instruction_seed stringlengths 15 5.67k | response_seed stringlengths 0 9.78k β | reasoning stringlengths 0 104k | deepseek_solution stringlengths 0 15.4k | __original_row_idx int64 0 40k β | source stringclasses 4
values | final_reasoning_trace stringlengths 19 106k | conversations listlengths 2 2 |
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What is the maximum possible value for $z$ in the equation $z = 3x^2 - 8x - 10$? | What is the maximum possible value for $z$ in the equation $z = 3x^2 - 8x - 10$? | Okay, so I need to find the maximum possible value for z in the equation z = 3xΒ² - 8x - 10. Hmm, let me think. I remember that quadratic equations graph as parabolas. Since the coefficient of xΒ² here is 3, which is positive, that means the parabola opens upwards. Wait, if it opens upwards, then the vertex would be the ... | To find the maximum possible value for \( z \) in the equation \( z = 3x^2 - 8x - 10 \), we first recognize that this is a quadratic equation. The coefficient of \( x^2 \) is 3, which is positive, indicating that the parabola opens upwards.
Since the parabola opens upwards, it has a minimum value at its vertex and no... | 25,122 | ai2-adapt-dev/openmath-2-math | <think>
Okay, so I need to find the maximum possible value for z in the equation z = 3xΒ² - 8x - 10. Hmm, let me think. I remember that quadratic equations graph as parabolas. Since the coefficient of xΒ² here is 3, which is positive, that means the parabola opens upwards. Wait, if it opens upwards, then the vertex would... | [
{
"from": "human",
"value": "What is the maximum possible value for $z$ in the equation $z = 3x^2 - 8x - 10$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the maximum possible value for z in the equation z = 3xΒ² - 8x - 10. Hmm, let me think. I remember that quadratic equations... |
The function $o$ is given by the table\[\begin{tabular}{|c||c|c|c|c|c|} \hline x & 1 & 2 & 3 & X & 5 \\ \hline o(x) & 1 & 3 & 4 & 5 & 2 \\ \hline \end{tabular}\] If $q_0=1$ and $q_{n+1} = o(q_n)$ for $n \ge 0$, find $q_{1999}. If we know the answer to the above question is 1, what is the value of unknown variabl... | To solve the problem, we need to analyze the function \( o \) given in the table and follow the sequence defined by \( q_{n+1} = o(q_n) \). The entries of the table indicate how the function \( o \) maps certain values:
\[\begin{array}{|c||c|c|c|c|c|} \hline x & 1 & 2 & 3 & X & 5 \\ \hline o(x) & 1 & 3 & 4 & 5 &... | Okay, let me try to figure out this problem. So, we have a function o defined by a table, and we need to determine the value of X such that when we start with qβ = 1 and apply the function o repeatedly, the 1999th term qββββ is 1. Hmm, let's break this down step by step.
First, let me understand the function o. The ta... | The function \( o \) is given by the table:
\[
\begin{tabular}{|c||c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & X & 5 \\
\hline
o(x) & 1 & 3 & 4 & 5 & 2 \\
\hline
\end{tabular}
\]
We need to determine the value of \( X \) such that starting from \( q_0 = 1 \), the sequence \( q_n \) defined by \( q_{n+1} = o(q_n) \) results in... | 4,086 | MetaMath-AIME | <think>
Okay, let me try to figure out this problem. So, we have a function o defined by a table, and we need to determine the value of X such that when we start with qβ = 1 and apply the function o repeatedly, the 1999th term qββββ is 1. Hmm, let's break this down step by step.
First, let me understand the function o... | [
{
"from": "human",
"value": "The function $o$ is given by the table\\[\\begin{tabular}{|c||c|c|c|c|c|} \\hline x & 1 & 2 & 3 & X & 5 \\\\ \\hline o(x) & 1 & 3 & 4 & 5 & 2 \\\\ \\hline \\end{tabular}\\] If $q_0=1$ and $q_{n+1} = o(q_n)$ for $n \\ge 0$, find $q_{1999}. If we know the answer to the abov... |
Given a finite soluble group \( G \) that admits a fixed-point-free automorphism \( \varphi \) satisfying an elementary abelian identity represented by a primitive polynomial \( f(x) \), if the degree of \( f(x) \) is \( d \) and the number of distinct irreducible factors of \( f(x) \) is \( c \), what is the upper bou... | Okay, so I need to figure out the upper bound for the Fitting height of a finite soluble group G that has a fixed-point-free automorphism Ο satisfying an elementary abelian identity given by a primitive polynomial f(x). The polynomial has degree d and c distinct irreducible factors. Hmm, let me start by recalling some ... | Given a finite soluble group \( G \) that admits a fixed-point-free automorphism \( \varphi \) satisfying an elementary abelian identity represented by a primitive polynomial \( f(x) \) with degree \( d \) and \( c \) distinct irreducible factors, we need to determine the upper bound for the Fitting height of \( G \).
... | 8,531 | mlfoundations-dev/gair_mathpile | <think>
Okay, so I need to figure out the upper bound for the Fitting height of a finite soluble group G that has a fixed-point-free automorphism Ο satisfying an elementary abelian identity given by a primitive polynomial f(x). The polynomial has degree d and c distinct irreducible factors. Hmm, let me start by recalli... | [
{
"from": "human",
"value": "Given a finite soluble group \\( G \\) that admits a fixed-point-free automorphism \\( \\varphi \\) satisfying an elementary abelian identity represented by a primitive polynomial \\( f(x) \\), if the degree of \\( f(x) \\) is \\( d \\) and the number of distinct irreducible fac... | |
"Consider the binary operation defined by $(a \\bullet b) = \\frac{a}{b}$. Find the value of $(3 \\b(...TRUNCATED) | "Consider the binary operation defined by $(a \\bullet b) = \\frac{a}{b}$. Find the value of $(3 \\b(...TRUNCATED) | "Okay, so I have this problem here: Consider the binary operation defined by (a β’ b) = a/b. Find t(...TRUNCATED) | "To solve the problem, we need to evaluate the expression \\((3 \\bullet 4) \\bullet (2 \\bullet 6)\(...TRUNCATED) | 5,860 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I have this problem here: Consider the binary operation defined by (a β’ b) = a/(...TRUNCATED) | [{"from":"human","value":"Consider the binary operation defined by $(a \\bullet b) = \\frac{a}{b}$. (...TRUNCATED) |
"Given a quadrilateral $ABCD$. $A ', B', C'$ and $D'$ are the midpoints of the sides $BC, CB, BA$ an(...TRUNCATED) | null | "Okay, let me try to figure out this problem. So, we have a quadrilateral ABCD. The midpoints are gi(...TRUNCATED) | "Given a quadrilateral \\(ABCD\\) with midpoints \\(A'\\), \\(B'\\), \\(C'\\), and \\(D'\\) on sides(...TRUNCATED) | null | AI-MO/NuminaMath-1.5 | "<think>\nOkay, let me try to figure out this problem. So, we have a quadrilateral ABCD. The midpoin(...TRUNCATED) | [{"from":"human","value":"Given a quadrilateral $ABCD$. $A ', B', C'$ and $D'$ are the midpoints of (...TRUNCATED) |
"In an isosceles triangle, two of the angles measure 30 degrees and x degrees. What is the total sum(...TRUNCATED) | "1. In an isosceles triangle, there are two equal angles. This means we have two cases to consider b(...TRUNCATED) | "Okay, let's see. I need to find the possible values of x in an isosceles triangle where two of the (...TRUNCATED) | "In an isosceles triangle, two of the angles measure 30 degrees and \\( x \\) degrees. We need to fi(...TRUNCATED) | 3,527 | MetaMath-AIME | "<think>\nOkay, let's see. I need to find the possible values of x in an isosceles triangle where tw(...TRUNCATED) | [{"from":"human","value":"In an isosceles triangle, two of the angles measure 30 degrees and x degre(...TRUNCATED) |
"Prove that the bipartite Kneser graph \\( H(n,k) \\) has a Hamilton cycle for any integers \\( k \\(...TRUNCATED) | "Okay, so I need to prove that the bipartite Kneser graph \\( H(n,k) \\) has a Hamilton cycle for an(...TRUNCATED) | "The bipartite Kneser graph \\( H(n,k) \\) has a Hamilton cycle for any integers \\( k \\geq 1 \\) a(...TRUNCATED) | 11,596 | mlfoundations-dev/gair_mathpile | "<think>\nOkay, so I need to prove that the bipartite Kneser graph \\( H(n,k) \\) has a Hamilton cyc(...TRUNCATED) | [{"from":"human","value":"Prove that the bipartite Kneser graph \\( H(n,k) \\) has a Hamilton cycle (...TRUNCATED) | |
"Given a micromaser with an interaction length \\( L \\) and an atomic transition frequency detuning(...TRUNCATED) | "Okay, so I have this problem about a micromaser and the transmission probability of excited atoms t(...TRUNCATED) | "The relationship between the cavity length \\( L \\), the atomic velocity \\( v \\), and the de Bro(...TRUNCATED) | 4,785 | mlfoundations-dev/gair_mathpile | "<think>\nOkay, so I have this problem about a micromaser and the transmission probability of excite(...TRUNCATED) | [{"from":"human","value":"Given a micromaser with an interaction length \\( L \\) and an atomic tran(...TRUNCATED) | |
"In a village, there are 10 houses, and each house has a different color. Each day, each villager vi(...TRUNCATED) | "In a village, there are 10 houses, and each house has a different color. Each day, each villager vi(...TRUNCATED) | "Okay, so I need to figure out how many days the villagers can keep visiting houses under these rule(...TRUNCATED) | "Given 10 houses, each with a different color, each villager visits exactly 3 different houses each (...TRUNCATED) | 37,356 | ai2-adapt-dev/openmath-2-math | "<think>\nOkay, so I need to figure out how many days the villagers can keep visiting houses under t(...TRUNCATED) | [{"from":"human","value":"In a village, there are 10 houses, and each house has a different color. E(...TRUNCATED) |
"3 [Mutual arrangement of altitudes, medians, bisectors, etc.]\n\nIn triangle $ABC$, the bisector dr(...TRUNCATED) | null | "Okay, so I need to find the angle at vertex A in triangle ABC where three specific lines intersect (...TRUNCATED) | "Given triangle \\(ABC\\) where the angle bisector from \\(A\\), the altitude from \\(B\\), and the (...TRUNCATED) | null | AI-MO/NuminaMath-1.5 | "<think>\nOkay, so I need to find the angle at vertex A in triangle ABC where three specific lines i(...TRUNCATED) | [{"from":"human","value":"3 [Mutual arrangement of altitudes, medians, bisectors, etc.]\n\nIn triang(...TRUNCATED) |
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