use_system_prompt bool 2
classes | question_language stringclasses 2
values | think_language stringclasses 2
values | answer_language stringclasses 2
values | system_prompt stringclasses 8
values | question stringlengths 18 1.49k | prompt stringlengths 126 1.66k | think stringlengths 3.63k 144k | answer stringlengths 394 5.62k | chosen stringlengths 5.27k 146k | rejected stringlengths 1.46k 93.5k |
|---|---|---|---|---|---|---|---|---|---|---|
false | Indonesian | Indonesian | Indonesian | null | Untuk polinomial $P(x)=1-\dfrac{1}{3}x+\dfrac{1}{6}x^{2}$, definisikan $Q(x)=P(x)P(x^{3})P(x^{5})P(x^{7})P(x^{9})=\sum_{i=0}^{50} a_ix^{i}$.
Maka $\sum_{i=0}^{50} |a_i|=\dfrac{m}{n}$, di mana $m$ dan $n$ adalah bilangan asli yang relatif prima. Tentukan $m + n$. | <|im_start|>user
Untuk polinomial $P(x)=1-\dfrac{1}{3}x+\dfrac{1}{6}x^{2}$, definisikan $Q(x)=P(x)P(x^{3})P(x^{5})P(x^{7})P(x^{9})=\sum_{i=0}^{50} a_ix^{i}$.
Maka $\sum_{i=0}^{50} |a_i|=\dfrac{m}{n}$, di mana $m$ dan $n$ adalah bilangan asli yang relatif prima. Tentukan $m + n$.<|im_end|>
<|im_start|>assistant
| Oke, fokus sekarang adalah pada permintaan pengguna untuk menyelesaikan soal tentang polinomial. Diberikan P(x) = 1 - (1/3)x + (1/6)x², lalu Q(x) adalah hasil kali P(x)P(x³)P(x⁵)P(x⁷)P(x⁹), dan kita diminta mencari jumlah absolut koefisien dari Q(x) hingga pangkat 50, yang dinyatakan sebagai m/n dengan m dan n relatif ... | Untuk menyelesaikan masalah ini, kita diberikan polinomial $P(x) = 1 - \frac{1}{3}x + \frac{1}{6}x^2$ dan didefinisikan $Q(x) = P(x)P(x^3)P(x^5)P(x^7)P(x^9)$. Tujuan kita adalah menghitung $\sum_{i=0}^{50} |a_i|$, di mana $Q(x) = \sum_{i=0}^{50} a_ix^i$, lalu menentukan $m + n$ untuk bentuk $\frac{m}{n}$ dengan $m$ dan... | <think>
Oke, fokus sekarang adalah pada permintaan pengguna untuk menyelesaikan soal tentang polinomial. Diberikan P(x) = 1 - (1/3)x + (1/6)x², lalu Q(x) adalah hasil kali P(x)P(x³)P(x⁵)P(x⁷)P(x⁹), dan kita diminta mencari jumlah absolut koefisien dari Q(x) hingga pangkat 50, yang dinyatakan sebagai m/n dengan m dan n ... | <think>
This is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.
Well, so we have this polynomial P(x) = 1 - (1/3)x + (1/6)x², and then Q(x) is the product of P(x^(2k-1)) for k from 1 to 5, right? Wait, no, it's P(x)P(x³)P(x⁵)P(x⁷)P(x⁹), so exponen... |
true | English | English | English | Always write your reasoning process in English, and always provide your answer in English | "Find the number of positive integers $m$ for which there exist nonnegative integers $x_0$ , $x_1$ ,(...TRUNCATED) | "<|im_start|>system\nAlways write your reasoning process in English, and always provide your answer (...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "To solve the problem, we are given a condition involving powers of $ m $:\n\n$$\nm^{x_0} = \\sum_{k(...TRUNCATED) | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) | "<think>\nMencatat permintaan: pengguna memerlukan saya untuk menentukan banyaknya bilangan bulat po(...TRUNCATED) |
true | English | English | English | Always write your reasoning process in English, and always provide your answer in English | "An urn contains $4$ green balls and $6$ blue balls. A second urn contains $16$ green balls and $N$ (...TRUNCATED) | "<|im_start|>system\nAlways write your reasoning process in English, and always provide your answer (...TRUNCATED) | "Okay, let's try to solve this problem step by step. First, let's make sure I understand the problem(...TRUNCATED) | "To solve the problem, we are given two urns:\n\n- **Urn 1**: 4 green balls and 6 blue balls (total (...TRUNCATED) | "<think>\nOkay, let's try to solve this problem step by step. First, let's make sure I understand th(...TRUNCATED) | "<think>\nInstruksi diterima. Pengguna telah meminta untuk menyelesaikan masalah probabilitas tentan(...TRUNCATED) |
true | Indonesian | English | English | Always write your reasoning process in English, and always provide your answer in English | "Grafik dari persamaan $9x + 223y = 2007$ digambar pada kertas berpetak dengan setiap kotak mewakili(...TRUNCATED) | "<|im_start|>system\nAlways write your reasoning process in English, and always provide your answer (...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "To solve the problem, we are asked to count how many **1 by 1 unit squares** on graph paper (with i(...TRUNCATED) | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) | "<think>\nPermintaan terverifikasi. Tugas saya adalah untuk menemukan berapa banyak kotak 1x1 di kua(...TRUNCATED) |
true | English | English | English | "Selalu tuliskan proses penalaranmu dalam bahasa Inggris, dan selalu berikan jawabanmu dalam bahasa (...TRUNCATED) | "For real number $x$ let $\\lfloor x\\rfloor$ be the greatest integer less than or equal to $x$ , an(...TRUNCATED) | "<|im_start|>system\nSelalu tuliskan proses penalaranmu dalam bahasa Inggris, dan selalu berikan jaw(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "To solve the problem, we are given a function $ f(x) = x \\{x\\} $, where $\\{x\\}$ is the fraction(...TRUNCATED) | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) | "<think>\nOke, fokus sekarang adalah pada permintaan pengguna untuk menyelesaikan soal matematika ya(...TRUNCATED) |
true | Indonesian | English | English | "Selalu tuliskan proses penalaranmu dalam bahasa Inggris, dan selalu berikan jawabanmu dalam bahasa (...TRUNCATED) | "Untuk sebarang bilangan bulat positif $k$, misalkan $f_1(k)$ adalah kuadrat dari jumlah digit dari (...TRUNCATED) | "<|im_start|>system\nSelalu tuliskan proses penalaranmu dalam bahasa Inggris, dan selalu berikan jaw(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "To solve the problem, we are given a recursive function defined as follows:\n\n- For any positive i(...TRUNCATED) | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) | "<think>\nBaiklah, pengguna meminta saya untuk menentukan $f_{1988}(11)$ dengan definisi fungsi yang(...TRUNCATED) |
true | English | Indonesian | English | Always write your reasoning process in Indonesian, and always provide your answer in English | "Triangle $ABC$ is inscribed in circle $\\omega$ with $AB=5$ , $BC=7$ , and $AC=3$ . The bisector of(...TRUNCATED) | "<|im_start|>system\nAlways write your reasoning process in Indonesian, and always provide your answ(...TRUNCATED) | "Menerima tugas dari pengguna untuk menyelesaikan masalah geometri yang cukup kompleks. Mari kita mu(...TRUNCATED) | "To solve the problem, we begin by placing triangle $ ABC $ in a coordinate system to simplify calcu(...TRUNCATED) | "<think>\nMenerima tugas dari pengguna untuk menyelesaikan masalah geometri yang cukup kompleks. Mar(...TRUNCATED) | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) |
true | Indonesian | Indonesian | English | Always write your reasoning process in Indonesian, and always provide your answer in English | Jika $\tan x + \tan y = 25$ dan $\cot x + \cot y = 30$, berapakah $\tan(x+y)$? | "<|im_start|>system\nAlways write your reasoning process in Indonesian, and always provide your answ(...TRUNCATED) | "Memproses perintah dari pengguna untuk mencari nilai dari tan(x + y) dengan diketahui bahwa tan x +(...TRUNCATED) | "To solve for $\\tan(x + y)$, we begin with the known trigonometric identity:\n\n$$\n\\tan(x + y) = (...TRUNCATED) | "<think>\nMemproses perintah dari pengguna untuk mencari nilai dari tan(x + y) dengan diketahui bahw(...TRUNCATED) | "<think>\nOkay, let's see. The problem says that tan x + tan y = 25 and cot x + cot y = 30, and we n(...TRUNCATED) |
true | English | Indonesian | English | "Selalu tuliskan proses penalaranmu dalam bahasa Indonesia, dan selalu berikan jawabanmu dalam bahas(...TRUNCATED) | "Let $ABCD$ be a parallelogram . Extend $\\overline{DA}$ through $A$ to a point $P,$ and let $\\ove(...TRUNCATED) | "<|im_start|>system\nSelalu tuliskan proses penalaranmu dalam bahasa Indonesia, dan selalu berikan j(...TRUNCATED) | "Mencatat permintaan: pengguna memerlukan saya untuk menyelesaikan soal geometri tentang jajaran gen(...TRUNCATED) | "To solve the problem, we are given a parallelogram $ABCD$, with point $P$ on line $DA$ extended pas(...TRUNCATED) | "<think>\nMencatat permintaan: pengguna memerlukan saya untuk menyelesaikan soal geometri tentang ja(...TRUNCATED) | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) |
true | Indonesian | Indonesian | English | "Selalu tuliskan proses penalaranmu dalam bahasa Indonesia, dan selalu berikan jawabanmu dalam bahas(...TRUNCATED) | "Sebuah laci berisi campuran kaus kaki merah dan biru, dengan total tidak lebih dari 1991. Ternyata,(...TRUNCATED) | "<|im_start|>system\nSelalu tuliskan proses penalaranmu dalam bahasa Indonesia, dan selalu berikan j(...TRUNCATED) | "Berdasarkan permintaan pengguna, saya akan memulai proses menyelesaikan masalah tentang kaus kaki m(...TRUNCATED) | "To solve the problem, we begin by modeling the situation mathematically.\n\nLet:\n- $ r $ be the nu(...TRUNCATED) | "<think>\nBerdasarkan permintaan pengguna, saya akan memulai proses menyelesaikan masalah tentang ka(...TRUNCATED) | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) |
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