messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Work through and solve this equation. Prove that $f(x)=9x^2+4x+6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+4x+6$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 18x +... | {
"type": "optimization",
"seed": 1337,
"index": 3300
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. -44x^2 + 117x + 29 = 97"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -44x^2 + 117x + 29 = 97 $\n\nMove all terms to the left (standard form):\n$ -44x^2 + 117x + -68 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3301
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}5&4\\\\\\-1&9\\end{pmatrix},\\quad b=\\begin{pmatrix}-55\\\\\\-38\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}5&4\\\\\\-1&9\\end{p... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3302
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Prove that $f(x)=10x^2+-10x+-1$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+-10x+-1$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$... | {
"type": "optimization",
"seed": 1337,
"index": 3303
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Compute the indefinite integral: $\\int -7e^{-3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -7e^{-3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\in... | {
"type": "calculus",
"seed": 1337,
"index": 3304
} |
[
{
"role": "user",
"content": "Please calculate this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-3&-1\\\\-5&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -3 & -1 \\\\ -5 & -8 \\end{pmatrix} $\n\nCompute the determi... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3305
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Prove that $f(x,y)=\\frac12(1x^2+4y^2)+0x+2y+-9$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+4y^2)+0x+2y+-9 $\n\n$ \\frac{\\partial^2 f}{\... | {
"type": "optimization",
"seed": 1337,
"index": 3306
} |
[
{
"role": "user",
"content": "Please work out this equation. Solve for $x$ (in radians): sin(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -1 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(-1) = -1.5708 $\n\nThe general s... | {
"type": "trigonometry",
"seed": 1337,
"index": 3307
} |
[
{
"role": "user",
"content": "solve 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 f}{\\partial x\\partial y} \... | {
"type": "optimization",
"seed": 1337,
"index": 3308
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Evaluate: ((-89 + -168/24) * 16) + 2^3 - log_9(6561) + (362 mod 20) + round(179/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-89 + -168/24) * 16) + 2^3 - log_9(6561) + (362 mod 20) + round(179/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 3309
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Prove that $f(x,y)=\\frac12(6x^2+1y^2)+4x+5y+-10$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(6x^2+1y^2)+4x+5y+-10 $\n\n$ \\frac{\\partial^2 f}{\\... | {
"type": "optimization",
"seed": 1337,
"index": 3310
} |
[
{
"role": "user",
"content": "Please resolve the math 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$ \\alph... | {
"type": "trigonometry",
"seed": 1337,
"index": 3311
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. 27x^2 - 57 + 69 = -181x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 27x^2 - 57 + 69 = -181x $\n\nMove all terms to the left (standard form):\n$ 27x^2 + 181x + 12 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3312
} |
[
{
"role": "user",
"content": "Determine the answer 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 = \\arcs... | {
"type": "trigonometry",
"seed": 1337,
"index": 3313
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Evaluate: ((184 + -64/16) * 12) + 3^5 - log_9(729) + (8 mod 11) + round(155/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((184 + -64/16) * 12) + 3^5 - log_9(729) + (8 mod 11) + round(155/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 3314
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((152 + -143/11) * 10) + 6^2 - log_3(81) + (369 mod 26) + round(-64/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((152 + -143/11) * 10) + 6^2 - log_3(81) + (369 mod 26) + round(-64/2) $\n\nCompute eac... | {
"type": "arithmetic",
"seed": 1337,
"index": 3315
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Compute the indefinite integral: $\\int \\ln(2x + 1)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(2x + 1)\\,dx $\n\nUse standard antiderivatives (and integration b... | {
"type": "calculus",
"seed": 1337,
"index": 3316
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. -950x + 213 = -310"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -950x + 213 = -310 $\n\nMove all terms to the left (standard form):\n$ -950x + 523 = 0 $\n\nIsolate the $x$ term:\n$ -950x = -523 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 3317
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Find $A^{-1}$ for $A=\\begin{pmatrix}2&-4\\\\9&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 2 & -4 \\\\ 9 & 4 \\end{pmatrix} $\n\nCompute the determ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3318
} |
[
{
"role": "user",
"content": "Solve the following math equation. 25 + 146 - 41x = 29x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 25 + 146 - 41x = 29x^2 $\n\nMove all terms to the left (standard form):\n$ -29x^2 + -41x + 171 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3319
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Evaluate: ((148 + 256/16) * 16) + 2^5 - log_6(46656) + (133 mod 28) + ceil(43/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((148 + 256/16) * 16) + 2^5 - log_6(46656) + (133 mod 28) + ceil(43/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 3320
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Evaluate: ((-134 + -222/6) * 12) + 2^4 - log_5(15625) + (327 mod 25) + ceil(183/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-134 + -222/6) * 12) + 2^4 - log_5(15625) + (327 mod 25) + ce... | {
"type": "arithmetic",
"seed": 1337,
"index": 3321
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. 924x + 406 = 46"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 924x + 406 = 46 $\n\nMove all terms to the left (standard form):\n$ 924x + 360 = 0 $\n\nIsolate the $x$ term:\n$ 924x = -360 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 3322
} |
[
{
"role": "user",
"content": "solve: \n\n 10 + 70x^2 + 43x = 180"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10 + 70x^2 + 43x = 180 $\n\nMove all terms to the left (standard form):\n$ 70x^2 + 43x + -170 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 -... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3323
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? 931 - 26x = -843"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 931 - 26x = -843 $\n\nMove all terms to the left (standard form):\n$ -26x + 1774 = 0 $\n\nIsolate the $x$ term:\n$ -26x = -1774 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 3324
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Compute the determinant: $A=\\begin{pmatrix}-9&5\\\\-4&7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-9&5\\\\\\-4&7\\end{pmatrix} ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3325
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. 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{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 3326
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. 550x + 761 = 410"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 550x + 761 = 410 $\n\nMove all terms to the left (standard form):\n$ 550x + 351 = 0 $\n\nIsolate the $x$ term:\n$ 550x = -351 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 3327
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Evaluate: ((-149 + 703/19) * 17) + 8^5 - log_9(59049) + (-177 mod 6) + round(-40/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-149 + 703/19) * 17) + 8^5 - log_9(59049) + (-177 mod 6) + round(-40/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 3328
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 3329
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Compute the indefinite integral: $\\int (-3x + 5)e^{1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-3x + 5)e^{1x}\\,dx $\n\nUse standard antiderivatives (and integration by pa... | {
"type": "calculus",
"seed": 1337,
"index": 3330
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Prove that $(\\mathbb{Z}_3, +)$ is a group under addition modulo 3."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_3=\\{0,1,\\dots,2\\}$ with operation $+$ modulo $3$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$,... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3331
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Compute the indefinite integral: $\\int 2e^{5x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 2e^{5x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n... | {
"type": "calculus",
"seed": 1337,
"index": 3332
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Evaluate: ((27 + 576/24) * 10) + 11^5 - log_3(81) + (26 mod 20) + round(141/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((27 + 576/24) * 10) + 11^5 - log_3(81) + (26 mod 20) + round(141/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 3333
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 25x + 90 - 46x^2 = -86"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 25x + 90 - 46x^2 = -86 $\n\nMove all terms to the left (standard form):\n$ -46x^2 + 25x + 176 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3334
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-4&-3\\\\\\-2&6\\end{pmatrix},\\quad b=\\begin{pmatrix}-5\\\\\\-40\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-4&-3\\\\\\-2... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3335
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Evaluate: ((81 + -920/23) * 14) + 8^3 - log_4(256) + (377 mod 24) + floor(59/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((81 + -920/23) * 14) + 8^3 - log_4(256) + (377 mod 24) + floor(59/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 3336
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. -35 - 115x + 97x^2 = -102"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -35 - 115x + 97x^2 = -102 $\n\nMove all terms to the left (standard form):\n$ 97x^2 + -115x + 67 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3337
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. -9x + 167 + 171 = -187x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -9x + 167 + 171 = -187x^2 $\n\nMove all terms to the left (standard form):\n$ 187x^2 + -9x + 338 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3338
} |
[
{
"role": "user",
"content": "Please find the solution of this 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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 3339
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((-66 + -70/5) * 20) + 9^3 - log_7(117649) + (130 mod 28) + ceil(-115/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-66 + -70/5) * 20) + 9^3 - log_7(117649) + (130 mod 28) + ceil(-115/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 3340
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. 867x + 128 = 110"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 867x + 128 = 110 $\n\nMove all terms to the left (standard form):\n$ 867x + 18 = 0 $\n\nIsolate the $x$ term:\n$ 867x = -18 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3341
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Evaluate: ((160 + 196/4) * 18) + 8^5 - log_7(117649) + (310 mod 26) + round(-35/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((160 + 196/4) * 18) + 8^5 - log_7(117649) + (310 mod 26) + round(-35/... | {
"type": "arithmetic",
"seed": 1337,
"index": 3342
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-9&-4\\\\\\-9&7\\end{pmatrix},\\quad b=\\begin{pmatrix}60\\\\\\93\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-9&-4\\\\\\-9&7\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3343
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. -811 + 243 = -193x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -811 + 243 = -193x $\n\nMove all terms to the left (standard form):\n$ 193x + -568 = 0 $\n\nIsolate the $x$ term:\n$ 193x = 568 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3344
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Evaluate: ((86 + -190/10) * 15) + 2^3 - log_10(10000) + (78 mod 13) + floor(158/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((86 + -190/10) * 15) + 2^3 - log_10(10000) + (78 mod 13) + floor(158... | {
"type": "arithmetic",
"seed": 1337,
"index": 3345
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((37 + 350/10) * 7) + 2^5 - log_9(6561) + (426 mod 28) + ceil(19/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((37 + 350/10) * 7) + 2^5 - log_9(6561) + (426 mod 28) + ceil(19/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 3346
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 603 + 252 = -759x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 603 + 252 = -759x $\n\nMove all terms to the left (standard form):\n$ 759x + 855 = 0 $\n\nIsolate the $x$ term:\n$ 759x = -855 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 3347
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 3348
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 19x + 62 - 141 = 192x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 19x + 62 - 141 = 192x^2 $\n\nMove all terms to the left (standard form):\n$ -192x^2 + 19x + -79 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3349
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: -16 - 133x^2 - 49 = 133x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -16 - 133x^2 - 49 = 133x $\n\nMove all terms to the left (standard form):\n$ -133x^2 + -133x + -65 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3350
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Evaluate: ((-80 + 245/7) * 14) + 8^3 - log_10(10) + (-247 mod 7) + ceil(-97/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-80 + 245/7) * 14) + 8^3 - log_10(10) + (-247 mod 7) + ceil(-97/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 3351
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Prove that $f(x)=7x^2+0x+-6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+0x+-6$.\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": 3352
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&3&4\\\\\\-1&-2&-5\\\\\\2&5&4\\end{pmatrix},\\quad b=\\begin{pmatrix}11\\\\\\-9\\\\\\13\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3353
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Compute the determinant: $A=\\begin{pmatrix}-9&2\\\\-7&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-9&2\\\\\\-7&-7\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3354
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Evaluate: ((140 + -400/10) * 8) + 8^3 - log_10(100) + (65 mod 5) + ceil(-112/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((140 + -400/10) * 8) + 8^3 - log_10(100) + (65 mod 5) + ceil(-112/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 3355
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Compute the determinant: $A=\\begin{pmatrix}-2&-3\\\\7&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-2&-3\\\\\\7&-3\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3356
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 618 - 680x = -617"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 618 - 680x = -617 $\n\nMove all terms to the left (standard form):\n$ -680x + 1235 = 0 $\n\nIsolate the $x$ term:\n$ -680x = -1235 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 3357
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Find the modular inverse of 21 modulo 25, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $21\\cdot a^{-1} \\equiv 1 \\pmod{25}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3358
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Compute $(-12+-38) \\bmod 15$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-12+-38) \\bmod 15 $\n\nUse the rule that addition is compatible with reduction mo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3359
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Evaluate: ((55 + -216/24) * 3) + 7^2 - log_3(3) + (-113 mod 13) + floor(-178/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((55 + -216/24) * 3) + 7^2 - log_3(3) + (-113 mod 13) + floor(-178/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 3360
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-2&-2&-5\\\\\\1&5&0\\\\\\-3&3&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}27\\\\\\-14\\\\\\18\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3361
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Prove that $f(x,y)=\\frac12(8x^2+1y^2)+2x+-4y+-2$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(8x^2+1y^2)+2x+-4y+-2 $\n\n$ \\frac{\\partial^2 ... | {
"type": "optimization",
"seed": 1337,
"index": 3362
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. -362 + 13 = -993x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -362 + 13 = -993x $\n\nMove all terms to the left (standard form):\n$ 993x + -349 = 0 $\n\nIsolate the $x$ term:\n$ 993x = 349 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 3363
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Prove that $(\\mathbb{Z}_11, +)$ is a group under addition modulo 11."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_11=\\{0,1,\\dots,10\\}$ with operation $+$ modulo $11$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3364
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}4&-1\\\\\\-4&4\\end{pmatrix},\\quad b=\\begin{pmatrix}-32\\\\\\44\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}4&-1\\\\\\-4&4... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3365
} |
[
{
"role": "user",
"content": "solve -23x - 56 + 185x^2 = -60"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -23x - 56 + 185x^2 = -60 $\n\nMove all terms to the left (standard form):\n$ 185x^2 + -23x + 4 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - 4... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3366
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Find $A^{-1}$ for $A=\\begin{pmatrix}-9&9\\\\8&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -9 & 9 \\\\ 8 & 4 \\end{pmatrix} $\n\nCompute the dete... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3367
} |
[
{
"role": "user",
"content": "Please solve this math problem. 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-... | {
"type": "optimization",
"seed": 1337,
"index": 3368
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Compute $(-142+-108) \\bmod 24$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-142+-108) \\bmod 24 $\n\nUse the rule that addition is compatible with reductio... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3369
} |
[
{
"role": "user",
"content": "Solve this equation step by step. -44 - 122x + 141 = 178x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -44 - 122x + 141 = 178x^2 $\n\nMove all terms to the left (standard form):\n$ -178x^2 + -122x + 97 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3370
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 33 - 173x^2 - 3 = 114x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 33 - 173x^2 - 3 = 114x $\n\nMove all terms to the left (standard form):\n$ -173x^2 + -114x + 30 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3371
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 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$... | {
"type": "trigonometry",
"seed": 1337,
"index": 3372
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Compute $(-12+85) \\bmod 18$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-12+85) \\bmod 18 $\n\nUse the rule that addition is compatible with reduction mod... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3373
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 3374
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Differentiate with respect to $x$: $f(x) = 4\\sin(5x) + 0\\cos(6x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4\\sin(5x) + 0\\cos(6x) $\n\nApply the standard differentiation rules:\n$ f'(... | {
"type": "calculus",
"seed": 1337,
"index": 3375
} |
[
{
"role": "user",
"content": "Please determine the outcome of 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": 3376
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Prove that $f(x)=7x^2+1x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+1x+0$.\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": 3377
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? -x + 104 + 36 = 111x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -x + 104 + 36 = 111x^2 $\n\nMove all terms to the left (standard form):\n$ -111x^2 + -1x + 140 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3378
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&5&5\\\\\\3&3&3\\\\\\-3&-2&0\\end{pmatrix},\\quad b=\\begin{pmatrix}-5\\\\\\-3\\\\\\6\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3379
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 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 = \\arc... | {
"type": "trigonometry",
"seed": 1337,
"index": 3380
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Evaluate: ((7 + 319/11) * 10) + 8^4 - log_4(64) + (346 mod 19) + round(183/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((7 + 319/11) * 10) + 8^4 - log_4(64) + (346 mod 19) + round(183/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 3381
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute the indefinite integral: $\\int \\ln(9x + 9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(9x + 9)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 3382
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. -7 + 149x - 110x^2 = -199"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -7 + 149x - 110x^2 = -199 $\n\nMove all terms to the left (standard form):\n$ -110x^2 + 149x + 192 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3383
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. -39x + 57x^2 - 27 = 59"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -39x + 57x^2 - 27 = 59 $\n\nMove all terms to the left (standard form):\n$ 57x^2 + -39x + -86 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3384
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Compute the determinant: $A=\\begin{pmatrix}-6&-7\\\\-8&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-6&-7\\\\\\-8&-4\\end{pmatrix} $\n\nUse $\\de... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3385
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. -602 - 187x = 802"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -602 - 187x = 802 $\n\nMove all terms to the left (standard form):\n$ -187x + -1404 = 0 $\n\nIsolate the $x$ term:\n$ -187x = 1404 ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3386
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. -40 + 519 = 393x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -40 + 519 = 393x $\n\nMove all terms to the left (standard form):\n$ -393x + 479 = 0 $\n\nIsolate the $x$ term:\n$ -393x = -479 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3387
} |
[
{
"role": "user",
"content": "solve: -15 - 1x + 6 = 77x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -15 - 1x + 6 = 77x^2 $\n\nMove all terms to the left (standard form):\n$ -77x^2 + -1x + -9 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3388
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Evaluate: ((52 + 200/10) * 1) + 5^3 - log_3(3) + (-22 mod 12) + floor(43/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((52 + 200/10) * 1) + 5^3 - log_3(3) + (-22 mod 12) + floor(43/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 3389
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. -19 + 139x^2 + 190x = -48"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -19 + 139x^2 + 190x = -48 $\n\nMove all terms to the left (standard form):\n$ 139x^2 + 190x + 29 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3390
} |
[
{
"role": "user",
"content": "Determine the correct answer 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 value).\n$... | {
"type": "trigonometry",
"seed": 1337,
"index": 3391
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Differentiate with respect to $x$: $f(x) = (-6x + 7)e^{3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-6x + 7)e^{3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-6e^{3x... | {
"type": "calculus",
"seed": 1337,
"index": 3392
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. -10x + 153x^2 - 25 = -133"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -10x + 153x^2 - 25 = -133 $\n\nMove all terms to the left (standard form):\n$ 153x^2 + -10x + 108 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3393
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Evaluate: ((80 + -208/16) * 7) + 12^4 - log_10(100000) + (401 mod 30) + ceil(176/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((80 + -208/16) * 7) + 12^4 - log_10(100000) + (401 mod 30) + ceil(176/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 3394
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 489 + 529x = -733"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 489 + 529x = -733 $\n\nMove all terms to the left (standard form):\n$ 529x + 1222 = 0 $\n\nIsolate the $x$ term:\n$ 529x = -1222 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 3395
} |
[
{
"role": "user",
"content": "Please evaluate and compute this 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": 3396
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. -46x + 195x^2 - 164 = -147"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -46x + 195x^2 - 164 = -147 $\n\nMove all terms to the left (standard form):\n$ 195x^2 + -46x + -17 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3397
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}0&4&-1\\\\\\5&3&-4\\\\\\-3&-1&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-6\\\\\\-16\\\\\\10\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3398
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Find the modular inverse of 17 modulo 39, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $17\\cdot a^{-1} \\equiv 1 \\pmod{39}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gua... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3399
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.