messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Can you evaluate this math equation? Solve for $x$ (in radians): tan(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(\\frac... | {
"type": "trigonometry",
"seed": 1337,
"index": 3000
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal v... | {
"type": "trigonometry",
"seed": 1337,
"index": 3001
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\al... | {
"type": "trigonometry",
"seed": 1337,
"index": 3002
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Differentiate with respect to $x$: $f(x) = \\ln(6x + -9)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(6x + -9) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\fra... | {
"type": "calculus",
"seed": 1337,
"index": 3003
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Solve for $x$ (in radians): tan(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(1) = 0.785398 $\... | {
"type": "trigonometry",
"seed": 1337,
"index": 3004
} |
[
{
"role": "user",
"content": "Evaluate the following equation. -47 - 110x - 154 = 112x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -47 - 110x - 154 = 112x^2 $\n\nMove all terms to the left (standard form):\n$ -112x^2 + -110x + -201 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3005
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. 5 + 38x - 191 = -115x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 5 + 38x - 191 = -115x^2 $\n\nMove all terms to the left (standard form):\n$ 115x^2 + 38x + -186 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3006
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Evaluate: ((146 + -559/13) * 10) + 12^3 - log_9(531441) + (-92 mod 24) + ceil(58/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((146 + -559/13) * 10) + 12^3 - log_9(531441) + (-92 mod 24) + ceil(58... | {
"type": "arithmetic",
"seed": 1337,
"index": 3007
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:... | {
"type": "optimization",
"seed": 1337,
"index": 3008
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. 10x - 200 + 174x^2 = -142"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10x - 200 + 174x^2 = -142 $\n\nMove all terms to the left (standard form):\n$ 174x^2 + 10x + -58 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3009
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. 50x - 4 - 115x^2 = 130"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 50x - 4 - 115x^2 = 130 $\n\nMove all terms to the left (standard form):\n$ -115x^2 + 50x + -134 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3010
} |
[
{
"role": "user",
"content": "Please calculate this equation. 342x + 19 = -526"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 342x + 19 = -526 $\n\nMove all terms to the left (standard form):\n$ 342x + 545 = 0 $\n\nIsolate the $x$ term:\n$ 342x = -545 $\n\nDivide both sides by the... | {
"type": "linear_equation",
"seed": 1337,
"index": 3011
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 229 - 755x = -540"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 229 - 755x = -540 $\n\nMove all terms to the left (standard form):\n$ -755x + 769 = 0 $\n\nIsolate the $x$ term:\n$ -755x = -769 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 3012
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Compute the indefinite integral: $\\int (-1x + 1)\\sin(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-1x + 1)\\sin(2x)\\,dx $\n\nUse standard antiderivatives (and integration b... | {
"type": "calculus",
"seed": 1337,
"index": 3013
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \... | {
"type": "trigonometry",
"seed": 1337,
"index": 3014
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Prove that $f(x,y)=\\frac12(10x^2+9y^2)+1x+5y+-2$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(10x^2+9y^2)+1x+5y+-2 $\n\n$ \\frac{\\partial^2 f}{\... | {
"type": "optimization",
"seed": 1337,
"index": 3015
} |
[
{
"role": "user",
"content": "Please solve this math problem. Find $A^{-1}$ for $A=\\begin{pmatrix}-4&7\\\\-5&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -4 & 7 \\\\ -5 & -6 \\end{pmatrix} $\n\nCompute the determina... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3016
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. -48 + 32x^2 - 20x = -151"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -48 + 32x^2 - 20x = -151 $\n\nMove all terms to the left (standard form):\n$ 32x^2 + -20x + 103 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3017
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Differentiate with respect to $x$: $f(x) = -4e^{3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -4e^{3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-12e^{3x}} $"
... | {
"type": "calculus",
"seed": 1337,
"index": 3018
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Evaluate: ((31 + 552/24) * 20) + 11^5 - log_7(2401) + (106 mod 23) + round(159/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((31 + 552/24) * 20) + 11^5 - log_7(2401) + (106 mod 23) + round(159/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 3019
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$... | {
"type": "trigonometry",
"seed": 1337,
"index": 3020
} |
[
{
"role": "user",
"content": "solve: Evaluate: ((194 + 210/14) * 13) + 11^3 - log_3(27) + (254 mod 3) + round(33/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((194 + 210/14) * 13) + 11^3 - log_3(27) + (254 mod 3) + round(33/2) $\n\nCompute each component:\n$ 210/14 = 15... | {
"type": "arithmetic",
"seed": 1337,
"index": 3021
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Compute the determinant: $A=\\begin{pmatrix}2&8\\\\-5&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}2&8\\\\\\-5&9\\end{pmatrix} $\n\nUse $\\det(A)=... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3022
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Evaluate: ((-104 + 817/19) * 7) + 5^3 - log_10(1000000) + (15 mod 28) + ceil(-64/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-104 + 817/19) * 7) + 5^3 - log_10(1000000) + (15 mod 28) + ceil(-64/... | {
"type": "arithmetic",
"seed": 1337,
"index": 3023
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Prove that $f(x)=3x^2+8x+-7$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=3x^2+8x+-7$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'... | {
"type": "optimization",
"seed": 1337,
"index": 3024
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Compute the indefinite integral: $\\int 5x^3 + 9x^2 + -4x + -19\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 5x^3 + 9x^2 + -4x + -19\\,dx $\n\nUse standard antiderivative... | {
"type": "calculus",
"seed": 1337,
"index": 3025
} |
[
{
"role": "user",
"content": "Work out the result of this equation. -928 - 549 = -944x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -928 - 549 = -944x $\n\nMove all terms to the left (standard form):\n$ 944x + -1477 = 0 $\n\nIsolate the $x$ term:\n$ 944x = 1477 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3026
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Prove that $(\\mathbb{Z}_19, +)$ is a group under addition modulo 19."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_19=\\{0,1,\\dots,18\\}$ with operation $+$ modulo $19$.\n\n**Closure:** If $a,b\\in\\mathbb{... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3027
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Evaluate: ((137 + 120/10) * 6) + 9^2 - log_8(4096) + (488 mod 23) + round(-30/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((137 + 120/10) * 6) + 9^2 - log_8(4096) + (488 mod 23) + round(-30/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 3028
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. 883 + 957x = -144"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 883 + 957x = -144 $\n\nMove all terms to the left (standard form):\n$ 957x + 1027 = 0 $\n\nIsolate the $x$ term:\n$ 957x = -1027 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 3029
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. 59 - 435x = 82"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 59 - 435x = 82 $\n\nMove all terms to the left (standard form):\n$ -435x + -23 = 0 $\n\nIsolate the $x$ term:\n$ -435x = 23 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 3030
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\... | {
"type": "optimization",
"seed": 1337,
"index": 3031
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Evaluate: ((154 + -931/19) * 3) + 11^3 - log_5(125) + (-312 mod 17) + ceil(-119/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((154 + -931/19) * 3) + 11^3 - log_5(125) + (-312 mod 17) + ceil(-119/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 3032
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. -44 + 166 - 92x^2 = -161x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -44 + 166 - 92x^2 = -161x $\n\nMove all terms to the left (standard form):\n$ -92x^2 + 161x + 122 = 0 $\n\nApply the quadr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3033
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 3034
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 166 - 129 = -508x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 166 - 129 = -508x $\n\nMove all terms to the left (standard form):\n$ 508x + 37 = 0 $\n\nIsolate the $x$ term:\n$ 508x = -37 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 3035
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. 251 + 60x = -853"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 251 + 60x = -853 $\n\nMove all terms to the left (standard form):\n$ 60x + 1104 = 0 $\n\nIsolate the $x$ term:\n$ 60x = -1104 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 3036
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Evaluate: ((-32 + -437/23) * 13) + 2^4 - log_10(100000) + (166 mod 4) + round(199/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-32 + -437/23) * 13) + 2^4 - log_10(100000) + (166 mod 4) + round(19... | {
"type": "arithmetic",
"seed": 1337,
"index": 3037
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{... | {
"type": "optimization",
"seed": 1337,
"index": 3038
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? 202 + 582 = -149x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 202 + 582 = -149x $\n\nMove all terms to the left (standard form):\n$ 149x + 784 = 0 $\n\nIsolate the $x$ term:\n$ 149x = -784 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 3039
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&-7\\\\\\-8&7\\end{pmatrix},\\quad b=\\begin{pmatrix}61\\\\\\19\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&-7\\\\\\-8&7\\end{pmat... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3040
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. -21x - 3 - 79x^2 = -176"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -21x - 3 - 79x^2 = -176 $\n\nMove all terms to the left (standard form):\n$ -79x^2 + -21x + 173 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3041
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(... | {
"type": "optimization",
"seed": 1337,
"index": 3042
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}5&-7\\\\-3&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 5 & -7 \\\\ -3 & 9 \\end{pmatrix} $\n\nCompute the dete... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3043
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}9&-8\\\\\\-9&-7\\end{pmatrix},\\quad b=\\begin{pmatrix}-117\\\\\\-18\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}9&-8\\\\\\-9&-7... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3044
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. 232 + 321x = 396"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 232 + 321x = 396 $\n\nMove all terms to the left (standard form):\n$ 321x + -164 = 0 $\n\nIsolate the $x$ term:\n$ 321x = 164 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 3045
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Compute the determinant: $A=\\begin{pmatrix}9&0\\\\4&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}9&0\\\\\\4&3\\end{pmatrix} $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3046
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hen... | {
"type": "optimization",
"seed": 1337,
"index": 3047
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. -12 - 46x^2 - 91 = 11x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -12 - 46x^2 - 91 = 11x $\n\nMove all terms to the left (standard form):\n$ -46x^2 + -11x + -103 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3048
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Evaluate: ((-136 + 324/18) * 5) + 3^2 - log_7(343) + (-483 mod 2) + round(40/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-136 + 324/18) * 5) + 3^2 - log_7(343) + (-483 mod 2) + round(40/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 3049
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(-\\frac{\... | {
"type": "trigonometry",
"seed": 1337,
"index": 3050
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4... | {
"type": "optimization",
"seed": 1337,
"index": 3051
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Compute $(115+-3) \\bmod 8$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (115+-3) \\bmod 8 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\n$ (a... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3052
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Prove that $(\\mathbb{Z}_30, +)$ is a group under addition modulo 30."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_30=\\{0,1,\\dots,29\\}$ with operation $+$ modulo $30$.\n\n**Closure:** If $a,b\\in\\mathb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3053
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Evaluate: ((129 + 1127/23) * 3) + 6^3 - log_6(46656) + (-139 mod 29) + floor(-38/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((129 + 1127/23) * 3) + 6^3 - log_6(46656) + (-139 mod 29) + floor(-38... | {
"type": "arithmetic",
"seed": 1337,
"index": 3054
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. 14 - 102x^2 - 168 = -66x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 14 - 102x^2 - 168 = -66x $\n\nMove all terms to the left (standard form):\n$ -102x^2 + 66x + -154 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3055
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Prove that $f(x,y)=\\frac12(10x^2+9y^2)+4x+1y+-5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(10x^2+9y^2)+4x+1y+-5 $\n\n$ \\frac{\\partial^2 f}{\... | {
"type": "optimization",
"seed": 1337,
"index": 3056
} |
[
{
"role": "user",
"content": "Solve the following math equation. Compute the indefinite integral: $\\int 4e^{-5x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 4e^{-5x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int... | {
"type": "calculus",
"seed": 1337,
"index": 3057
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((179 + -759/23) * 6) + 5^3 - log_5(3125) + (159 mod 20) + round(14/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((179 + -759/23) * 6) + 5^3 - log_5(3125) + (159 mod 20) + round(14/2) $\n\nCompute eac... | {
"type": "arithmetic",
"seed": 1337,
"index": 3058
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Prove that $f(x)=4x^2+0x+-2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+0x+-2$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f... | {
"type": "optimization",
"seed": 1337,
"index": 3059
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Evaluate: ((177 + -231/21) * 1) + 10^4 - log_6(1296) + (-188 mod 24) + ceil(-58/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((177 + -231/21) * 1) + 10^4 - log_6(1296) + (-188 mod 24) + ceil(-58/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 3060
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. -9x^2 + 105 + 121 = -13x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -9x^2 + 105 + 121 = -13x $\n\nMove all terms to the left (standard form):\n$ -9x^2 + 13x + 226 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3061
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&6\\\\\\7&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}-8\\\\\\24\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&6\\\\\\7&-1\\e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3062
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Compute the indefinite integral: $\\int (-4x + -10)e^{5x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-4x + -10)e^{5x}\\,dx $\n\nUse standard antiderivatives (and integration by p... | {
"type": "calculus",
"seed": 1337,
"index": 3063
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. -24x^2 - 35 - 80x = 18"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -24x^2 - 35 - 80x = 18 $\n\nMove all terms to the left (standard form):\n$ -24x^2 + -80x + -53 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3064
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Compute the determinant: $A=\\begin{pmatrix}-1&3\\\\3&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-1&3\\\\\\3&-2\\end{pmatrix} $\n\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3065
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 3066
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Find the modular inverse of 34 modulo 35, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $34\\cdot a^{-1} \\equiv 1 \\pmod{35}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantee... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3067
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 14x^2 - 194x + 50 = -119"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 14x^2 - 194x + 50 = -119 $\n\nMove all terms to the left (standard form):\n$ 14x^2 + -194x + 169 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3068
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Evaluate: ((-37 + -208/13) * 8) + 9^4 - log_5(125) + (-6 mod 16) + ceil(-116/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-37 + -208/13) * 8) + 9^4 - log_5(125) + (-6 mod 16) + ceil(-116/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 3069
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Solve for $x$ (in radians): tan(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(... | {
"type": "trigonometry",
"seed": 1337,
"index": 3070
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Solve for $x$ (in radians): tan(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\ar... | {
"type": "trigonometry",
"seed": 1337,
"index": 3071
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}7&2\\\\\\8&-8\\end{pmatrix},\\quad b=\\begin{pmatrix}65\\\\\\-8\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}7&2\\\\\\8&-8\\e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3072
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Compute the determinant: $A=\\begin{pmatrix}-3&1\\\\0&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-3&1\\\\\\0&-4\\end{pmatrix} ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3073
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Prove that $f(x)=8x^2+-5x+8$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=8x^2+-5x+8$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x)... | {
"type": "optimization",
"seed": 1337,
"index": 3074
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 49 - 99x - 175 = -196x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 49 - 99x - 175 = -196x^2 $\n\nMove all terms to the left (standard form):\n$ 196x^2 + -99x + -126 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3075
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Solve for $x$ (in radians): tan(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(1) = 0.785398 $\n\... | {
"type": "trigonometry",
"seed": 1337,
"index": 3076
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. 912 + 156 = 420x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 912 + 156 = 420x $\n\nMove all terms to the left (standard form):\n$ -420x + 1068 = 0 $\n\nIsolate the $x$ term:\n$ -420x = -1068 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 3077
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Solve for $x$ (in radians): cos(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -1 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(-1) = 3.14159 $\n\nTh... | {
"type": "trigonometry",
"seed": 1337,
"index": 3078
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hen... | {
"type": "optimization",
"seed": 1337,
"index": 3079
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. -104x + 960 = 657"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -104x + 960 = 657 $\n\nMove all terms to the left (standard form):\n$ -104x + 303 = 0 $\n\nIsolate the $x$ term:\n$ -104x = -303 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3080
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence... | {
"type": "optimization",
"seed": 1337,
"index": 3081
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 15 + 136x - 163x^2 = -81"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 15 + 136x - 163x^2 = -81 $\n\nMove all terms to the left (standard form):\n$ -163x^2 + 136x + 96 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3082
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 3083
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Evaluate: ((-40 + -45/9) * 20) + 2^5 - log_2(4) + (234 mod 23) + ceil(-30/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-40 + -45/9) * 20) + 2^5 - log_2(4) + (234 mod 23) + ceil(-30/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 3084
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Differentiate with respect to $x$: $f(x) = (-5x + -10)\\sin(3x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-5x + -10)\\sin(3x) $\n\nApply the standard differentiation rules:\n$ f'(x) = ... | {
"type": "calculus",
"seed": 1337,
"index": 3085
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Solve for $x$ (in radians): tan(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 3086
} |
[
{
"role": "user",
"content": "solve Prove that $f(x,y)=\\frac12(8x^2+7y^2)+-3x+-6y+-2$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(8x^2+7y^2)+-3x+-6y+-2 $\n\n$ \\frac{\\partial^2 f}{\\partial x^2} = 8,\\quad \\frac{\\... | {
"type": "optimization",
"seed": 1337,
"index": 3087
} |
[
{
"role": "user",
"content": "solve Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x^2-1)=0 \\Rightarrow x\\in\\... | {
"type": "optimization",
"seed": 1337,
"index": 3088
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}6&3\\\\\\-8&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}9\\\\\\-7\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}6&3\\\\\\-8&-3... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3089
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, henc... | {
"type": "optimization",
"seed": 1337,
"index": 3090
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}4&8\\\\\\3&8\\end{pmatrix},\\quad b=\\begin{pmatrix}-4\\\\\\-13\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}4&8\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3091
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Solve for $x$ (in radians): tan(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arct... | {
"type": "trigonometry",
"seed": 1337,
"index": 3092
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Compute the determinant: $A=\\begin{pmatrix}7&1\\\\-3&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}7&1\\\\\\-3&4\\end{pmatrix} $\n\nUse $\\det(A)=ad-... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3093
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Evaluate: ((169 + 580/20) * 5) + 8^4 - log_3(9) + (-38 mod 4) + ceil(19/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((169 + 580/20) * 5) + 8^4 - log_3(9) + (-38 mod 4) + ceil(19/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 3094
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Evaluate: ((-143 + -902/22) * 6) + 10^4 - log_7(117649) + (-289 mod 16) + ceil(-167/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-143 + -902/22) * 6) + 10^4 - log_7(117649) + (-289 mod 16) + ceil(-... | {
"type": "arithmetic",
"seed": 1337,
"index": 3095
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x... | {
"type": "optimization",
"seed": 1337,
"index": 3096
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Evaluate: ((152 + 50/10) * 20) + 11^2 - log_5(125) + (330 mod 12) + round(-37/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((152 + 50/10) * 20) + 11^2 - log_5(125) + (330 mod 12) + round(-37/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 3097
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Differentiate with respect to $x$: $f(x) = 5x^3 + 5x^2 + -10x + -14$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 5x^3 + 5x^2 + -10x + -14 $\n\nApply the standard differentiation rules:\n$... | {
"type": "calculus",
"seed": 1337,
"index": 3098
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. 11 - 87x^2 - 36x = -109"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 11 - 87x^2 - 36x = -109 $\n\nMove all terms to the left (standard form):\n$ -87x^2 + -36x + 120 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3099
} |
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