selanjutnya diketahui bahwa p, q, dan s membentuk barisan geometri. Sehingga
Karena r =45, maka
Sehingga b=0 atau b=15.
Jika b=0, maka p = q = r = s = t = 45. Akibatnya didapatkan rasio r = 1. Sehingga tidak memenuhi.
Maka b = 15.
Nah, itulah beberapa kumpulan latihan soal UTBK Matematika Saintek yang bisa kamu jadikan bahan belajarmu untuk persiapan SBMPTN 2022 mendatang. Mau dapat persiapan ekstra untuk UTBK? Kamu bisa bergabung di dalam #PelatnasUTBK! Dapatkan program harian yang dirancang khusus oleh tim Ruangguru untuk membantu persiapanmu. Tidak hanya materi pelajaran, #PelatnasUTBK juga akan memberikan pelatihan kesiapan mental, sehingga fisik dan mentalmu lebih siap dan optimal. Daftar dengan klik di bawah ini ya.
Yuk, berlatih lebih banyak soal lagi dengan ikut tryout UTBK di ruanguji. Psst, soal-soal dan sistem penilaiannya sama seperti UTBK aslinya, lho! Yakin nggak mau cobain?
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<h1 class="content-title">
Latihan Soal & Pembahasan UTBK 2022: Matematika Saintek </h1>
<div class="content-meta">
<p class="content-author"><a href="https://www.ruangguru.com/blog/author/shabrina-alfari" class="">Shabrina Alfari</a> </p>
<p class="content-info"><span>February 7, 2022 • </span> <span>8 minutes read</span></p>
<br />
</div>
<div class="content-body">
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/PK%20-%20Latihan%20soal%20UTBK%20Matematika-01.jpg" alt="Latihan soal UTBK Matematika Saintek" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<blockquote>
<p style="font-size: 16px; text-align: center;">Sudah siap hadapi UTBK tahun 2022 nanti? Yuk, tingkatkan persiapanmu dengan latihan soal UTBK 2022 Matematika Saintek beserta pembahasannya di bawah ini. Selamat mengerjakan!</p>
</blockquote>
<p style="text-align: center;">—</p>
<p style="text-align: center;"><span id="more-3685"></span></p>
<p style="text-align: center;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<h2><span style="font-size: 16px;"><strong>Topik: </strong><a href="/blog/barisan-dan-deret-geometri-rumus-un-sn-dan-deret-geometri-tak-hingga" rel="noopener"><strong>Barisan dan Deret </strong></a></span></h2>
<p><strong><span>Subtopik</span></strong> <strong><span>: Latihan Soal Barisan dan Deret</span></strong></p>
<p><span></span><span>1. Diketahui <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1-Oct-25-2021-10-16-50-75-AM.png" alt="1-Oct-25-2021-10-16-50-75-AM" width="19" loading="lazy" style="width: 19px;"></span><span>menyatakan suku ke-<em>n</em></span><span> suatu barisan aritmetika. </span><span>Jika <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2-Oct-25-2021-10-16-50-93-AM.png" alt="2-Oct-25-2021-10-16-50-93-AM" width="153" loading="lazy" style="width: 153px;"></span><span>, maka nilai dari <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/3-Oct-25-2021-10-16-50-80-AM.png" alt="3-Oct-25-2021-10-16-50-80-AM" width="24" loading="lazy" style="width: 24px;"></span><span> adalah ….</span></p>
<ol style="list-style-type: upper-alpha;">
<li>-689</li>
<li>-637</li>
<li>-585</li>
<li>585</li>
<li>689</li>
</ol>
<p><strong><span> </span></strong></p>
<p><strong><span>Jawaban: C</span></strong></p>
<p><strong><span>Pembahasan: </span></strong></p>
<p><span>Dari persamaan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2-Oct-25-2021-10-16-50-93-AM.png" alt="2-Oct-25-2021-10-16-50-93-AM" width="153" loading="lazy" style="width: 153px;"></span><span>, apabila dilakukan substitusi <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/4-Oct-25-2021-10-16-50-81-AM.png" alt="4-Oct-25-2021-10-16-50-81-AM" width="40" loading="lazy" style="width: 40px;"></span><span>, didapat perhitungan sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/5-Oct-25-2021-10-16-50-82-AM.png" alt="5-Oct-25-2021-10-16-50-82-AM" width="166" loading="lazy" style="width: 166px;"><br /></span></p>
<p><span>Kemudian, apabila dilakukan substitusi <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/6-Oct-25-2021-10-16-50-83-AM.png" alt="6-Oct-25-2021-10-16-50-83-AM" width="49" loading="lazy" style="width: 49px;"></span><span> dan gunakan pula nilai <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/7-Oct-25-2021-10-16-51-60-AM.png" alt="7-Oct-25-2021-10-16-51-60-AM" width="75" loading="lazy" style="width: 75px;"></span><span>didapat perhitungan sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8-Oct-25-2021-10-16-50-88-AM.png" alt="8-Oct-25-2021-10-16-50-88-AM" width="206" loading="lazy" style="width: 206px;"><br /></span></p>
<p><span>Selanjutnya, beda dari barisan aritmetika tersebut dapat dihitung sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/9-Oct-25-2021-10-16-50-92-AM.png" alt="9-Oct-25-2021-10-16-50-92-AM" width="193" loading="lazy" style="width: 193px;"><br /></span></p>
<p><span>Dengan demikian, nilai dari <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/3-Oct-25-2021-10-16-50-80-AM.png" alt="3-Oct-25-2021-10-16-50-80-AM" width="24" loading="lazy" style="width: 24px;"></span><span> dapat dihitung sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/10-Oct-25-2021-10-16-50-97-AM.png" alt="10-Oct-25-2021-10-16-50-97-AM" width="194" loading="lazy" style="width: 194px;"><br /></span></p>
<p><strong><u><span>Jadi, jawaban yang tepat adalah C.</span></u></strong></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<h2 style="font-size: 16px;"><strong><span>Topik: </span></strong><a href="/blog/konsep-limit-fungsi-aljabar-dan-sifat-sifatnya" rel="noopener"><strong><span>Limit Fungsi Aljabar</span></strong></a></h2>
<p><strong><span>Subtopik</span></strong> <strong><span>: </span></strong><strong><span> Limit Fungsi Aljabar & Sifat Limit</span></strong></p>
<p><span style="background-color: transparent; font-size: 1rem;">2. Diketahui <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/11-Oct-25-2021-10-24-42-83-AM.png" alt="11-Oct-25-2021-10-24-42-83-AM" width="116" loading="lazy" style="width: 116px;"> </span><span style="background-color: transparent; font-size: 1rem;">dengan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/12-Oct-25-2021-10-24-42-78-AM.png" alt="12-Oct-25-2021-10-24-42-78-AM" width="38" loading="lazy" style="width: 38px;"></span><span style="background-color: transparent; font-size: 1rem;">. Hasil dari <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/13-Oct-25-2021-10-24-42-86-AM.png" alt="13-Oct-25-2021-10-24-42-86-AM" width="188" loading="lazy" style="width: 188px;"> </span><span style="background-color: transparent; font-size: 1rem;"></span><span style="background-color: transparent; font-size: 1rem;">adalah ….</span></p>
<p><span style="background-color: transparent; font-size: 1rem;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/14-Oct-25-2021-10-24-42-76-AM.png" alt="14-Oct-25-2021-10-24-42-76-AM" width="58" loading="lazy" style="width: 58px;"></span></p>
<p> </p>
<p><strong><span>Jawaban: E</span></strong></p>
<p><strong><span>Pembahasan:</span></strong></p>
<p><span>Akan dihitung nilai dari <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/15-Oct-25-2021-10-24-43-53-AM.png" alt="15-Oct-25-2021-10-24-43-53-AM" width="94" loading="lazy" style="width: 94px;"></span><span> terlebih dahulu.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/16-Oct-25-2021-10-24-42-86-AM.png" alt="16-Oct-25-2021-10-24-42-86-AM" width="263" loading="lazy" style="width: 263px;"><br /></span></p>
<p style="text-align: justify;"><span>Didapat hasil dengan penyebutnya bernilai nol. </span><span>Namun, diketahui nilai limitnya ada. Oleh karena itu, pembilangnya haruslah bernilai nol sehingga didapat nilai </span><span> sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/17-Oct-25-2021-10-24-43-60-AM.png" alt="17-Oct-25-2021-10-24-43-60-AM" width="81" loading="lazy" style="width: 81px;"><br /></span></p>
<p><span>Substitusi</span><span> <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/18-Oct-25-2021-10-24-43-61-AM.png" alt="18-Oct-25-2021-10-24-43-61-AM" width="183" loading="lazy" style="width: 183px;"> </span><span>sehingga didapat perhitungan sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/19-Oct-25-2021-10-24-43-72-AM.png" alt="19-Oct-25-2021-10-24-43-72-AM" width="304" loading="lazy" style="width: 304px;"><br /></span></p>
<p><span>Oleh karena itu, nilai dari <span style="background-color: transparent; font-size: 1px;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/13-Oct-25-2021-10-24-42-86-AM.png" alt="13-Oct-25-2021-10-24-42-86-AM" width="188" loading="lazy" style="width: 188px;"></span></span><span> dapat dihitung sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/20-Oct-25-2021-10-24-43-69-AM.png" alt="20-Oct-25-2021-10-24-43-69-AM" width="282" loading="lazy" style="width: 282px;"><br /></span></p>
<p><span>Kemudian, ingat bahwa <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/21-Oct-25-2021-10-24-42-92-AM.png" alt="21-Oct-25-2021-10-24-42-92-AM" width="61" loading="lazy" style="width: 61px;"></span><span> dengan<em> k</em></span><span> adalah suatu konstanta.</span></p>
<p><span>Akibatnya, didapat hasil perhitungan sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/22-Oct-25-2021-10-24-42-94-AM.png" alt="22-Oct-25-2021-10-24-42-94-AM" width="254" loading="lazy" style="width: 254px;"></span></p>
<p><span>Dengan demikian, hasil dari <span style="background-color: transparent; font-size: 1px;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/13-Oct-25-2021-10-24-42-86-AM.png" alt="13-Oct-25-2021-10-24-42-86-AM" width="188" loading="lazy" style="width: 188px;"></span></span><span> adalah </span><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/23-Oct-25-2021-10-24-43-68-AM.png" alt="23-Oct-25-2021-10-24-43-68-AM" width="15" loading="lazy" style="width: 15px;"></span></p>
<p><strong><u><span>Jadi, jawaban yang tepat adalah E.</span></u></strong></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<h2 style="font-size: 16px;"><strong><span>Topik: </span></strong><strong><span>Geometri Saintek</span></strong></h2>
<p><strong><span>Subtopik</span></strong><strong><span>: </span></strong><strong><span> Dimensi Tiga</span></strong></p>
<p style="text-align: justify;"><span></span><span>3. Diketahui kubus ABCD.EFGH memiliki panjang rusuk 3 cm. Jika titik O terletak di tengah diagonal FH dan titik S berada di ruas garis AE sedemikian sehingga AS : ES = 1 : 2, jarak titik E ke bidang FHS adalah … cm.</span></p>
<p><strong><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/24-Oct-25-2021-10-30-35-20-AM.png" alt="24-Oct-25-2021-10-30-35-20-AM" width="82" loading="lazy" style="width: 82px;"></span></strong></p>
<p><strong><span> </span></strong></p>
<p><strong><span>Jawaban: E</span></strong></p>
<p><strong><span>Pembahasan:</span></strong></p>
<p><span>Dapat diperhatikan bahwa gambar kubus yang dimaksud pada soal adalah sebagai berikut.</span></p>
<p><span> <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/25-Oct-25-2021-10-30-35-27-AM.png" alt="25-Oct-25-2021-10-30-35-27-AM" width="267" loading="lazy" style="width: 267px;"></span></p>
<p style="text-align: justify;"><span>Dapat diperhatikan bahwa SF dan SH akan memiliki panjang yang sama sehingga proyeksi titik E pada bidang SFH akan berada pada garis OS.</span></p>
<p style="text-align: justify;"><span>Dalam hal ini, jarak titik E ke bidang FHS adalah panjang EP, dengan P adalah titik yang terletak di ruas garis OS sedemikian sehingga EP tegak lurus dengan OS.</span></p>
<p><span>Kemudian, perhatikan segitiga siku-siku SEO berikut ini!</span></p>
<p><span> <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/26-Oct-25-2021-10-30-35-27-AM.png" alt="26-Oct-25-2021-10-30-35-27-AM" width="212" loading="lazy" style="width: 212px;"></span></p>
<p><span>Panjang SO dapat dihitung menggunakan Teorema Pythagoras sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/27-Oct-25-2021-10-30-35-27-AM.png" alt="27-Oct-25-2021-10-30-35-27-AM" width="119" loading="lazy" style="width: 119px;"></span></p>
<p><span>Oleh karena itu, akan dicari panjang ES dan panjang EO terlebih dahulu.</span></p>
<p style="text-align: justify;"><span>Panjang EO sama dengan setengah dari diagonal bidang EG. Ingat bahwa panjang diagonal bidang suatu kubus sama dengan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/28-Oct-25-2021-10-30-35-28-AM.png" alt="28-Oct-25-2021-10-30-35-28-AM" width="31" loading="lazy" style="width: 31px;"></span><span>, dengan<em> s</em></span><span><em> </em>merupakan panjang rusuk kubus. Akibatnya, panjang EO adalah sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/29-Oct-25-2021-10-30-35-30-AM.png" alt="29-Oct-25-2021-10-30-35-30-AM" width="95" loading="lazy" style="width: 95px;"><br /></span></p>
<p style="text-align: justify;"><span>Kemudian, panjang ES didapat dari perbandingan AS : ES = 1 : 2. </span><span>Akibatnya, panjang ES dapat dihitung sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/30-Oct-25-2021-10-30-35-31-AM.png" alt="30-Oct-25-2021-10-30-35-31-AM" width="90" loading="lazy" style="width: 90px;"><br /></span></p>
<p><span>Oleh karena itu, panjang SO adalah sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/31-Oct-25-2021-10-30-35-33-AM.png" alt="31-Oct-25-2021-10-30-35-33-AM" width="134" loading="lazy" style="width: 134px;"><br /></span></p>
<p><span>Akibatnya, panjang EP dapat dihitung sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/32-Oct-25-2021-10-30-35-35-AM.png" alt="32-Oct-25-2021-10-30-35-35-AM" width="118" loading="lazy" style="width: 118px;"><br /></span></p>
<p><span>Dengan demikian, jarak titik E ke bidang FHS adalah </span><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/33-Oct-25-2021-10-30-35-34-AM.png" alt="33-Oct-25-2021-10-30-35-34-AM" width="64" loading="lazy" style="width: 64px;"></span></p>
<p><strong><u><span>Jadi, jawaban yang tepat adalah E.</span></u></strong></p>
<p><strong><u><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></span></u></strong></p>
<h2 style="font-size: 16px;"><strong><span>Topik: </span></strong><strong><span>Fungsi <a href="/blog/apa-itu-trigonometri" rel="noopener">Trigonometri</a></span></strong></h2>
<p><strong><span>Subtopik</span></strong> <strong><span>: </span></strong><strong><span> Fungsi Trigonometri</span></strong></p>
<p><span style="background-color: transparent; font-size: 1rem;">4. Diketahui <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/34-Oct-25-2021-10-35-38-17-AM.png" alt="34-Oct-25-2021-10-35-38-17-AM" width="260" loading="lazy" style="width: 260px;"></span><span style="background-color: transparent; font-size: 1rem;"> Jika <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/36-Oct-25-2021-10-35-38-29-AM.png" alt="36-Oct-25-2021-10-35-38-29-AM" width="111" loading="lazy" style="width: 111px;"></span><span style="background-color: transparent; font-size: 1rem;"> maka titik potong grafik fungsi <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/37-Oct-25-2021-10-35-38-20-AM.png" alt="37-Oct-25-2021-10-35-38-20-AM" width="28" loading="lazy" style="width: 28px;"></span><span style="background-color: transparent; font-size: 1rem;"> terhadap sumbu –<em>y</em></span><span style="background-color: transparent; font-size: 1rem;"> adalah ….</span></p>
<ol style="list-style-type: upper-alpha;">
<li><span></span><span>(0, 2)</span></li>
<li><span></span><span>(0, 3)</span></li>
<li><span></span><span>(0, 6)</span></li>
<li><span></span><span>(0, 9)</span></li>
<li><span></span><span>(0, 11)</span></li>
</ol>
<p><strong><span> </span></strong></p>
<p><strong><span>Jawaban: E</span></strong></p>
<p><strong><span>Pembahasan: </span></strong></p>
<p><span>Perhatikan perhitungan dari bentuk pertidaksamaan berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/38-Oct-25-2021-10-35-38-20-AM.png" alt="38-Oct-25-2021-10-35-38-20-AM" width="279" loading="lazy" style="width: 279px;"></span><span></span></p>
<p><span>Diketahui bahwa <span style="background-color: transparent; font-size: 1px;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/36-Oct-25-2021-10-35-38-29-AM.png" alt="36-Oct-25-2021-10-35-38-29-AM" width="111" loading="lazy" style="width: 111px;">.</span></span><span> Oleh karena itu, didapat dua persamaan sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/39-Oct-25-2021-10-35-38-21-AM.png" alt="39-Oct-25-2021-10-35-38-21-AM" width="146" loading="lazy" style="width: 146px;"><br /></span></p>
<p><span>Eliminasi persamaan (1) dan (2), sehingga diperoleh nilai sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/40-Oct-25-2021-10-35-38-26-AM.png" alt="40-Oct-25-2021-10-35-38-26-AM" width="121" loading="lazy" style="width: 121px;"><br /></span></p>
<p><span>Diperoleh nilai<em> q</em> = 2</span><span>.</span></p>
<p><span>Substitusi nilai <em>q</em></span><span> ke persamaan (2), sehingga diperoleh nilai <em>p</em></span><span> sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/41-Oct-25-2021-10-35-38-27-AM.png" alt="41-Oct-25-2021-10-35-38-27-AM" width="92" loading="lazy" style="width: 92px;"><br /></span></p>
<p><span>Diketahui bahwa <em>p,q</em> > 0</span><span> sehingga didapat <em>p =</em> 3</span><span>.</span></p>
<p><span>Dengan demikian, fungsi <span style="background-color: transparent; font-size: 1px;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/37-Oct-25-2021-10-35-38-20-AM.png" alt="37-Oct-25-2021-10-35-38-20-AM" width="28" loading="lazy" style="width: 28px;"></span></span><span> adalah sebagai berikut.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/42-Oct-25-2021-10-35-38-30-AM.png" alt="42-Oct-25-2021-10-35-38-30-AM" width="172" loading="lazy" style="width: 172px;"><br /></span></p>
<p><span>Titik potong fungsi <span style="background-color: transparent; font-size: 1px;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/37-Oct-25-2021-10-35-38-20-AM.png" alt="37-Oct-25-2021-10-35-38-20-AM" width="28" loading="lazy" style="width: 28px;"></span></span><span> terhadap sumbu-<em>y</em></span><span><em> </em>dapat ditentukan pada saat nilai <em>x</em> = 0</span><span>.</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/43-Oct-25-2021-10-35-38-34-AM.png" alt="43-Oct-25-2021-10-35-38-34-AM" width="156" loading="lazy" style="width: 156px;"><br /></span></p>
<p><span>Dengan demikian, titik potong fungsi <span style="background-color: transparent; font-size: 1px;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/37-Oct-25-2021-10-35-38-20-AM.png" alt="37-Oct-25-2021-10-35-38-20-AM" width="28" loading="lazy" style="width: 28px;"></span></span><span> terhadap sumbu-<em>y</em></span><span> adalah (0, 11)</span><span>.</span></p>
<p><strong><u><span>Jadi, jawaban yang tepat adalah E.</span></u></strong></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<h2 style="font-size: 16px;"><strong><span>Topik: Teori <a href="/blog/mengetahui-percobaan-ruang-sampel-dan-menghitung-peluang-kejadian" rel="noopener">Peluang</a></span></strong></h2>
<p><strong><span>Subtopik</span></strong> <strong><span>: </span></strong><strong><span> Kaidah Pencacahan</span></strong></p>
<p style="text-align: justify;"><span></span><span>5. Sebanyak 5 siswa berprestasi yang terdiri dari 2 pria dan 3 wanita akan melakukan sesi foto. Banyak susunan berfoto berjajar untuk kelima siswa tersebut dengan 2 siswa pria tidak boleh berdekatan adalah ….</span></p>
<ol style="list-style-type: upper-alpha;">
<li><span></span><span>36</span></li>
<li><span></span><span>48</span></li>
<li><span></span><span>60</span></li>
<li><span></span><span>72</span></li>
<li><span></span><span>90</span></li>
</ol>
<p><strong><span> </span></strong></p>
<p><strong><span>Jawaban: D</span></strong></p>
<p><strong><span>Pembahasan:</span></strong></p>
<p><span>Banyak susunan berfoto untuk kelima siswa tersebut tanpa syarat adalah sebagai berikut.</span></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/44-Oct-25-2021-10-40-20-05-AM.png" alt="44-Oct-25-2021-10-40-20-05-AM" width="209" loading="lazy" style="width: 209px;"></p>
<p style="text-align: justify;"><span>Untuk menentukan banyak susunan berfoto dengan 2 siswa pria selalu berdekatan adalah dengan menganggap 2 siswa pria tersebut menjadi 1 unsur sehingga banyak unsur yang disusun adalah 4 dan banyak susunan dari 2 pria yang berdekatan adalah 2! = 2</span><span>.</span></p>
<p><span>Akibatnya, banyak susunan berfoto jika 2 pria harus berdekatan adalah sebagai berikut.</span></p>
<p><span> <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/45-Oct-25-2021-10-40-20-06-AM.png" alt="45-Oct-25-2021-10-40-20-06-AM" width="217" loading="lazy" style="width: 217px;"></span></p>
<p><span>Dengan demikian, banyak susunan berfoto berjajar untuk kelima siswa tersebut dengan 2 siswa pria tidak boleh berdekatan adalah 120 – 48 = 72.</span></p>
<p><strong><u><span>Jadi, jawaban yang tepat adalah D.</span></u></strong></p>
<p><strong><u><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></span></u></strong></p>
<h2 style="font-size: 16px;"><span><strong>Topik: Turunan II </strong></span></h2>
<p><span><strong>SUBTOPIK : Turunan Fungsi Trigonometri</strong></span></p>
<p><span>6. Jika <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069109.png?width=130&name=1-405577069109.png" alt="1-405577069109" width="130" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069109.png?width=65&name=1-405577069109.png 65w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069109.png?width=130&name=1-405577069109.png 130w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069109.png?width=195&name=1-405577069109.png 195w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069109.png?width=260&name=1-405577069109.png 260w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069109.png?width=325&name=1-405577069109.png 325w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069109.png?width=390&name=1-405577069109.png 390w" sizes="auto, (max-width: 130px) 100vw, 130px" loading="lazy">, maka <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-108.png?width=72&name=2-108.png" alt="2-108" width="72" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-108.png?width=36&name=2-108.png 36w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-108.png?width=72&name=2-108.png 72w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-108.png?width=108&name=2-108.png 108w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-108.png?width=144&name=2-108.png 144w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-108.png?width=180&name=2-108.png 180w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-108.png?width=216&name=2-108.png 216w" sizes="auto, (max-width: 72px) 100vw, 72px" loading="lazy"></span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-69.png?width=64&name=3-69.png" alt="3-69" width="64" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-69.png?width=32&name=3-69.png 32w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-69.png?width=64&name=3-69.png 64w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-69.png?width=96&name=3-69.png 96w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-69.png?width=128&name=3-69.png 128w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-69.png?width=160&name=3-69.png 160w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-69.png?width=192&name=3-69.png 192w" sizes="auto, (max-width: 64px) 100vw, 64px" loading="lazy"></span></p>
<p> </p>
<p><span><strong>JAWABAN : C</strong></span></p>
<p><span><strong>PEMBAHASAN :</strong></span></p>
<p><span>Perhatikan bahwa</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-37.png?width=246&name=4-37.png" alt="soal matematika IPA UTBK SBMPTN 2020" width="246" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-37.png?width=123&name=4-37.png 123w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-37.png?width=246&name=4-37.png 246w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-37.png?width=369&name=4-37.png 369w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-37.png?width=492&name=4-37.png 492w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-37.png?width=615&name=4-37.png 615w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-37.png?width=738&name=4-37.png 738w" sizes="auto, (max-width: 246px) 100vw, 246px" loading="lazy"></span></p>
<p><span>Misalkan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-57.png?width=140&name=5-57.png" alt="5-57" width="140" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-57.png?width=70&name=5-57.png 70w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-57.png?width=140&name=5-57.png 140w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-57.png?width=210&name=5-57.png 210w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-57.png?width=280&name=5-57.png 280w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-57.png?width=350&name=5-57.png 350w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-57.png?width=420&name=5-57.png 420w" sizes="auto, (max-width: 140px) 100vw, 140px" loading="lazy"> dan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-61.png?width=93&name=6-61.png" alt="6-61" width="93" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-61.png?width=47&name=6-61.png 47w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-61.png?width=93&name=6-61.png 93w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-61.png?width=140&name=6-61.png 140w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-61.png?width=186&name=6-61.png 186w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-61.png?width=233&name=6-61.png 233w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-61.png?width=279&name=6-61.png 279w" sizes="auto, (max-width: 93px) 100vw, 93px" loading="lazy">, maka</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-35.png?width=220&name=7-35.png" alt="soal matematika IPA UTBK SBMPTN 2020" width="220" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-35.png?width=110&name=7-35.png 110w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-35.png?width=220&name=7-35.png 220w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-35.png?width=330&name=7-35.png 330w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-35.png?width=440&name=7-35.png 440w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-35.png?width=550&name=7-35.png 550w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-35.png?width=660&name=7-35.png 660w" sizes="auto, (max-width: 220px) 100vw, 220px" loading="lazy"></span></p>
<p><span>Perhatikan bahwa</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-39.png?width=222&name=8-39.png" alt="8-39" width="222" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-39.png?width=111&name=8-39.png 111w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-39.png?width=222&name=8-39.png 222w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-39.png?width=333&name=8-39.png 333w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-39.png?width=444&name=8-39.png 444w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-39.png?width=555&name=8-39.png 555w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-39.png?width=666&name=8-39.png 666w" sizes="auto, (max-width: 222px) 100vw, 222px" loading="lazy"></span></p>
<p><span>Perhatikan pula bahwa</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-35.png?width=157&name=9-35.png" alt="9-35" width="157" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-35.png?width=79&name=9-35.png 79w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-35.png?width=157&name=9-35.png 157w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-35.png?width=236&name=9-35.png 236w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-35.png?width=314&name=9-35.png 314w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-35.png?width=393&name=9-35.png 393w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-35.png?width=471&name=9-35.png 471w" sizes="auto, (max-width: 157px) 100vw, 157px" loading="lazy"></span></p>
<p><span>dan</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-29.png?width=122&name=10-29.png" alt="10-29" width="122" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-29.png?width=61&name=10-29.png 61w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-29.png?width=122&name=10-29.png 122w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-29.png?width=183&name=10-29.png 183w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-29.png?width=244&name=10-29.png 244w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-29.png?width=305&name=10-29.png 305w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-29.png?width=366&name=10-29.png 366w" sizes="auto, (max-width: 122px) 100vw, 122px" loading="lazy"></span></p>
<p><span>Sehingga</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-137.png?width=221&name=11-137.png" alt="11-137" width="221" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-137.png?width=111&name=11-137.png 111w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-137.png?width=221&name=11-137.png 221w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-137.png?width=332&name=11-137.png 332w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-137.png?width=442&name=11-137.png 442w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-137.png?width=553&name=11-137.png 553w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-137.png?width=663&name=11-137.png 663w" sizes="auto, (max-width: 221px) 100vw, 221px" loading="lazy"></span></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<h2 style="font-size: 16px;"><span><strong>Topik: Integral</strong></span></h2>
<p><span><strong>SUBTOPIK : Integral Aljabar</strong></span></p>
<p><span>7. Suatu fungsi memenuhi <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069110.png?width=106&name=1-405577069110.png" alt="1-405577069110" width="106" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069110.png?width=53&name=1-405577069110.png 53w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069110.png?width=106&name=1-405577069110.png 106w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069110.png?width=159&name=1-405577069110.png 159w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069110.png?width=212&name=1-405577069110.png 212w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069110.png?width=265&name=1-405577069110.png 265w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069110.png?width=318&name=1-405577069110.png 318w" sizes="auto, (max-width: 106px) 100vw, 106px" loading="lazy"> Diketahui</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-109.png?width=111&name=2-109.png" alt="2-109" width="111" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-109.png?width=56&name=2-109.png 56w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-109.png?width=111&name=2-109.png 111w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-109.png?width=167&name=2-109.png 167w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-109.png?width=222&name=2-109.png 222w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-109.png?width=278&name=2-109.png 278w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-109.png?width=333&name=2-109.png 333w" sizes="auto, (max-width: 111px) 100vw, 111px" loading="lazy"></span></p>
<p><span>Maka nilai dari <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-70.png?width=133&name=3-70.png" alt="3-70" width="133" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-70.png?width=67&name=3-70.png 67w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-70.png?width=133&name=3-70.png 133w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-70.png?width=200&name=3-70.png 200w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-70.png?width=266&name=3-70.png 266w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-70.png?width=333&name=3-70.png 333w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-70.png?width=399&name=3-70.png 399w" sizes="auto, (max-width: 133px) 100vw, 133px" loading="lazy">adalah ….</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-38.png?width=113&name=4-38.png" alt="4-38" width="113" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-38.png?width=57&name=4-38.png 57w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-38.png?width=113&name=4-38.png 113w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-38.png?width=170&name=4-38.png 170w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-38.png?width=226&name=4-38.png 226w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-38.png?width=283&name=4-38.png 283w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-38.png?width=339&name=4-38.png 339w" sizes="auto, (max-width: 113px) 100vw, 113px" loading="lazy"></span></p>
<p> </p>
<p><span><strong>JAWABAN : B</strong></span></p>
<p><span><strong>PEMBAHASAN :</strong></span></p>
<p><span>Diketahui</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-58.png?width=109&name=5-58.png" alt="5-58" width="109" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-58.png?width=55&name=5-58.png 55w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-58.png?width=109&name=5-58.png 109w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-58.png?width=164&name=5-58.png 164w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-58.png?width=218&name=5-58.png 218w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-58.png?width=273&name=5-58.png 273w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-58.png?width=327&name=5-58.png 327w" sizes="auto, (max-width: 109px) 100vw, 109px" loading="lazy"></span></p>
<p><span>Perhatikan bahwa</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-62.png?width=298&name=6-62.png" alt="6-62" width="298" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-62.png?width=149&name=6-62.png 149w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-62.png?width=298&name=6-62.png 298w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-62.png?width=447&name=6-62.png 447w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-62.png?width=596&name=6-62.png 596w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-62.png?width=745&name=6-62.png 745w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-62.png?width=894&name=6-62.png 894w" sizes="auto, (max-width: 298px) 100vw, 298px" loading="lazy"></span></p>
<p><span>Perhatikan bentuk integral berikut</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-36.png?width=88&name=7-36.png" alt="7-36" width="88" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-36.png?width=44&name=7-36.png 44w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-36.png?width=88&name=7-36.png 88w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-36.png?width=132&name=7-36.png 132w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-36.png?width=176&name=7-36.png 176w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-36.png?width=220&name=7-36.png 220w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-36.png?width=264&name=7-36.png 264w" sizes="auto, (max-width: 88px) 100vw, 88px" loading="lazy"></span></p>
<p><span>Misalkan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-40.png?width=63&name=8-40.png" alt="8-40" width="63" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-40.png?width=32&name=8-40.png 32w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-40.png?width=63&name=8-40.png 63w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-40.png?width=95&name=8-40.png 95w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-40.png?width=126&name=8-40.png 126w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-40.png?width=158&name=8-40.png 158w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-40.png?width=189&name=8-40.png 189w" sizes="auto, (max-width: 63px) 100vw, 63px" loading="lazy">, maka <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-36.png?width=91&name=9-36.png" alt="9-36" width="91" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-36.png?width=46&name=9-36.png 46w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-36.png?width=91&name=9-36.png 91w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-36.png?width=137&name=9-36.png 137w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-36.png?width=182&name=9-36.png 182w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-36.png?width=228&name=9-36.png 228w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-36.png?width=273&name=9-36.png 273w" sizes="auto, (max-width: 91px) 100vw, 91px" loading="lazy">.</span></p>
<p><span>Untuk batasnya, jika <em>x=0</em>, maka <em>w=0</em> dan jika <em>x=-3a</em>, maka <em>w=a</em>.</span></p>
<p><span>Sehingga</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-30.png?width=256&name=10-30.png" alt="10-30" width="256" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-30.png?width=128&name=10-30.png 128w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-30.png?width=256&name=10-30.png 256w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-30.png?width=384&name=10-30.png 384w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-30.png?width=512&name=10-30.png 512w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-30.png?width=640&name=10-30.png 640w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-30.png?width=768&name=10-30.png 768w" sizes="auto, (max-width: 256px) 100vw, 256px" loading="lazy"></span></p>
<p><span>Selanjutnya perhatikan bentuk integral berikut</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-138.png?width=84&name=11-138.png" alt="11-138" width="84" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-138.png?width=42&name=11-138.png 42w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-138.png?width=84&name=11-138.png 84w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-138.png?width=126&name=11-138.png 126w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-138.png?width=168&name=11-138.png 168w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-138.png?width=210&name=11-138.png 210w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-138.png?width=252&name=11-138.png 252w" sizes="auto, (max-width: 84px) 100vw, 84px" loading="lazy"></span></p>
<p><span>Misalkan <em>x=2w</em>, maka <em>dx=2dw</em>.</span></p>
<p><span>Untuk batasnya, jika <em>x=0</em>, maka <em>w=0</em> dan jika <em>x=2a</em>, maka <em>w=a</em>.</span></p>
<p><span>Sehingga</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-26.png?width=215&name=12-26.png" alt="12-26" width="215" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-26.png?width=108&name=12-26.png 108w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-26.png?width=215&name=12-26.png 215w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-26.png?width=323&name=12-26.png 323w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-26.png?width=430&name=12-26.png 430w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-26.png?width=538&name=12-26.png 538w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-26.png?width=645&name=12-26.png 645w" sizes="auto, (max-width: 215px) 100vw, 215px" loading="lazy"></span></p>
<p><span>Selanjutnya perhatikan bahwa</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-23.png?width=145&name=13-23.png" alt="13-23" width="145" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-23.png?width=73&name=13-23.png 73w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-23.png?width=145&name=13-23.png 145w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-23.png?width=218&name=13-23.png 218w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-23.png?width=290&name=13-23.png 290w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-23.png?width=363&name=13-23.png 363w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-23.png?width=435&name=13-23.png 435w" sizes="auto, (max-width: 145px) 100vw, 145px" loading="lazy"></span></p>
<p><span>Sehingga</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069086.png?width=399&name=14-5577069086.png" alt="14-5577069086" width="399" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069086.png?width=200&name=14-5577069086.png 200w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069086.png?width=399&name=14-5577069086.png 399w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069086.png?width=599&name=14-5577069086.png 599w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069086.png?width=798&name=14-5577069086.png 798w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069086.png?width=998&name=14-5577069086.png 998w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069086.png?width=1197&name=14-5577069086.png 1197w" sizes="auto, (max-width: 399px) 100vw, 399px" loading="lazy"></span></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="font-size: 16px;"><span><strong>Topik: Teori Peluang</strong></span></p>
<p><span><strong>SUBTOPIK : Aturan Perkalian, Kombinasi</strong></span></p>
<p><span style="font-weight: normal;">8. Banyak bilangan berbentuk <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069111.png?width=85&name=1-405577069111.png" alt="1-405577069111" width="85" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069111.png?width=43&name=1-405577069111.png 43w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069111.png?width=85&name=1-405577069111.png 85w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069111.png?width=128&name=1-405577069111.png 128w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069111.png?width=170&name=1-405577069111.png 170w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069111.png?width=213&name=1-405577069111.png 213w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069111.png?width=255&name=1-405577069111.png 255w" sizes="auto, (max-width: 85px) 100vw, 85px" loading="lazy"> dengan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-110.png?width=161&name=2-110.png" alt="2-110" width="161" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-110.png?width=81&name=2-110.png 81w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-110.png?width=161&name=2-110.png 161w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-110.png?width=242&name=2-110.png 242w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-110.png?width=322&name=2-110.png 322w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-110.png?width=403&name=2-110.png 403w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-110.png?width=483&name=2-110.png 483w" sizes="auto, (max-width: 161px) 100vw, 161px" loading="lazy">adalah ….<u></u></span><strong><u><span><br /></span></u></strong></p>
<ol style="list-style-type: upper-alpha;">
<li><span>372</span></li>
<li><span>420</span></li>
<li><span>444</span></li>
<li><span>462</span></li>
<li><span>504</span></li>
</ol>
<p> </p>
<p><span><strong>JAWABAN : D</strong></span></p>
<p><span><strong>PEMBAHASAN :</strong></span></p>
<p><span>Perhatikan bahwa <em>a,b,c,d,e</em>, dan <em>f</em> dapat ditempati oleh bilangan berapapun dari 0 sampai 9. Namun angka pertama tidak boleh ditempati dengan 0. Sehingga <em>a>0</em>.</span></p>
<p><span>Maka <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-71.png?width=190&name=3-71.png" alt="3-71" width="190" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-71.png?width=95&name=3-71.png 95w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-71.png?width=190&name=3-71.png 190w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-71.png?width=285&name=3-71.png 285w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-71.png?width=380&name=3-71.png 380w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-71.png?width=475&name=3-71.png 475w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-71.png?width=570&name=3-71.png 570w" sizes="auto, (max-width: 190px) 100vw, 190px" loading="lazy">.</span></p>
<p><span>Hal ini berarti <em>a,b,c,d,e</em>, dan <em>f </em>hanya dapat ditempati oleh bilangan dari 1 sampai 9.</span></p>
<p><span>Perhatikan bahwa terdapat empat kondisi yang dapat terjadi, yaitu</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-39.png?width=227&name=4-39.png" alt="4-39" width="227" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-39.png?width=114&name=4-39.png 114w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-39.png?width=227&name=4-39.png 227w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-39.png?width=341&name=4-39.png 341w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-39.png?width=454&name=4-39.png 454w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-39.png?width=568&name=4-39.png 568w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-39.png?width=681&name=4-39.png 681w" sizes="auto, (max-width: 227px) 100vw, 227px" loading="lazy"></span></p>
<p><span>Untuk kondisi pertama, berarti sama saja dengan memilih 6 angka berbeda dari 9 angka yang tersedia yang dapat dihitung sebagai</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-59.png?width=306&name=5-59.png" alt="5-59" width="306" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-59.png?width=153&name=5-59.png 153w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-59.png?width=306&name=5-59.png 306w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-59.png?width=459&name=5-59.png 459w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-59.png?width=612&name=5-59.png 612w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-59.png?width=765&name=5-59.png 765w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-59.png?width=918&name=5-59.png 918w" sizes="auto, (max-width: 306px) 100vw, 306px" loading="lazy"></span></p>
<p><span>Untuk kondisi kedua, berarti sama saja dengan memilih 5 angka berbeda dari 9 angka yang tersedia yang dapat dihitung sebagai</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-63.png?width=334&name=6-63.png" alt="6-63" width="334" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-63.png?width=167&name=6-63.png 167w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-63.png?width=334&name=6-63.png 334w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-63.png?width=501&name=6-63.png 501w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-63.png?width=668&name=6-63.png 668w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-63.png?width=835&name=6-63.png 835w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-63.png?width=1002&name=6-63.png 1002w" sizes="auto, (max-width: 334px) 100vw, 334px" loading="lazy"></span></p>
<p><span>Untuk kondisi ketiga, berarti sama saja dengan memilih 5 angka berbeda dari 9 angka yang tersedia yang dapat dihitung sebagai</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-37.png?width=85&name=7-37.png" alt="7-37" width="85" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-37.png?width=43&name=7-37.png 43w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-37.png?width=85&name=7-37.png 85w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-37.png?width=128&name=7-37.png 128w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-37.png?width=170&name=7-37.png 170w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-37.png?width=213&name=7-37.png 213w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-37.png?width=255&name=7-37.png 255w" sizes="auto, (max-width: 85px) 100vw, 85px" loading="lazy"></span></p>
<p><span>Untuk kondisi keempat, berarti sama saja dengan memilih 4 angka berbeda dari 9 angka yang tersedia yang dapat dihitung sebagai</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-41.png?width=341&name=8-41.png" alt="8-41" width="341" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-41.png?width=171&name=8-41.png 171w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-41.png?width=341&name=8-41.png 341w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-41.png?width=512&name=8-41.png 512w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-41.png?width=682&name=8-41.png 682w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-41.png?width=853&name=8-41.png 853w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-41.png?width=1023&name=8-41.png 1023w" sizes="auto, (max-width: 341px) 100vw, 341px" loading="lazy"></span></p>
<p><span>Sehingga banyaknya bilangan yang terbentuk adalah</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-37.png?width=224&name=9-37.png" alt="9-37" width="224" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-37.png?width=112&name=9-37.png 112w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-37.png?width=224&name=9-37.png 224w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-37.png?width=336&name=9-37.png 336w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-37.png?width=448&name=9-37.png 448w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-37.png?width=560&name=9-37.png 560w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-37.png?width=672&name=9-37.png 672w" sizes="auto, (max-width: 224px) 100vw, 224px" loading="lazy"></span></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<h2 style="font-size: 16px;"><span><strong>Topik: Trigonometri</strong></span></h2>
<p><span><strong>SUBTOPIK : Jumlah Selisih Sudut, Sudut Rangkap</strong></span></p>
<p><span>9. Jika <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=76&name=1-405577069112.png" alt="1-405577069112" width="76" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=38&name=1-405577069112.png 38w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=76&name=1-405577069112.png 76w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=114&name=1-405577069112.png 114w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=152&name=1-405577069112.png 152w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=190&name=1-405577069112.png 190w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=228&name=1-405577069112.png 228w" sizes="auto, (max-width: 76px) 100vw, 76px" loading="lazy"> maka <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-111.png?width=84&name=2-111.png" alt="2-111" width="84" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-111.png?width=42&name=2-111.png 42w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-111.png?width=84&name=2-111.png 84w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-111.png?width=126&name=2-111.png 126w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-111.png?width=168&name=2-111.png 168w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-111.png?width=210&name=2-111.png 210w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-111.png?width=252&name=2-111.png 252w" sizes="auto, (max-width: 84px) 100vw, 84px" loading="lazy">….</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-72.png?width=212&name=3-72.png" alt="3-72" width="212" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-72.png?width=106&name=3-72.png 106w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-72.png?width=212&name=3-72.png 212w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-72.png?width=318&name=3-72.png 318w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-72.png?width=424&name=3-72.png 424w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-72.png?width=530&name=3-72.png 530w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-72.png?width=636&name=3-72.png 636w" sizes="auto, (max-width: 212px) 100vw, 212px" loading="lazy"></span></p>
<p> </p>
<p><span><strong>JAWABAN : C</strong></span></p>
<p><span><strong>PEMBAHASAN :</strong></span></p>
<p><span>Dari <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=76&name=1-405577069112.png" alt="1-405577069112" width="76" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=38&name=1-405577069112.png 38w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=76&name=1-405577069112.png 76w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=114&name=1-405577069112.png 114w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=152&name=1-405577069112.png 152w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=190&name=1-405577069112.png 190w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069112.png?width=228&name=1-405577069112.png 228w" sizes="auto, (max-width: 76px) 100vw, 76px" loading="lazy"> didapat bahwa</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-40.png?width=201&name=4-40.png" alt="4-40" width="201" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-40.png?width=101&name=4-40.png 101w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-40.png?width=201&name=4-40.png 201w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-40.png?width=302&name=4-40.png 302w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-40.png?width=402&name=4-40.png 402w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-40.png?width=503&name=4-40.png 503w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-40.png?width=603&name=4-40.png 603w" sizes="auto, (max-width: 201px) 100vw, 201px" loading="lazy"></span></p>
<p><span>Sehingga</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-60.png?width=137&name=5-60.png" alt="5-60" width="137" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-60.png?width=69&name=5-60.png 69w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-60.png?width=137&name=5-60.png 137w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-60.png?width=206&name=5-60.png 206w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-60.png?width=274&name=5-60.png 274w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-60.png?width=343&name=5-60.png 343w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-60.png?width=411&name=5-60.png 411w" sizes="auto, (max-width: 137px) 100vw, 137px" loading="lazy"></span></p>
<p><span>Dan</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-64.png?width=153&name=6-64.png" alt="6-64" width="153" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-64.png?width=77&name=6-64.png 77w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-64.png?width=153&name=6-64.png 153w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-64.png?width=230&name=6-64.png 230w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-64.png?width=306&name=6-64.png 306w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-64.png?width=383&name=6-64.png 383w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-64.png?width=459&name=6-64.png 459w" sizes="auto, (max-width: 153px) 100vw, 153px" loading="lazy"></span></p>
<p><span>Perhatikan bahwa</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-38.png?width=255&name=7-38.png" alt="7-38" width="255" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-38.png?width=128&name=7-38.png 128w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-38.png?width=255&name=7-38.png 255w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-38.png?width=383&name=7-38.png 383w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-38.png?width=510&name=7-38.png 510w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-38.png?width=638&name=7-38.png 638w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-38.png?width=765&name=7-38.png 765w" sizes="auto, (max-width: 255px) 100vw, 255px" loading="lazy"></span></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<h2 style="font-size: 16px;"><span><strong>Topik: Limit</strong></span></h2>
<p><span><strong>SUBTOPIK : Limit Fungsi Aljabar</strong></span></p>
<p><span>10. Jika <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=32&name=1-405577069113.png" alt="1-405577069113" width="32" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=16&name=1-405577069113.png 16w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=32&name=1-405577069113.png 32w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=48&name=1-405577069113.png 48w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=64&name=1-405577069113.png 64w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=80&name=1-405577069113.png 80w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=96&name=1-405577069113.png 96w" sizes="auto, (max-width: 32px) 100vw, 32px" loading="lazy">adalah fungsi kontinu dengan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=67&name=2-112.png" alt="2-112" width="67" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=34&name=2-112.png 34w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=67&name=2-112.png 67w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=101&name=2-112.png 101w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=134&name=2-112.png 134w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=168&name=2-112.png 168w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=201&name=2-112.png 201w" sizes="auto, (max-width: 67px) 100vw, 67px" loading="lazy"> maka ….</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-41.png?width=71&name=4-41.png" alt="4-41" width="71" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-41.png?width=36&name=4-41.png 36w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-41.png?width=71&name=4-41.png 71w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-41.png?width=107&name=4-41.png 107w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-41.png?width=142&name=4-41.png 142w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-41.png?width=178&name=4-41.png 178w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-41.png?width=213&name=4-41.png 213w" sizes="auto, (max-width: 71px) 100vw, 71px" loading="lazy"></span></p>
<p> </p>
<p><span><strong>JAWABAN : D</strong></span></p>
<p><span><strong>PEMBAHASAN :</strong></span></p>
<p><span>Karena <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=32&name=1-405577069113.png" alt="1-405577069113" width="32" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=16&name=1-405577069113.png 16w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=32&name=1-405577069113.png 32w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=48&name=1-405577069113.png 48w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=64&name=1-405577069113.png 64w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=80&name=1-405577069113.png 80w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069113.png?width=96&name=1-405577069113.png 96w" sizes="auto, (max-width: 32px) 100vw, 32px" loading="lazy"> adalah fungsi kontinu dengan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=67&name=2-112.png" alt="2-112" width="67" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=34&name=2-112.png 34w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=67&name=2-112.png 67w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=101&name=2-112.png 101w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=134&name=2-112.png 134w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=168&name=2-112.png 168w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-112.png?width=201&name=2-112.png 201w" sizes="auto, (max-width: 67px) 100vw, 67px" loading="lazy"> maka</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-61.png?width=95&name=5-61.png" alt="5-61" width="95" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-61.png?width=48&name=5-61.png 48w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-61.png?width=95&name=5-61.png 95w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-61.png?width=143&name=5-61.png 143w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-61.png?width=190&name=5-61.png 190w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-61.png?width=238&name=5-61.png 238w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-61.png?width=285&name=5-61.png 285w" sizes="auto, (max-width: 95px) 100vw, 95px" loading="lazy"></span></p>
<p><span>Sehingga perhatikan bahwa</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-65.png?width=372&name=6-65.png" alt="6-65" width="372" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-65.png?width=186&name=6-65.png 186w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-65.png?width=372&name=6-65.png 372w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-65.png?width=558&name=6-65.png 558w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-65.png?width=744&name=6-65.png 744w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-65.png?width=930&name=6-65.png 930w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-65.png?width=1116&name=6-65.png 1116w" sizes="auto, (max-width: 372px) 100vw, 372px" loading="lazy"></span></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<h2 style="font-size: 16px;"><span><strong>Topik: Polinomial</strong></span></h2>
<p><span><strong>SUBTOPIK : Pembagian Polinomial, Teorema Sisa</strong></span></p>
<p><span style="font-weight: normal;">11. Sisa pembagian <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069114.png?width=179&name=1-405577069114.png" alt="1-405577069114" width="179" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069114.png?width=90&name=1-405577069114.png 90w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069114.png?width=179&name=1-405577069114.png 179w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069114.png?width=269&name=1-405577069114.png 269w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069114.png?width=358&name=1-405577069114.png 358w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069114.png?width=448&name=1-405577069114.png 448w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069114.png?width=537&name=1-405577069114.png 537w" sizes="auto, (max-width: 179px) 100vw, 179px" loading="lazy"> oleh <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=42&name=2-113.png" alt="2-113" width="42" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=21&name=2-113.png 21w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=42&name=2-113.png 42w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=63&name=2-113.png 63w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=84&name=2-113.png 84w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=105&name=2-113.png 105w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=126&name=2-113.png 126w" sizes="auto, (max-width: 42px) 100vw, 42px" loading="lazy"> adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=52&name=3-74.png" alt="3-74" width="52" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=26&name=3-74.png 26w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=52&name=3-74.png 52w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=78&name=3-74.png 78w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=104&name=3-74.png 104w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=130&name=3-74.png 130w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=156&name=3-74.png 156w" sizes="auto, (max-width: 52px) 100vw, 52px" loading="lazy"> Nilai dari <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-42.png?width=134&name=4-42.png" alt="4-42" width="134" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-42.png?width=67&name=4-42.png 67w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-42.png?width=134&name=4-42.png 134w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-42.png?width=201&name=4-42.png 201w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-42.png?width=268&name=4-42.png 268w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-42.png?width=335&name=4-42.png 335w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-42.png?width=402&name=4-42.png 402w" sizes="auto, (max-width: 134px) 100vw, 134px" loading="lazy"></span><strong><u><span><br /></span></u></strong></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-62.png?width=77&name=5-62.png" alt="5-62" width="77" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-62.png?width=39&name=5-62.png 39w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-62.png?width=77&name=5-62.png 77w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-62.png?width=116&name=5-62.png 116w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-62.png?width=154&name=5-62.png 154w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-62.png?width=193&name=5-62.png 193w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-62.png?width=231&name=5-62.png 231w" sizes="auto, (max-width: 77px) 100vw, 77px" loading="lazy"></span></p>
<p> </p>
<p><span><strong>JAWABAN : E</strong></span></p>
<p><span><strong>PEMBAHASAN :</strong></span></p>
<p><span>Perhatikan bahwa <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-66.png?width=35&name=6-66.png" alt="6-66" width="35" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-66.png?width=18&name=6-66.png 18w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-66.png?width=35&name=6-66.png 35w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-66.png?width=53&name=6-66.png 53w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-66.png?width=70&name=6-66.png 70w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-66.png?width=88&name=6-66.png 88w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-66.png?width=105&name=6-66.png 105w" sizes="auto, (max-width: 35px) 100vw, 35px" loading="lazy"> jika dibagi oleh <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=42&name=2-113.png" alt="2-113" width="42" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=21&name=2-113.png 21w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=42&name=2-113.png 42w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=63&name=2-113.png 63w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=84&name=2-113.png 84w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=105&name=2-113.png 105w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-113.png?width=126&name=2-113.png 126w" sizes="auto, (max-width: 42px) 100vw, 42px" loading="lazy"> dan bersisa <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=52&name=3-74.png" alt="3-74" width="52" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=26&name=3-74.png 26w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=52&name=3-74.png 52w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=78&name=3-74.png 78w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=104&name=3-74.png 104w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=130&name=3-74.png 130w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-74.png?width=156&name=3-74.png 156w" sizes="auto, (max-width: 52px) 100vw, 52px" loading="lazy"> dapat ditulis sebagai berikut</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-39.png?width=217&name=7-39.png" alt="7-39" width="217" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-39.png?width=109&name=7-39.png 109w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-39.png?width=217&name=7-39.png 217w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-39.png?width=326&name=7-39.png 326w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-39.png?width=434&name=7-39.png 434w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-39.png?width=543&name=7-39.png 543w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-39.png?width=651&name=7-39.png 651w" sizes="auto, (max-width: 217px) 100vw, 217px" loading="lazy"></span></p>
<p><span>dengan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-42.png?width=36&name=8-42.png" alt="8-42" width="36" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-42.png?width=18&name=8-42.png 18w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-42.png?width=36&name=8-42.png 36w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-42.png?width=54&name=8-42.png 54w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-42.png?width=72&name=8-42.png 72w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-42.png?width=90&name=8-42.png 90w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-42.png?width=108&name=8-42.png 108w" sizes="auto, (max-width: 36px) 100vw, 36px" loading="lazy"> adalah hasil baginya.</span></p>
<p><span>Sehingga</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-38.png?width=269&name=9-38.png" alt="9-38" width="269" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-38.png?width=135&name=9-38.png 135w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-38.png?width=269&name=9-38.png 269w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-38.png?width=404&name=9-38.png 404w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-38.png?width=538&name=9-38.png 538w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-38.png?width=673&name=9-38.png 673w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-38.png?width=807&name=9-38.png 807w" sizes="auto, (max-width: 269px) 100vw, 269px" loading="lazy"></span></p>
<p><span>Misalkan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-31.png?width=45&name=10-31.png" alt="10-31" width="45" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-31.png?width=23&name=10-31.png 23w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-31.png?width=45&name=10-31.png 45w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-31.png?width=68&name=10-31.png 68w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-31.png?width=90&name=10-31.png 90w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-31.png?width=113&name=10-31.png 113w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-31.png?width=135&name=10-31.png 135w" sizes="auto, (max-width: 45px) 100vw, 45px" loading="lazy"> maka</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-139.png?width=398&name=11-139.png" alt="11-139" width="398" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-139.png?width=199&name=11-139.png 199w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-139.png?width=398&name=11-139.png 398w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-139.png?width=597&name=11-139.png 597w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-139.png?width=796&name=11-139.png 796w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-139.png?width=995&name=11-139.png 995w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-139.png?width=1194&name=11-139.png 1194w" sizes="auto, (max-width: 398px) 100vw, 398px" loading="lazy"></span></p>
<p><span>Selanjutnya misalkan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-27.png?width=58&name=12-27.png" alt="12-27" width="58" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-27.png?width=29&name=12-27.png 29w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-27.png?width=58&name=12-27.png 58w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-27.png?width=87&name=12-27.png 87w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-27.png?width=116&name=12-27.png 116w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-27.png?width=145&name=12-27.png 145w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-27.png?width=174&name=12-27.png 174w" sizes="auto, (max-width: 58px) 100vw, 58px" loading="lazy">, maka</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-24.png?width=510&name=13-24.png" alt="13-24" width="510" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-24.png?width=255&name=13-24.png 255w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-24.png?width=510&name=13-24.png 510w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-24.png?width=765&name=13-24.png 765w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-24.png?width=1020&name=13-24.png 1020w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-24.png?width=1275&name=13-24.png 1275w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-24.png?width=1530&name=13-24.png 1530w" sizes="auto, (max-width: 510px) 100vw, 510px" loading="lazy"></span></p>
<p><span>Perhatikan bahwa</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069087.png?width=167&name=14-5577069087.png" alt="14-5577069087" width="167" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069087.png?width=84&name=14-5577069087.png 84w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069087.png?width=167&name=14-5577069087.png 167w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069087.png?width=251&name=14-5577069087.png 251w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069087.png?width=334&name=14-5577069087.png 334w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069087.png?width=418&name=14-5577069087.png 418w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069087.png?width=501&name=14-5577069087.png 501w" sizes="auto, (max-width: 167px) 100vw, 167px" loading="lazy"></span></p>
<p><span>Sehingga perhatikan bahwa</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//15-19.png?width=255&name=15-19.png" alt="15-19" width="255" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//15-19.png?width=128&name=15-19.png 128w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//15-19.png?width=255&name=15-19.png 255w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//15-19.png?width=383&name=15-19.png 383w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//15-19.png?width=510&name=15-19.png 510w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//15-19.png?width=638&name=15-19.png 638w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//15-19.png?width=765&name=15-19.png 765w" sizes="auto, (max-width: 255px) 100vw, 255px" loading="lazy"></span></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<h2 style="font-size: 16px;"><span><strong>Topik: Bidang Ruang: Jarak</strong></span></h2>
<p><span><strong>SUBTOPIK : Jarak Titik ke Titik</strong></span></p>
<p><span style="font-weight: normal;">12. Diketahui balok ABCD.EFGH dengan panjang, lebar, dan tinggi yang berbeda. Jika diketahui panjang, lebar, dan tingginya dipilih dari himpunan {3 cm, 4 cm, 12 cm} dan panjang AF < AH < AC, maka luas persegi panjang BDHF adalah ….</span><strong><u><span><br /></span></u></strong></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069115.png?width=87&name=1-405577069115.png" alt="1-405577069115" width="87" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069115.png?width=44&name=1-405577069115.png 44w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069115.png?width=87&name=1-405577069115.png 87w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069115.png?width=131&name=1-405577069115.png 131w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069115.png?width=174&name=1-405577069115.png 174w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069115.png?width=218&name=1-405577069115.png 218w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069115.png?width=261&name=1-405577069115.png 261w" sizes="auto, (max-width: 87px) 100vw, 87px" loading="lazy"></span></p>
<p> </p>
<p><span><strong>JAWABAN : B</strong></span></p>
<p><span><strong>PEMBAHASAN :</strong></span></p>
<p><span>Perhatikan sketsa balok ABCD.EFGH sebagai berikut</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-114.png?width=245&name=2-114.png" alt="2-114" width="245" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-114.png?width=123&name=2-114.png 123w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-114.png?width=245&name=2-114.png 245w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-114.png?width=368&name=2-114.png 368w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-114.png?width=490&name=2-114.png 490w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-114.png?width=613&name=2-114.png 613w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-114.png?width=735&name=2-114.png 735w" sizes="auto, (max-width: 245px) 100vw, 245px" loading="lazy"></span></p>
<p><span>Misalkan <em>AB = p, BC = l, CG = t</em> dan dengan <em>p, l,</em> dan <em>t</em> dipilih dari panjang sisi-sisi yang telah diketahui yaitu 3 cm, 4 cm, dan 12 cm.</span></p>
<p><span>Sehingga</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-75.png?width=231&name=3-75.png" alt="3-75" width="231" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-75.png?width=116&name=3-75.png 116w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-75.png?width=231&name=3-75.png 231w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-75.png?width=347&name=3-75.png 347w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-75.png?width=462&name=3-75.png 462w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-75.png?width=578&name=3-75.png 578w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-75.png?width=693&name=3-75.png 693w" sizes="auto, (max-width: 231px) 100vw, 231px" loading="lazy"></span></p>
<p><span>Perhatikan bahwa</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-43.png?width=234&name=4-43.png" alt="4-43" width="234" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-43.png?width=117&name=4-43.png 117w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-43.png?width=234&name=4-43.png 234w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-43.png?width=351&name=4-43.png 351w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-43.png?width=468&name=4-43.png 468w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-43.png?width=585&name=4-43.png 585w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-43.png?width=702&name=4-43.png 702w" sizes="auto, (max-width: 234px) 100vw, 234px" loading="lazy"></span></p>
<p><span>Perhatikan bahwa karena panjang <em>p, l,</em> dan <em>t</em> adalah bilangan positif, maka</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-63.png?width=124&name=5-63.png" alt="5-63" width="124" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-63.png?width=62&name=5-63.png 62w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-63.png?width=124&name=5-63.png 124w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-63.png?width=186&name=5-63.png 186w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-63.png?width=248&name=5-63.png 248w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-63.png?width=310&name=5-63.png 310w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-63.png?width=372&name=5-63.png 372w" sizes="auto, (max-width: 124px) 100vw, 124px" loading="lazy"></span></p>
<p><span>Kemudian</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-67.png?width=142&name=6-67.png" alt="6-67" width="142" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-67.png?width=71&name=6-67.png 71w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-67.png?width=142&name=6-67.png 142w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-67.png?width=213&name=6-67.png 213w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-67.png?width=284&name=6-67.png 284w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-67.png?width=355&name=6-67.png 355w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-67.png?width=426&name=6-67.png 426w" sizes="auto, (max-width: 142px) 100vw, 142px" loading="lazy"></span></p>
<p><span>Sehingga didapatkan bahwa</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-40.png?width=91&name=7-40.png" alt="7-40" width="91" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-40.png?width=46&name=7-40.png 46w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-40.png?width=91&name=7-40.png 91w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-40.png?width=137&name=7-40.png 137w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-40.png?width=182&name=7-40.png 182w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-40.png?width=228&name=7-40.png 228w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-40.png?width=273&name=7-40.png 273w" sizes="auto, (max-width: 91px) 100vw, 91px" loading="lazy"></span></p>
<p><span>Karena panjang sisi-sisi yang telah diketahui yaitu 3 cm, 4 cm, dan 12 cm, maka</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-43.png?width=88&name=8-43.png" alt="8-43" width="88" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-43.png?width=44&name=8-43.png 44w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-43.png?width=88&name=8-43.png 88w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-43.png?width=132&name=8-43.png 132w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-43.png?width=176&name=8-43.png 176w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-43.png?width=220&name=8-43.png 220w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-43.png?width=264&name=8-43.png 264w" sizes="auto, (max-width: 88px) 100vw, 88px" loading="lazy"></span></p>
<p><span>Maka luas persegi panjang BDHF adalah</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-39.png?width=145&name=9-39.png" alt="9-39" width="145" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-39.png?width=73&name=9-39.png 73w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-39.png?width=145&name=9-39.png 145w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-39.png?width=218&name=9-39.png 218w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-39.png?width=290&name=9-39.png 290w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-39.png?width=363&name=9-39.png 363w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-39.png?width=435&name=9-39.png 435w" sizes="auto, (max-width: 145px) 100vw, 145px" loading="lazy"></span></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<h2 style="font-size: 16px;"><span><strong>Topik: Lingkaran</strong></span></h2>
<p><span><strong>SUBTOPIK : Persamaan Lingkaran</strong></span></p>
<p><span>13. Lingkaran <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=190&name=1-405577069116.png" alt="1-405577069116" width="190" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=95&name=1-405577069116.png 95w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=190&name=1-405577069116.png 190w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=285&name=1-405577069116.png 285w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=380&name=1-405577069116.png 380w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=475&name=1-405577069116.png 475w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=570&name=1-405577069116.png 570w" sizes="auto, (max-width: 190px) 100vw, 190px" loading="lazy">memiliki jari-jari <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=17&name=2-115.png" alt="2-115" width="17" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=9&name=2-115.png 9w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=17&name=2-115.png 17w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=26&name=2-115.png 26w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=34&name=2-115.png 34w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=43&name=2-115.png 43w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=51&name=2-115.png 51w" sizes="auto, (max-width: 17px) 100vw, 17px" loading="lazy"> Jari-jari dari lingkaran <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=216&name=8-44.png" alt="8-44" width="216" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=108&name=8-44.png 108w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=216&name=8-44.png 216w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=324&name=8-44.png 324w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=432&name=8-44.png 432w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=540&name=8-44.png 540w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=648&name=8-44.png 648w" sizes="auto, (max-width: 216px) 100vw, 216px" loading="lazy">adalah ….</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-44.png?width=75&name=4-44.png" alt="4-44" width="75" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-44.png?width=38&name=4-44.png 38w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-44.png?width=75&name=4-44.png 75w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-44.png?width=113&name=4-44.png 113w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-44.png?width=150&name=4-44.png 150w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-44.png?width=188&name=4-44.png 188w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-44.png?width=225&name=4-44.png 225w" sizes="auto, (max-width: 75px) 100vw, 75px" loading="lazy"></span></p>
<p> </p>
<p><span><strong>JAWABAN : E</strong></span></p>
<p><span><strong>PEMBAHASAN :</strong></span></p>
<p><span>Perhatikan bahwa jari-jari dari lingkaran <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-64.png?width=185&name=5-64.png" alt="5-64" width="185" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-64.png?width=93&name=5-64.png 93w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-64.png?width=185&name=5-64.png 185w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-64.png?width=278&name=5-64.png 278w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-64.png?width=370&name=5-64.png 370w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-64.png?width=463&name=5-64.png 463w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-64.png?width=555&name=5-64.png 555w" sizes="auto, (max-width: 185px) 100vw, 185px" loading="lazy"> adalah</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-68.png?width=165&name=6-68.png" alt="6-68" width="165" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-68.png?width=83&name=6-68.png 83w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-68.png?width=165&name=6-68.png 165w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-68.png?width=248&name=6-68.png 248w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-68.png?width=330&name=6-68.png 330w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-68.png?width=413&name=6-68.png 413w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-68.png?width=495&name=6-68.png 495w" sizes="auto, (max-width: 165px) 100vw, 165px" loading="lazy"></span></p>
<p><span>Karena lingkaran <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=190&name=1-405577069116.png" alt="1-405577069116" width="190" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=95&name=1-405577069116.png 95w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=190&name=1-405577069116.png 190w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=285&name=1-405577069116.png 285w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=380&name=1-405577069116.png 380w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=475&name=1-405577069116.png 475w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069116.png?width=570&name=1-405577069116.png 570w" sizes="auto, (max-width: 190px) 100vw, 190px" loading="lazy">memiliki jari-jari <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=17&name=2-115.png" alt="2-115" width="17" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=9&name=2-115.png 9w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=17&name=2-115.png 17w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=26&name=2-115.png 26w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=34&name=2-115.png 34w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=43&name=2-115.png 43w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-115.png?width=51&name=2-115.png 51w" sizes="auto, (max-width: 17px) 100vw, 17px" loading="lazy"> maka</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-41.png?width=193&name=7-41.png" alt="7-41" width="193" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-41.png?width=97&name=7-41.png 97w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-41.png?width=193&name=7-41.png 193w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-41.png?width=290&name=7-41.png 290w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-41.png?width=386&name=7-41.png 386w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-41.png?width=483&name=7-41.png 483w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-41.png?width=579&name=7-41.png 579w" sizes="auto, (max-width: 193px) 100vw, 193px" loading="lazy"></span></p>
<p><span>Selanjutnya, jari-jari dari lingkaran <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=216&name=8-44.png" alt="8-44" width="216" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=108&name=8-44.png 108w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=216&name=8-44.png 216w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=324&name=8-44.png 324w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=432&name=8-44.png 432w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=540&name=8-44.png 540w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-44.png?width=648&name=8-44.png 648w" sizes="auto, (max-width: 216px) 100vw, 216px" loading="lazy"> yaitu</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-40.png?width=211&name=9-40.png" alt="9-40" width="211" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-40.png?width=106&name=9-40.png 106w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-40.png?width=211&name=9-40.png 211w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-40.png?width=317&name=9-40.png 317w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-40.png?width=422&name=9-40.png 422w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-40.png?width=528&name=9-40.png 528w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-40.png?width=633&name=9-40.png 633w" sizes="auto, (max-width: 211px) 100vw, 211px" loading="lazy"></span></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<h2 style="font-size: 16px;"><span><strong>Topik: Vektor</strong></span></h2>
<p><span><strong>SUBTOPIK : Vektor Posisi dan Komponen, Perkalian Vektor</strong></span></p>
<p><span>14. Diketahui <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=28&name=1-405577069117.png" alt="1-405577069117" width="28" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=14&name=1-405577069117.png 14w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=28&name=1-405577069117.png 28w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=42&name=1-405577069117.png 42w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=56&name=1-405577069117.png 56w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=70&name=1-405577069117.png 70w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=84&name=1-405577069117.png 84w" sizes="auto, (max-width: 28px) 100vw, 28px" loading="lazy">dan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=38&name=2-116.png" alt="2-116" width="38" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=19&name=2-116.png 19w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=38&name=2-116.png 38w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=57&name=2-116.png 57w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=76&name=2-116.png 76w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=95&name=2-116.png 95w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=114&name=2-116.png 114w" sizes="auto, (max-width: 38px) 100vw, 38px" loading="lazy"> adalah dua buah vektor yang saling tegak lurus dengan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-77.png?width=50&name=3-77.png" alt="3-77" width="50" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-77.png?width=25&name=3-77.png 25w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-77.png?width=50&name=3-77.png 50w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-77.png?width=75&name=3-77.png 75w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-77.png?width=100&name=3-77.png 100w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-77.png?width=125&name=3-77.png 125w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//3-77.png?width=150&name=3-77.png 150w" sizes="auto, (max-width: 50px) 100vw, 50px" loading="lazy"> dan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-45.png?width=52&name=4-45.png" alt="4-45" width="52" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-45.png?width=26&name=4-45.png 26w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-45.png?width=52&name=4-45.png 52w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-45.png?width=78&name=4-45.png 78w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-45.png?width=104&name=4-45.png 104w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-45.png?width=130&name=4-45.png 130w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//4-45.png?width=156&name=4-45.png 156w" sizes="auto, (max-width: 52px) 100vw, 52px" loading="lazy">. Maka <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-65.png?width=83&name=5-65.png" alt="5-65" width="83" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-65.png?width=42&name=5-65.png 42w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-65.png?width=83&name=5-65.png 83w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-65.png?width=125&name=5-65.png 125w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-65.png?width=166&name=5-65.png 166w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-65.png?width=208&name=5-65.png 208w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//5-65.png?width=249&name=5-65.png 249w" sizes="auto, (max-width: 83px) 100vw, 83px" loading="lazy"></span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-69.png?width=74&name=6-69.png" alt="6-69" width="74" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-69.png?width=37&name=6-69.png 37w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-69.png?width=74&name=6-69.png 74w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-69.png?width=111&name=6-69.png 111w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-69.png?width=148&name=6-69.png 148w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-69.png?width=185&name=6-69.png 185w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//6-69.png?width=222&name=6-69.png 222w" sizes="auto, (max-width: 74px) 100vw, 74px" loading="lazy"></span></p>
<p> </p>
<p><span><strong>JAWABAN : B</strong></span></p>
<p><span><strong>PEMBAHASAN :</strong></span></p>
<p><span>Karena<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=28&name=1-405577069117.png" alt="1-405577069117" width="28" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=14&name=1-405577069117.png 14w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=28&name=1-405577069117.png 28w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=42&name=1-405577069117.png 42w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=56&name=1-405577069117.png 56w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=70&name=1-405577069117.png 70w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//1-405577069117.png?width=84&name=1-405577069117.png 84w" sizes="auto, (max-width: 28px) 100vw, 28px" loading="lazy">dan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=38&name=2-116.png" alt="2-116" width="38" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=19&name=2-116.png 19w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=38&name=2-116.png 38w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=57&name=2-116.png 57w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=76&name=2-116.png 76w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=95&name=2-116.png 95w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//2-116.png?width=114&name=2-116.png 114w" sizes="auto, (max-width: 38px) 100vw, 38px" loading="lazy"> adalah dua buah vektor yang saling tegak lurus, maka</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-42.png?width=140&name=7-42.png" alt="7-42" width="140" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-42.png?width=70&name=7-42.png 70w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-42.png?width=140&name=7-42.png 140w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-42.png?width=210&name=7-42.png 210w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-42.png?width=280&name=7-42.png 280w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-42.png?width=350&name=7-42.png 350w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//7-42.png?width=420&name=7-42.png 420w" sizes="auto, (max-width: 140px) 100vw, 140px" loading="lazy"></span></p>
<p><span>Perhatikan bahwa</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-45.png?width=206&name=8-45.png" alt="8-45" width="206" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-45.png?width=103&name=8-45.png 103w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-45.png?width=206&name=8-45.png 206w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-45.png?width=309&name=8-45.png 309w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-45.png?width=412&name=8-45.png 412w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-45.png?width=515&name=8-45.png 515w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//8-45.png?width=618&name=8-45.png 618w" sizes="auto, (max-width: 206px) 100vw, 206px" loading="lazy"></span></p>
<p><span>Maka</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-41.png?width=175&name=9-41.png" alt="9-41" width="175" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-41.png?width=88&name=9-41.png 88w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-41.png?width=175&name=9-41.png 175w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-41.png?width=263&name=9-41.png 263w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-41.png?width=350&name=9-41.png 350w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-41.png?width=438&name=9-41.png 438w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//9-41.png?width=525&name=9-41.png 525w" sizes="auto, (max-width: 175px) 100vw, 175px" loading="lazy"></span></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="font-size: 16px;"><span><strong>Topik: Barisan dan Deret</strong></span></p>
<p><span><strong>SUBTOPIK : Barisan & Deret Aritmetika, Barisan & Deret Geometri</strong></span></p>
<p><span>15. Diketahui bilangan-bilangan <em>p, q, r, s</em>, dan<em> t</em> membentuk barisan aritmetika dengan rata-rata 45. Jika <em>p, q</em>, dan<em> s</em> membentuk barisan geometri dengan rasio <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-32.png?width=39&name=10-32.png" alt="10-32" width="39" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-32.png?width=20&name=10-32.png 20w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-32.png?width=39&name=10-32.png 39w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-32.png?width=59&name=10-32.png 59w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-32.png?width=78&name=10-32.png 78w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-32.png?width=98&name=10-32.png 98w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//10-32.png?width=117&name=10-32.png 117w" sizes="auto, (max-width: 39px) 100vw, 39px" loading="lazy">, maka beda barisan aritmetika tersebut adalah ….</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-140.png?width=71&name=11-140.png" alt="11-140" width="71" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-140.png?width=36&name=11-140.png 36w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-140.png?width=71&name=11-140.png 71w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-140.png?width=107&name=11-140.png 107w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-140.png?width=142&name=11-140.png 142w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-140.png?width=178&name=11-140.png 178w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//11-140.png?width=213&name=11-140.png 213w" sizes="auto, (max-width: 71px) 100vw, 71px" loading="lazy"></span></p>
<p> </p>
<p><span><strong>JAWABAN : E</strong></span></p>
<p><span><strong>PEMBAHASAN :</strong></span></p>
<p><span>Misalkan barisan aritmetika tersebut memiliki beda <em>b</em>.</span></p>
<p><span>Dengan acuan bilangan <em>r</em>, maka didapat</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-28.png?width=106&name=12-28.png" alt="12-28" width="106" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-28.png?width=53&name=12-28.png 53w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-28.png?width=106&name=12-28.png 106w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-28.png?width=159&name=12-28.png 159w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-28.png?width=212&name=12-28.png 212w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-28.png?width=265&name=12-28.png 265w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//12-28.png?width=318&name=12-28.png 318w" sizes="auto, (max-width: 106px) 100vw, 106px" loading="lazy"></span></p>
<p><span>Karena rata-ratanya adalah 45, maka</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-25.png?width=364&name=13-25.png" alt="13-25" width="364" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-25.png?width=182&name=13-25.png 182w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-25.png?width=364&name=13-25.png 364w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-25.png?width=546&name=13-25.png 546w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-25.png?width=728&name=13-25.png 728w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-25.png?width=910&name=13-25.png 910w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//13-25.png?width=1092&name=13-25.png 1092w" sizes="auto, (max-width: 364px) 100vw, 364px" loading="lazy"></span></p>
<p><span>Selanjutnya diketahui bahwa <em>p, q</em>, dan<em> s</em> membentuk barisan geometri. Sehingga</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069088.png?width=235&name=14-5577069088.png" alt="14-5577069088" width="235" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069088.png?width=118&name=14-5577069088.png 118w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069088.png?width=235&name=14-5577069088.png 235w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069088.png?width=353&name=14-5577069088.png 353w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069088.png?width=470&name=14-5577069088.png 470w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069088.png?width=588&name=14-5577069088.png 588w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//14-5577069088.png?width=705&name=14-5577069088.png 705w" sizes="auto, (max-width: 235px) 100vw, 235px" loading="lazy"></span></p>
<p><span>Karena <em>r </em>=45, maka</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs//16-18.png?width=121&name=16-18.png" alt="16-18" width="121" srcset="https://cdn-web.ruangguru.com/landing-pages/assets/hs//16-18.png?width=61&name=16-18.png 61w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//16-18.png?width=121&name=16-18.png 121w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//16-18.png?width=182&name=16-18.png 182w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//16-18.png?width=242&name=16-18.png 242w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//16-18.png?width=303&name=16-18.png 303w, https://cdn-web.ruangguru.com/landing-pages/assets/hs//16-18.png?width=363&name=16-18.png 363w" sizes="auto, (max-width: 121px) 100vw, 121px" loading="lazy"></span></p>
<p><span>Sehingga <em>b</em>=0 atau <em>b</em>=15.</span></p>
<p><span>Jika <em>b</em>=0, maka <em>p = q = r = s = t</em> = 45. Akibatnya didapatkan rasio<em> r</em> = 1. Sehingga tidak memenuhi.</span></p>
<p><span>Maka <em>b</em> = 15.</span></p>
<p><span> <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM.png" alt="LS_-_Separator_Semua_Mapel_+_Corona_SMA-Oct-25-2021-10-42-07-35-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></span></p>
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<img class="icon-call-us" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/4b58468a-b2f9-40e4-867f-d3242a065dcf.png" loading="lazy" alt="Logo Whatsapp Footer" />0815 7441 0000</a>
</address>
</nav>
<nav class="footer-menu social d-none d-lg-block">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
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<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
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</picture>
</a>
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<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
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<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<div class="col-lg-9">
<div class="row">
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Ruangguru</p>
<ul type="none">
<li><a href="https://roboguru.ruangguru.com" target="_blank">Roboguru</a></li>
<li><a href="https://www.ruangguru.com/roboguruplus">Roboguru Plus</a></li>
<li><a href="https://www.ruangguru.com/dafa-lulu">Dafa dan Lulu</a></li>
<li><a href="https://www.ruangguru.com/for-kids/kursus">Kursus for Kids</a></li>
<li><a href="https://www.ruangguru.com/for-kids">Ruangguru for Kids</a></li>
<li><a href="https://www.ruangguru.com/bisnis">Ruangguru for Business</a></li>
<li><a href="https://www.ruangguru.com/ruanguji">Ruanguji</a></li>
<li><a href="https://www.ruangguru.com/blog">Ruangbaca</a></li>
<li><a href="https://www.ruangguru.com/ruangkelas">Ruangkelas</a></li>
<li><a href="https://www.ruangguru.com/ruangbelajar">Ruangbelajar</a></li>
<li><a href="https://pengajar.ruangguru.com/">Ruangpengajar</a></li>
<li><a href="https://www.ruangguru.com/privat">Ruangguru Privat</a></li>
<li><a href="https://www.ruangpeduli.org/" target="_blank">Ruangpeduli</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Bantuan & Panduan</p>
<ul type="none">
<li><a href="https://www.ruangguru.com/company-credentials">Company Credentials</a></li>
<li><a href="https://www.ruangguru.com/beasiswa">Beasiswa Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/cicilan">Cicilan Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/promo">Promo Ruangguru</a></li>
<li><a href="https://ticketing.ruangguru.com/help?request_type_id=459" target="_blank">Vulnerability Report</a></li>
<li><a href="https://www.ruangguru.com/bantuan#layanan">Layanan Pengaduan</a></li>
<li><a href="https://www.ruangguru.com/terms-conditions">Syarat & Ketentuan</a></li>
<li><a href="https://www.ruangguru.com/privacy-policy">Kebijakan Privasi</a></li>
<li><a href="https://www.ruangguru.com/about-us">Tentang Kami</a></li>
<li><a href="https://www.ruangguru.com/contact-us">Kontak Kami</a></li>
<li><a href="https://www.ruangguru.com/press">Press Kit</a></li>
<li><a href="https://www.ruangguru.com/bantuan">Bantuan</a></li>
<li><a href="https://career.ruangguru.com/">Karier</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Lainnya</p>
<ul type="none">
<li><a href="https://www.brainacademy.id/" target="_blank">Brain Academy</a></li>
<li><a href="https://www.english-academy.id/" target="_blank">English Academy</a></li>
<li><a href="https://skillacademy.com/" target="_blank">Skill Academy</a></li>
<li><a href="https://www.ruangkerja.id/" target="_blank">Ruangkerja</a></li>
<li><a href="https://www.schoters.com/id/" target="_blank">Schoters</a></li>
<li><a href="https://www.kalananti.id/" target="_blank">Kalananti</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
<a target="_blank" rel="nofollow" href="https://apps.apple.com/id/app/ruangguru-solusi-belajar/id1099742206?l=id">
<img src="https://cdn-web-2.ruangguru.com/static/appstore.png" loading="lazy" alt="Button App Store Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://appgallery.huawei.com/#/app/C102352375">
<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
</div>
</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
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<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
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</body>
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