messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Please solve this mathematical equation. Evaluate: ((163 + -672/16) * 4) + 6^2 - log_6(1296) + (-211 mod 25) + floor(-97/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((163 + -672/16) * 4) + 6^2 - log_6(1296) + (-211 mod 25) + floor(-97/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 3200
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Evaluate: ((174 + -836/22) * 12) + 7^2 - log_10(1000) + (322 mod 4) + floor(-158/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((174 + -836/22) * 12) + 7^2 - log_10(1000) + (322 mod 4) + floor(-158/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 3201
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Differentiate with respect to $x$: $f(x) = 3\\sin(5x) + 0\\cos(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3\\sin(5x) + 0\\cos(4x) $\n\nApply the standard differentiation rules:\n$ f'(... | {
"type": "calculus",
"seed": 1337,
"index": 3202
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Compute the indefinite integral: $\\int (4x + -5)\\sin(4x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (4x + -5)\\sin(4x)\\,dx $\n\nUse standard antiderivatives (and integration ... | {
"type": "calculus",
"seed": 1337,
"index": 3203
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. -622 + 929 = 309x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -622 + 929 = 309x $\n\nMove all terms to the left (standard form):\n$ -309x + 307 = 0 $\n\nIsolate the $x$ term:\n$ -309x = -307 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3204
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Find the modular inverse of 3 modulo 16, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $3\\cdot a^{-1} \\equiv 1 \\pmod{16}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gua... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3205
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Prove that $f(x,y)=\\frac12(7x^2+5y^2)+5x+5y+6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+5y^2)+5x+5y+6 $\n\n$ \\frac{\\partial^2 f}{\... | {
"type": "optimization",
"seed": 1337,
"index": 3206
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Evaluate: ((9 + 405/9) * 8) + 9^5 - log_2(4) + (-408 mod 30) + floor(-22/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((9 + 405/9) * 8) + 9^5 - log_2(4) + (-408 mod 30) + floor(-22/2) $\n\nCompute each compo... | {
"type": "arithmetic",
"seed": 1337,
"index": 3207
} |
[
{
"role": "user",
"content": "Solve the math equation and present 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 $f'(x)=0$, h... | {
"type": "optimization",
"seed": 1337,
"index": 3208
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Prove that $f(x,y)=\\frac12(1x^2+7y^2)+-4x+4y+4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+7y^2)+-4x+4y+4 $\n\n$ \\frac{\\partial... | {
"type": "optimization",
"seed": 1337,
"index": 3209
} |
[
{
"role": "user",
"content": "Please work out this equation. -43 - 112 - 67x^2 = 144x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -43 - 112 - 67x^2 = 144x $\n\nMove all terms to the left (standard form):\n$ -67x^2 + -144x + -155 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3210
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Differentiate with respect to $x$: $f(x) = (4x + -2)\\sin(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (4x + -2)\\sin(5x) $\n\nApply the standard differentiation rules:\n$ f'(... | {
"type": "calculus",
"seed": 1337,
"index": 3211
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Evaluate: ((-164 + 26/13) * 6) + 8^5 - log_9(6561) + (86 mod 20) + floor(-188/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-164 + 26/13) * 6) + 8^5 - log_9(6561) + (86 mod 20) + floor(-188/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 3212
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Differentiate with respect to $x$: $f(x) = 2e^{5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2e^{5x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{10e^{5x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 3213
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. -2 + 961 = -272x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -2 + 961 = -272x $\n\nMove all terms to the left (standard form):\n$ 272x + 959 = 0 $\n\nIsolate the $x$ term:\n$ 272x = -959 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 3214
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. -496x - 14 = -709"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -496x - 14 = -709 $\n\nMove all terms to the left (standard form):\n$ -496x + 695 = 0 $\n\nIsolate the $x$ term:\n$ -496x = -695 $\n\... | {
"type": "linear_equation",
"seed": 1337,
"index": 3215
} |
[
{
"role": "user",
"content": "Can you compute this equation? -680 - 418x = -79"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -680 - 418x = -79 $\n\nMove all terms to the left (standard form):\n$ -418x + -601 = 0 $\n\nIsolate the $x$ term:\n$ -418x = 601 $\n\nDivide both sides by ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3216
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Evaluate: ((-101 + -672/24) * 20) + 6^5 - log_10(10000) + (-262 mod 3) + floor(157/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-101 + -672/24) * 20) + 6^5 - log_10(10000) + (-262 mod 3) + floor(1... | {
"type": "arithmetic",
"seed": 1337,
"index": 3217
} |
[
{
"role": "user",
"content": "Compute the final answer to this 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 $\n\nThe genera... | {
"type": "trigonometry",
"seed": 1337,
"index": 3218
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Evaluate: ((68 + 90/10) * 10) + 4^5 - log_3(27) + (371 mod 9) + round(-16/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((68 + 90/10) * 10) + 4^5 - log_3(27) + (371 mod 9) + round(-16/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 3219
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}5&7\\\\\\-9&-9\\end{pmatrix},\\quad b=\\begin{pmatrix}0\\\\\\18\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}5&7\\\\\\-9&-9\\end{pmatrix}... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3220
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this 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\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 3221
} |
[
{
"role": "user",
"content": "Work through and solve this equation. 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 $\n\nThe ge... | {
"type": "trigonometry",
"seed": 1337,
"index": 3222
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. x^2 - 133x - 8 = -130"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ x^2 - 133x - 8 = -130 $\n\nMove all terms to the left (standard form):\n$ 1x^2 + -133x + 122 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3223
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical 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 = ... | {
"type": "trigonometry",
"seed": 1337,
"index": 3224
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. -693x + 88 = 849"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -693x + 88 = 849 $\n\nMove all terms to the left (standard form):\n$ -693x + -761 = 0 $\n\nIsolate the $x$ term:\n$ -693x = 761 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 3225
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Compute the indefinite integral: $\\int \\ln(1x + -9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(1x + -9)\\,dx $\n\nUse standard antiderivatives (and integration by par... | {
"type": "calculus",
"seed": 1337,
"index": 3226
} |
[
{
"role": "user",
"content": "Find the solution to the following 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$... | {
"type": "trigonometry",
"seed": 1337,
"index": 3227
} |
[
{
"role": "user",
"content": "solve: 26x^2 - 23x - 121 = 174"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 26x^2 - 23x - 121 = 174 $\n\nMove all terms to the left (standard form):\n$ 26x^2 + -23x + -295 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3228
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Compute $(-94+-11) \\bmod 8$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-94+-11) \\bmod 8 $\n\nUse the rule that addition is compatible with re... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3229
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute $(-19+-154) \\bmod 2$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-19+-154) \\bmod 2 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3230
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Evaluate: ((-8 + 665/19) * 13) + 2^3 - log_10(100000) + (-331 mod 24) + floor(-104/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-8 + 665/19) * 13) + 2^3 - log_10(100000) + (-331 mod 24) + floor(-104/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 3231
} |
[
{
"role": "user",
"content": "Solve the following math equation. -203 - 575x = 264"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -203 - 575x = 264 $\n\nMove all terms to the left (standard form):\n$ -575x + -467 = 0 $\n\nIsolate the $x$ term:\n$ -575x = 467 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 3232
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Evaluate: ((-163 + 30/10) * 4) + 10^3 - log_10(10) + (-246 mod 17) + ceil(125/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-163 + 30/10) * 4) + 10^3 - log_10(10) + (-246 mod 17) + ceil(125/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 3233
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. 41x - 112 + 186 = 17x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 41x - 112 + 186 = 17x^2 $\n\nMove all terms to the left (standard form):\n$ -17x^2 + 41x + 74 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3234
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. 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": 3235
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&-3&1\\\\\\0&1&-5\\\\\\5&4&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}14\\\\\\-17\\\\\\-25\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $A... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3236
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. 10 - 8x + 65x^2 = 134"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10 - 8x + 65x^2 = 134 $\n\nMove all terms to the left (standard form):\n$ 65x^2 + -8x + -124 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3237
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((3 + -85/5) * 16) + 9^3 - log_9(81) + (-269 mod 13) + round(190/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((3 + -85/5) * 16) + 9^3 - log_9(81) + (-269 mod 13) + round(190/2) $\n\nCompute each comp... | {
"type": "arithmetic",
"seed": 1337,
"index": 3238
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Evaluate: ((189 + -360/24) * 8) + 12^2 - log_4(4) + (231 mod 7) + floor(-180/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((189 + -360/24) * 8) + 12^2 - log_4(4) + (231 mod 7) + floor(-180/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 3239
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Prove that $f(x)=2x^2+-1x+-9$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+-1x+-9$.\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": 3240
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Evaluate: ((5 + -81/3) * 4) + 12^3 - log_5(15625) + (-371 mod 26) + floor(25/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((5 + -81/3) * 4) + 12^3 - log_5(15625) + (-371 mod 26) + floor(25/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 3241
} |
[
{
"role": "user",
"content": "Solve the following math equation. Compute the indefinite integral: $\\int (1x + -10)e^{3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (1x + -10)e^{3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if n... | {
"type": "calculus",
"seed": 1337,
"index": 3242
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-9&6\\\\\\-5&-6\\end{pmatrix},\\quad b=\\begin{pmatrix}-69\\\\\\-1\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-9&6\\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3243
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 3244
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Evaluate: ((-95 + -55/11) * 2) + 5^2 - log_7(117649) + (-166 mod 4) + ceil(154/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-95 + -55/11) * 2) + 5^2 - log_7(117649) + (-166 mod 4) + ceil(154/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 3245
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 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\... | {
"type": "trigonometry",
"seed": 1337,
"index": 3246
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Prove that $(\\mathbb{Z}_12, +)$ is a group under addition modulo 12."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_12=\\{0,1,\\dots,11\\}$ with operation $+$ modulo $12$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3247
} |
[
{
"role": "user",
"content": "Calculate 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$ 4x(x... | {
"type": "optimization",
"seed": 1337,
"index": 3248
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&1&-1\\\\\\0&0&-1\\\\\\-1&-3&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}-8\\\\\\-1\\\\\\10\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by Gaussian elimina... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3249
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. -796 + 168x = -301"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -796 + 168x = -301 $\n\nMove all terms to the left (standard form):\n$ 168x + -495 = 0 $\n\nIsolate the $x$ term:\n$ 168x = 495 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 3250
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Find the modular inverse of 11 modulo 12, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{12}$.\n\nSince $\\gcd(a,m)=1$, Bézout's ident... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3251
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Find the modular inverse of 14 modulo 17, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $14\\cdot a^{-1} \\equiv 1 \\pmod{17}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gua... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3252
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Compute the determinant: $A=\\begin{pmatrix}3&7\\\\-6&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&7\\\\\\-6&-6\\end{pmatrix} $\n\nUse... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3253
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. -22 - 55x^2 + 29x = -46"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -22 - 55x^2 + 29x = -46 $\n\nMove all terms to the left (standard form):\n$ -55x^2 + 29x + 24 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3254
} |
[
{
"role": "user",
"content": "Please work out this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-1&-2&-4\\\\\\1&-4&-5\\\\\\2&5&4\\end{pmatrix},\\quad b=\\begin{pmatrix}-1\\\\\\-5\\\\\\14\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by G... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3255
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Compute $(-113+-193) \\bmod 18$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-113+-193) \\bmod 18 $\n\nUse the rule that addition is compatible with re... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3256
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Compute the indefinite integral: $\\int (5x + 5)\\sin(3x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (5x + 5)\\sin(3x)\\,dx $\n\nUse standard antiderivatives (and integration by p... | {
"type": "calculus",
"seed": 1337,
"index": 3257
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Compute $(121+-99) \\bmod 19$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (121+-99) \\bmod 19 $\n\nUse the rule that addition is compatible with reduction mod... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3258
} |
[
{
"role": "user",
"content": "Please solve this mathematical 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": 3259
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Differentiate with respect to $x$: $f(x) = (1x + 10)e^{4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (1x + 10)e^{4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{1e^{4x} + (1x +... | {
"type": "calculus",
"seed": 1337,
"index": 3260
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Prove that $f(x)=2x^2+-7x+-10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+-7x+-10$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ ... | {
"type": "optimization",
"seed": 1337,
"index": 3261
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&-3&5\\\\\\-2&1&-4\\\\\\4&-3&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}28\\\\\\-17\\\\\\-1\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by Gaussian elimin... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3262
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Evaluate: ((11 + 224/16) * 14) + 12^3 - log_3(9) + (66 mod 2) + floor(193/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((11 + 224/16) * 14) + 12^3 - log_3(9) + (66 mod 2) + floor(193/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 3263
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Evaluate: ((145 + 66/2) * 13) + 6^4 - log_6(36) + (400 mod 8) + round(-80/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((145 + 66/2) * 13) + 6^4 - log_6(36) + (400 mod 8) + round(-80/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 3264
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Solve for $x$ (in radians): tan(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 0 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(0) = 0 $\n\nThe general solut... | {
"type": "trigonometry",
"seed": 1337,
"index": 3265
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Compute $(71+122) \\bmod 18$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (71+122) \\bmod 18 $\n\nUse the rule that addition is compatible with reducti... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3266
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. -45x^2 - 161x + 2 = -70"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -45x^2 - 161x + 2 = -70 $\n\nMove all terms to the left (standard form):\n$ -45x^2 + -161x + 72 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3267
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. 762 + 844x = 62"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 762 + 844x = 62 $\n\nMove all terms to the left (standard form):\n$ 844x + 700 = 0 $\n\nIsolate the $x$ term:\n$ 844x = -700 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3268
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Evaluate: ((87 + 325/25) * 3) + 7^4 - log_6(6) + (398 mod 16) + floor(-152/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((87 + 325/25) * 3) + 7^4 - log_6(6) + (398 mod 16) + floor(-152/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 3269
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Prove that $f(x)=9x^2+3x+-6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+3x+-6$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\... | {
"type": "optimization",
"seed": 1337,
"index": 3270
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Evaluate: ((2 + -451/11) * 20) + 10^5 - log_4(1024) + (-139 mod 2) + ceil(63/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((2 + -451/11) * 20) + 10^5 - log_4(1024) + (-139 mod 2) + ceil(63/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 3271
} |
[
{
"role": "user",
"content": "Work through and solve this equation. -7 + 107x - 37x^2 = -171"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -7 + 107x - 37x^2 = -171 $\n\nMove all terms to the left (standard form):\n$ -37x^2 + 107x + 164 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3272
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Compute the indefinite integral: $\\int -3e^{5x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3e^{5x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):... | {
"type": "calculus",
"seed": 1337,
"index": 3273
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Evaluate: ((-25 + 105/15) * 20) + 6^3 - log_4(64) + (355 mod 12) + round(-194/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-25 + 105/15) * 20) + 6^3 - log_4(64) + (355 mod 12) + round(-194/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 3274
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Compute the indefinite integral: $\\int (-4x + -7)e^{6x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-4x + -7)e^{6x}\\,dx $\n\nUse standard antiderivatives (and integration by p... | {
"type": "calculus",
"seed": 1337,
"index": 3275
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. 34 - 86x^2 + 68 = -69x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 34 - 86x^2 + 68 = -69x $\n\nMove all terms to the left (standard form):\n$ -86x^2 + 69x + 102 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3276
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 359 + 534x = -517"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 359 + 534x = -517 $\n\nMove all terms to the left (standard form):\n$ 534x + 876 = 0 $\n\nIsolate the $x$ term:\n$ 534x = -876 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 3277
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. -21 + 19x + 26x^2 = -115"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -21 + 19x + 26x^2 = -115 $\n\nMove all terms to the left (standard form):\n$ 26x^2 + 19x + 94 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3278
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((146 + 88/4) * 14) + 10^3 - log_5(15625) + (-378 mod 3) + floor(-181/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((146 + 88/4) * 14) + 10^3 - log_5(15625) + (-378 mod 3) + floor(-181/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 3279
} |
[
{
"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": 3280
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. 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": 3281
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. -9 - 110x - 194x^2 = -25"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -9 - 110x - 194x^2 = -25 $\n\nMove all terms to the left (standard form):\n$ -194x^2 + -110x + 16 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3282
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. 37 + 184x - 85x^2 = -181"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 37 + 184x - 85x^2 = -181 $\n\nMove all terms to the left (standard form):\n$ -85x^2 + 184x + 218 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3283
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Compute the indefinite integral: $\\int -8e^{-1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -8e^{-1x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if need... | {
"type": "calculus",
"seed": 1337,
"index": 3284
} |
[
{
"role": "user",
"content": "Compute the result for the following 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 = \\arc... | {
"type": "trigonometry",
"seed": 1337,
"index": 3285
} |
[
{
"role": "user",
"content": "Find the answer to the following 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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 3286
} |
[
{
"role": "user",
"content": "solve: \n\n Evaluate: ((-156 + 44/2) * 18) + 8^2 - log_3(243) + (-163 mod 5) + round(-91/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-156 + 44/2) * 18) + 8^2 - log_3(243) + (-163 mod 5) + round(-91/2) $\n\nCompute each component:\n$ 44/2 ... | {
"type": "arithmetic",
"seed": 1337,
"index": 3287
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. 779 - 666x = 511"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 779 - 666x = 511 $\n\nMove all terms to the left (standard form):\n$ -666x + 268 = 0 $\n\nIsolate the $x$ term:\n$ -666x = -268 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 3288
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. -6 - 109x - 116x^2 = -52"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -6 - 109x - 116x^2 = -52 $\n\nMove all terms to the left (standard form):\n$ -116x^2 + -109x + 46 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3289
} |
[
{
"role": "user",
"content": "solve: Prove that $f(x)=6x^2+9x+-1$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=6x^2+9x+-1$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 12x + 9 $\n$ f''(x) = 12 $\n\nSin... | {
"type": "optimization",
"seed": 1337,
"index": 3290
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. -749 - 983 = 931x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -749 - 983 = 931x $\n\nMove all terms to the left (standard form):\n$ -931x + -1732 = 0 $\n\nIsolate the $x$ term:\n$ -931x = 1732 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 3291
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-6&-8\\\\8&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -6 & -8 \\\\ 8 & -6 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3292
} |
[
{
"role": "user",
"content": "Compute the correct solution for 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": 3293
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. -x + 50x^2 - 166 = 36"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -x + 50x^2 - 166 = 36 $\n\nMove all terms to the left (standard form):\n$ 50x^2 + -1x + -202 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3294
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. -633 - 603 = -697x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -633 - 603 = -697x $\n\nMove all terms to the left (standard form):\n$ 697x + -1236 = 0 $\n\nIsolate the $x$ term:\n$ 697x = 1236 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 3295
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Evaluate: ((-194 + 860/20) * 11) + 10^5 - log_7(7) + (-366 mod 26) + round(-17/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-194 + 860/20) * 11) + 10^5 - log_7(7) + (-366 mod 26) + round(-17/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 3296
} |
[
{
"role": "user",
"content": "Please solve this math problem. 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) = 0 $\n\nThe general solutions... | {
"type": "trigonometry",
"seed": 1337,
"index": 3297
} |
[
{
"role": "user",
"content": "Find the final answer to the given 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$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 3298
} |
[
{
"role": "user",
"content": "solve: \n\n Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-7&4\\\\\\0&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}28\\\\\\-14\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-7&4\\\\\\0&-2\\end{pmatrix} ,\\quad b=\\begin... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3299
} |
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