messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Find the solution of the math equation below. Compute the indefinite integral: $\\int (3x + -5)e^{3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (3x + -5)e^{3x}\\,dx $\n\nUse standard antiderivatives (and integration by p... | {
"type": "calculus",
"seed": 1337,
"index": 0
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}3&-3\\\\\\2&-6\\end{pmatrix},\\quad b=\\begin{pmatrix}3\\\\\\-10\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}3&-3\\\\\\2&-... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 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$... | {
"type": "trigonometry",
"seed": 1337,
"index": 2
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Evaluate: ((177 + 432/12) * 1) + 7^2 - log_9(81) + (314 mod 7) + ceil(153/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((177 + 432/12) * 1) + 7^2 - log_9(81) + (314 mod 7) + ceil(153/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 3
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Differentiate with respect to $x$: $f(x) = (-5x + 10)\\sin(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-5x + 10)\\sin(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-5\\s... | {
"type": "calculus",
"seed": 1337,
"index": 4
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Evaluate: ((134 + 56/8) * 2) + 12^2 - log_5(25) + (-209 mod 5) + ceil(183/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((134 + 56/8) * 2) + 12^2 - log_5(25) + (-209 mod 5) + ceil(183/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 5
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. 919 + 251x = -316"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 919 + 251x = -316 $\n\nMove all terms to the left (standard form):\n$ 251x + 1235 = 0 $\n\nIsolate the $x$ term:\n$ 251x = -1235 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. 138 + 488x = 323"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 138 + 488x = 323 $\n\nMove all terms to the left (standard form):\n$ 488x + -185 = 0 $\n\nIsolate the $x$ term:\n$ 488x = 185 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 7
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Prove that $f(x,y)=\\frac12(1x^2+8y^2)+5x+5y+8$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+8y^2)+5x+5y+8 $\n\n$ \\frac{\\partial^2 f}{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 8
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Prove that $f(x)=9x^2+5x+7$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+5x+7$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 18x + 5 $\n... | {
"type": "optimization",
"seed": 1337,
"index": 9
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}8&9\\\\\\-1&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}-101\\\\\\12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}8&9\\\\\\-1&-1\\end{pmatri... | {
"type": "linear_algebra",
"seed": 1337,
"index": 10
} |
[
{
"role": "user",
"content": "Please compute the answer to 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{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 11
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. 19x^2 - 71 - 173 = 83x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 19x^2 - 71 - 173 = 83x $\n\nMove all terms to the left (standard form):\n$ 19x^2 + -83x + -244 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 12
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Compute the determinant: $A=\\begin{pmatrix}4&0\\\\-5&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}4&0\\\\\\-5&-8\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 13
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Solve for $x$ (in radians): cos(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(... | {
"type": "trigonometry",
"seed": 1337,
"index": 14
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Evaluate: ((146 + 84/21) * 20) + 6^3 - log_5(25) + (-99 mod 17) + floor(83/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((146 + 84/21) * 20) + 6^3 - log_5(25) + (-99 mod 17) + floor(83/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 15
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. -8 + 1x + 119x^2 = -101"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -8 + 1x + 119x^2 = -101 $\n\nMove all terms to the left (standard form):\n$ 119x^2 + 1x + 93 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 16
} |
[
{
"role": "user",
"content": "Please solve this math problem. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&-9\\\\\\8&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-32\\\\\\32\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&-9\\\\\\8&-3\\end{pmat... | {
"type": "linear_algebra",
"seed": 1337,
"index": 17
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Evaluate: ((6 + -315/21) * 8) + 6^5 - log_8(262144) + (-353 mod 14) + ceil(190/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((6 + -315/21) * 8) + 6^5 - log_8(262144) + (-353 mod 14) + ceil(190/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 18
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Evaluate: ((162 + -21/21) * 15) + 2^4 - log_3(27) + (39 mod 17) + round(-129/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((162 + -21/21) * 15) + 2^4 - log_3(27) + (39 mod 17) + round(-129/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 19
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Differentiate with respect to $x$: $f(x) = \\ln(2x + -2)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(2x + -2) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{2}{... | {
"type": "calculus",
"seed": 1337,
"index": 20
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. 620x + 469 = -564"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 620x + 469 = -564 $\n\nMove all terms to the left (standard form):\n$ 620x + 1033 = 0 $\n\nIsolate the $x$ term:\n$ 620x = -1033 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 21
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Differentiate with respect to $x$: $f(x) = 7\\sin(1x) + 8\\cos(8x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 7\\sin(1x) + 8\\cos(8x) $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 22
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. -696x - 45 = -835"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -696x - 45 = -835 $\n\nMove all terms to the left (standard form):\n$ -696x + 790 = 0 $\n\nIsolate the $x$ term:\n$ -696x = -790 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 23
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Compute the determinant: $A=\\begin{pmatrix}-4&-3\\\\-4&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&-3\\\\\\-4&-2\\end{pmatrix} $\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 24
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Compute the indefinite integral: $\\int \\ln(7x + 0)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(7x + 0)\\,dx $\n\nUse standard antiderivatives (and integration by part... | {
"type": "calculus",
"seed": 1337,
"index": 25
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. -126 - 276x = 623"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -126 - 276x = 623 $\n\nMove all terms to the left (standard form):\n$ -276x + -749 = 0 $\n\nIsolate the $x$ term:\n$ -276x = 749 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 26
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. -968 + 859x = -387"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -968 + 859x = -387 $\n\nMove all terms to the left (standard form):\n$ 859x + -581 = 0 $\n\nIsolate the $x$ term:\n$ 859x = 581 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 27
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Compute the determinant: $A=\\begin{pmatrix}-7&-4\\\\8&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-7&-4\\\\\\8&3\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 28
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Differentiate with respect to $x$: $f(x) = \\ln(4x + 4)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(4x + 4) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{4}{4x +... | {
"type": "calculus",
"seed": 1337,
"index": 29
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Prove that $(\\mathbb{Z}_17, +)$ is a group under addition modulo 17."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_17=\\{0,1,\\dots,16\\}$ with operation $+$ modulo $17$.\n\n**Closure:** If $a,b\\in\\mathbb{... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 30
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. -861 + 738x = 331"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -861 + 738x = 331 $\n\nMove all terms to the left (standard form):\n$ 738x + -1192 = 0 $\n\nIsolate the $x$ term:\n$ 738x = 1192 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 31
} |
[
{
"role": "user",
"content": "Solve this equation accurately. -2 - 186 - 200x^2 = 147x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -2 - 186 - 200x^2 = 147x $\n\nMove all terms to the left (standard form):\n$ -200x^2 + -147x + -188 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 32
} |
[
{
"role": "user",
"content": "Find the numerical solution to 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": 33
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Compute the indefinite integral: $\\int -9\\sin(7x) + 0\\cos(8x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -9\\sin(7x) + 0\\cos(8x)\\,dx $\n\nUse standard antiderivatives (and in... | {
"type": "calculus",
"seed": 1337,
"index": 34
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. 361 - 339x = -973"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 361 - 339x = -973 $\n\nMove all terms to the left (standard form):\n$ -339x + 1334 = 0 $\n\nIsolate the $x$ term:\n$ -339x = -1334 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 35
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Compute the determinant: $A=\\begin{pmatrix}2&4\\\\4&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}2&4\\\\\\4&3\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 36
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. 13 + 145 - 106x = -103x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 13 + 145 - 106x = -103x^2 $\n\nMove all terms to the left (standard form):\n$ 103x^2 + -106x + 158 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 37
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Prove that $f(x,y)=\\frac12(7x^2+4y^2)+3x+-5y+-3$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+4y^2)+3x+-5y+-3 $\n\n$ \\frac{\\partial^2 f... | {
"type": "optimization",
"seed": 1337,
"index": 38
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. -48 + 17x + 67x^2 = 79"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -48 + 17x + 67x^2 = 79 $\n\nMove all terms to the left (standard form):\n$ 67x^2 + 17x + -127 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 39
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. 454x + 797 = 5"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 454x + 797 = 5 $\n\nMove all terms to the left (standard form):\n$ 454x + 792 = 0 $\n\nIsolate the $x$ term:\n$ 454x = -792 $\n\nDivide both sides by ... | {
"type": "linear_equation",
"seed": 1337,
"index": 40
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-3&-6\\\\\\8&-9\\end{pmatrix},\\quad b=\\begin{pmatrix}6\\\\\\-91\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-3&-6\\\\\\8&-9... | {
"type": "linear_algebra",
"seed": 1337,
"index": 41
} |
[
{
"role": "user",
"content": "Solve the following math equation. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha =... | {
"type": "trigonometry",
"seed": 1337,
"index": 42
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Prove that $f(x)=10x^2+3x+4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+3x+4$.\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": 43
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report 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 $f'(x)=0$,... | {
"type": "optimization",
"seed": 1337,
"index": 44
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Solve for $x$ (in radians): sin(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(\\... | {
"type": "trigonometry",
"seed": 1337,
"index": 45
} |
[
{
"role": "user",
"content": "Solve the following mathematical 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{\\par... | {
"type": "optimization",
"seed": 1337,
"index": 46
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. -700x - 779 = -532"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -700x - 779 = -532 $\n\nMove all terms to the left (standard form):\n$ -700x + -247 = 0 $\n\nIsolate the $x$ term:\n$ -700x = 247 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 47
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. 358x + 686 = -456"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 358x + 686 = -456 $\n\nMove all terms to the left (standard form):\n$ 358x + 1142 = 0 $\n\nIsolate the $x$ term:\n$ 358x = -1142 $\n\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 48
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. 267x - 557 = -665"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 267x - 557 = -665 $\n\nMove all terms to the left (standard form):\n$ 267x + 108 = 0 $\n\nIsolate the $x$ term:\n$ 267x = -108 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 49
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Compute $(-57+47) \\bmod 23$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-57+47) \\bmod 23 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 50
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. -37 + 190 - 96x^2 = -126x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -37 + 190 - 96x^2 = -126x $\n\nMove all terms to the left (standard form):\n$ -96x^2 + 126x + 153 = 0 $\n\nApply the quad... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 51
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? -514 + 613 = -279x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -514 + 613 = -279x $\n\nMove all terms to the left (standard form):\n$ 279x + 99 = 0 $\n\nIsolate the $x$ term:\n$ 279x = -99 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 52
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Compute the indefinite integral: $\\int (2x + 8)e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (2x + 8)e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if... | {
"type": "calculus",
"seed": 1337,
"index": 53
} |
[
{
"role": "user",
"content": "solve: \n\n -27 + 166x^2 - 16 = 165x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -27 + 166x^2 - 16 = 165x $\n\nMove all terms to the left (standard form):\n$ 166x^2 + -165x + -43 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 54
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Prove that $f(x)=5x^2+7x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+7x+0$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 10x... | {
"type": "optimization",
"seed": 1337,
"index": 55
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Evaluate: ((-52 + 893/19) * 9) + 8^4 - log_7(117649) + (157 mod 4) + floor(101/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-52 + 893/19) * 9) + 8^4 - log_7(117649) + (157 mod 4) + flo... | {
"type": "arithmetic",
"seed": 1337,
"index": 56
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Evaluate: ((-35 + -348/12) * 5) + 8^5 - log_9(531441) + (80 mod 27) + floor(107/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-35 + -348/12) * 5) + 8^5 - log_9(531441) + (80 mod 27) + floor(107/... | {
"type": "arithmetic",
"seed": 1337,
"index": 57
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Compute the indefinite integral: $\\int 3x^3 + -3x^2 + 14x + 4\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3x^3 + -3x^2 + 14x + 4\\,dx $\n\nUse standard antiderivative... | {
"type": "calculus",
"seed": 1337,
"index": 58
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Evaluate: ((68 + -28/14) * 20) + 11^5 - log_9(531441) + (-370 mod 20) + floor(182/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((68 + -28/14) * 20) + 11^5 - log_9(531441) + (-370 mod 20) + floor(182/... | {
"type": "arithmetic",
"seed": 1337,
"index": 59
} |
[
{
"role": "user",
"content": "solve: -322x - 735 = -484"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -322x - 735 = -484 $\n\nMove all terms to the left (standard form):\n$ -322x + -251 = 0 $\n\nIsolate the $x$ term:\n$ -322x = 251 $\n\nDivide both sides by the coefficient of $x... | {
"type": "linear_equation",
"seed": 1337,
"index": 60
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Solve for $x$ (in radians): sin(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin... | {
"type": "trigonometry",
"seed": 1337,
"index": 61
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. -6x + 147 + 11 = -134x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -6x + 147 + 11 = -134x^2 $\n\nMove all terms to the left (standard form):\n$ 134x^2 + -6x + 158 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 62
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Evaluate: ((-23 + 406/14) * 14) + 10^2 - log_6(6) + (243 mod 14) + floor(62/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-23 + 406/14) * 14) + 10^2 - log_6(6) + (243 mod 14) + floor(62/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 63
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 915 + 169 = -519x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 915 + 169 = -519x $\n\nMove all terms to the left (standard form):\n$ 519x + 1084 = 0 $\n\nIsolate the $x$ term:\n$ 519x = -1084 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 64
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. -944 + 506 = 939x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -944 + 506 = 939x $\n\nMove all terms to the left (standard form):\n$ -939x + -438 = 0 $\n\nIsolate the $x$ term:\n$ -939x = 438 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 65
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Prove that $f(x)=10x^2+0x+-6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+0x+-6$.\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": 66
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Compute $(104+163) \\bmod 11$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (104+163) \\bmod 11 $\n\nUse the rule that addition is compatible with reduction modu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 67
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. 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{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 68
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Evaluate: ((189 + 63/9) * 6) + 2^5 - log_3(81) + (-92 mod 15) + ceil(191/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((189 + 63/9) * 6) + 2^5 - log_3(81) + (-92 mod 15) + ceil(191/2) $\n\nCompute each compon... | {
"type": "arithmetic",
"seed": 1337,
"index": 69
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. 40x^2 + 167 + 65x = -107"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 40x^2 + 167 + 65x = -107 $\n\nMove all terms to the left (standard form):\n$ 40x^2 + 65x + 274 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 70
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Solve for $x$ (in radians): sin(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 0 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(0) = 0 $\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 71
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Compute the indefinite integral: $\\int \\ln(1x + 0)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(1x + 0)\\,dx $\n\nUse standard antiderivatives (and integration by parts if... | {
"type": "calculus",
"seed": 1337,
"index": 72
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 11x + 1 - 144 = -21x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 11x + 1 - 144 = -21x^2 $\n\nMove all terms to the left (standard form):\n$ 21x^2 + 11x + -143 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 73
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Compute the indefinite integral: $\\int 5e^{-3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 5e^{-3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed... | {
"type": "calculus",
"seed": 1337,
"index": 74
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}5&3\\\\\\8&9\\end{pmatrix},\\quad b=\\begin{pmatrix}-46\\\\\\-82\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}5&3\\\\\\8&... | {
"type": "linear_algebra",
"seed": 1337,
"index": 75
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Prove that $(\\mathbb{Z}_22, +)$ is a group under addition modulo 22."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_22=\\{0,1,\\dots,21\\}$ with operation $+$ modulo $22$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, then $(a+b)\\bmod n\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 76
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. 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": 77
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Compute the indefinite integral: $\\int (-2x + 2)e^{5x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-2x + 2)e^{5x}\\,dx $\n\nUse standard antiderivatives (and integration by pa... | {
"type": "calculus",
"seed": 1337,
"index": 78
} |
[
{
"role": "user",
"content": "Calculate the answer for 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$... | {
"type": "optimization",
"seed": 1337,
"index": 79
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. -303x + 397 = -776"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -303x + 397 = -776 $\n\nMove all terms to the left (standard form):\n$ -303x + 1173 = 0 $\n\nIsolate the $x$ term:\n$ -303x = -1173 $... | {
"type": "linear_equation",
"seed": 1337,
"index": 80
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 791 + 584 = 150x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 791 + 584 = 150x $\n\nMove all terms to the left (standard form):\n$ -150x + 1375 = 0 $\n\nIsolate the $x$ term:\n$ -150x = -1375 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 81
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 30 + 27 - 88x = -31x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 30 + 27 - 88x = -31x^2 $\n\nMove all terms to the left (standard form):\n$ 31x^2 + -88x + 57 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 82
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Differentiate with respect to $x$: $f(x) = -2\\sin(4x) + 7\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -2\\sin(4x) + 7\\cos(7x) $\n\nApply the standard differentiation rules:\n$ f'(x) = ... | {
"type": "calculus",
"seed": 1337,
"index": 83
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Differentiate with respect to $x$: $f(x) = 6x^3 + -9x^2 + -12x + -6$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 6x^3 + -9x^2 + -12x + -6 $\n\nApply the standard differentiation rules:\n$... | {
"type": "calculus",
"seed": 1337,
"index": 84
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}8&6\\\\\\7&-8\\end{pmatrix},\\quad b=\\begin{pmatrix}-66\\\\\\35\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}8&6\\\\\\7&-8... | {
"type": "linear_algebra",
"seed": 1337,
"index": 85
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((56 + -370/10) * 11) + 10^4 - log_7(16807) + (-31 mod 28) + floor(26/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((56 + -370/10) * 11) + 10^4 - log_7(16807) + (-31 mod 28) + floor(26/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 86
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Prove that $f(x)=4x^2+-2x+-2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+-2x+-2$.\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": 87
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Compute $(-124+174) \\bmod 9$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-124+174) \\bmod 9 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 88
} |
[
{
"role": "user",
"content": "Evaluate the following equation. -712x - 257 = 478"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -712x - 257 = 478 $\n\nMove all terms to the left (standard form):\n$ -712x + -735 = 0 $\n\nIsolate the $x$ term:\n$ -712x = 735 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 89
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. -16 + 67x + 9x^2 = -72"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -16 + 67x + 9x^2 = -72 $\n\nMove all terms to the left (standard form):\n$ 9x^2 + 67x + 56 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 90
} |
[
{
"role": "user",
"content": "Calculate and solve 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{\\partial^2 ... | {
"type": "optimization",
"seed": 1337,
"index": 91
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Evaluate: ((-65 + 156/12) * 13) + 3^4 - log_4(64) + (36 mod 18) + round(34/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-65 + 156/12) * 13) + 3^4 - log_4(64) + (36 mod 18) + round(34/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 92
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&4&-3\\\\\\3&-1&0\\\\\\-5&5&4\\end{pmatrix},\\quad b=\\begin{pmatrix}26\\\\\\0\\\\\\-2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 93
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. 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$ \\al... | {
"type": "trigonometry",
"seed": 1337,
"index": 94
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Find $A^{-1}$ for $A=\\begin{pmatrix}-1&3\\\\8&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -1 & 3 \\\\ 8 & -4 \\end{pmatrix} $\n\nCompute... | {
"type": "linear_algebra",
"seed": 1337,
"index": 95
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Evaluate: ((-22 + 374/22) * 18) + 11^2 - log_7(2401) + (-263 mod 29) + ceil(-29/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-22 + 374/22) * 18) + 11^2 - log_7(2401) + (-263 mod 29) + ceil(-29/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 96
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Differentiate with respect to $x$: $f(x) = -2\\sin(6x) + -1\\cos(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -2\\sin(6x) + -1\\cos(4x) $\n\nApply the standard differentiation rules:\n$ f'(x... | {
"type": "calculus",
"seed": 1337,
"index": 97
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&5&-5\\\\\\-1&5&-1\\\\\\5&0&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}13\\\\\\21\\\\\\-15\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 98
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Find the modular inverse of 7 modulo 8, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{8}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantee... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 99
} |
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