messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Find the numerical solution to 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\nTh... | {
"type": "trigonometry",
"seed": 1337,
"index": 5200
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Prove that $f(x)=5x^2+-3x+-8$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+-3x+-8$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) =... | {
"type": "optimization",
"seed": 1337,
"index": 5201
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Evaluate: ((195 + -85/17) * 18) + 4^4 - log_10(10) + (-225 mod 15) + floor(-124/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((195 + -85/17) * 18) + 4^4 - log_10(10) + (-225 mod 15) + floor(-124/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 5202
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 303 - 829x = -197"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 303 - 829x = -197 $\n\nMove all terms to the left (standard form):\n$ -829x + 500 = 0 $\n\nIsolate the $x$ term:\n$ -829x = -500 $\... | {
"type": "linear_equation",
"seed": 1337,
"index": 5203
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}2&4\\\\\\-3&1\\end{pmatrix},\\quad b=\\begin{pmatrix}-26\\\\\\-24\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}2&4\\\\\\-3&1\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5204
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&-4&-2\\\\\\-5&1&5\\\\\\3&1&0\\end{pmatrix},\\quad b=\\begin{pmatrix}1\\\\\\-11\\\\\\2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "So... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5205
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Evaluate: ((-48 + -80/4) * 11) + 10^4 - log_9(729) + (76 mod 18) + ceil(-21/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-48 + -80/4) * 11) + 10^4 - log_9(729) + (76 mod 18) + ceil(-21/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 5206
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 53 - 8 = -135x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 53 - 8 = -135x $\n\nMove all terms to the left (standard form):\n$ 135x + 45 = 0 $\n\nIsolate the $x$ term:\n$ 135x = -45 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 5207
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Differentiate with respect to $x$: $f(x) = -9\\sin(4x) + -8\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -9\\sin(4x) + -8\\cos(7x) $\n\nApply the standard differentiation rule... | {
"type": "calculus",
"seed": 1337,
"index": 5208
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. 25 - 8x^2 + 4 = 52x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 25 - 8x^2 + 4 = 52x $\n\nMove all terms to the left (standard form):\n$ -8x^2 + -52x + 29 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5209
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Differentiate with respect to $x$: $f(x) = -6e^{-2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6e^{-2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{12e^{-2x}}... | {
"type": "calculus",
"seed": 1337,
"index": 5210
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Differentiate with respect to $x$: $f(x) = 1e^{3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1e^{3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{3e^{3x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 5211
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Prove that $(\\mathbb{Z}_7, +)$ is a group under addition modulo 7."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_7=\\{0,1,\\dots,6\\}$ with operation $+$ modulo $7$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, then $(a+... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5212
} |
[
{
"role": "user",
"content": "Please calculate 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(\\frac{1}{2... | {
"type": "trigonometry",
"seed": 1337,
"index": 5213
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Evaluate: ((-103 + -44/22) * 10) + 5^4 - log_6(1296) + (197 mod 28) + floor(53/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-103 + -44/22) * 10) + 5^4 - log_6(1296) + (197 mod 28) + floor(53/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 5214
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Evaluate: ((46 + -552/12) * 6) + 9^5 - log_9(729) + (-343 mod 23) + floor(115/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((46 + -552/12) * 6) + 9^5 - log_9(729) + (-343 mod 23) + floor(115/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 5215
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. -168x + 897 = -547"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -168x + 897 = -547 $\n\nMove all terms to the left (standard form):\n$ -168x + 1444 = 0 $\n\nIsolate the $x$ term:\n$ -168x = -1444 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 5216
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Prove that $f(x)=9x^2+3x+-8$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+3x+-8$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 18x + 3 $\n$ f''(x) = 18 ... | {
"type": "optimization",
"seed": 1337,
"index": 5217
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Evaluate: ((-89 + 38/2) * 5) + 10^5 - log_5(5) + (185 mod 15) + ceil(-187/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-89 + 38/2) * 5) + 10^5 - log_5(5) + (185 mod 15) + ceil(-187/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 5218
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-3&5&0\\\\\\5&5&-1\\\\\\-3&-5&1\\end{pmatrix},\\quad b=\\begin{pmatrix}20\\\\\\17\\\\\\-17\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $A... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5219
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 28 - 194x^2 + 111x = 149"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 28 - 194x^2 + 111x = 149 $\n\nMove all terms to the left (standard form):\n$ -194x^2 + 111x + -121 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5220
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. 11x^2 + 196 - 156 = -31x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 11x^2 + 196 - 156 = -31x $\n\nMove all terms to the left (standard form):\n$ 11x^2 + 31x + 40 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5221
} |
[
{
"role": "user",
"content": "Find the correct solution for 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$... | {
"type": "trigonometry",
"seed": 1337,
"index": 5222
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Evaluate: ((38 + -360/24) * 7) + 7^2 - log_5(3125) + (298 mod 10) + ceil(-153/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((38 + -360/24) * 7) + 7^2 - log_5(3125) + (298 mod 10) + ceil(-153/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 5223
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Evaluate: ((118 + -248/8) * 6) + 8^3 - log_10(1000000) + (-489 mod 20) + round(170/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((118 + -248/8) * 6) + 8^3 - log_10(1000000) + (-489 mod 20) + round(... | {
"type": "arithmetic",
"seed": 1337,
"index": 5224
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. 19x^2 - 67 + 177 = -28x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 19x^2 - 67 + 177 = -28x $\n\nMove all terms to the left (standard form):\n$ 19x^2 + 28x + 110 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5225
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Evaluate: ((66 + 294/14) * 9) + 6^4 - log_2(16) + (-114 mod 30) + ceil(-144/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((66 + 294/14) * 9) + 6^4 - log_2(16) + (-114 mod 30) + ceil(-144/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 5226
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Compute the indefinite integral: $\\int (-4x + -7)e^{1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-4x + -7)e^{1x}\\,dx $\n\nUse standard antiderivatives (and integration by pa... | {
"type": "calculus",
"seed": 1337,
"index": 5227
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Evaluate: ((-172 + 10/5) * 17) + 4^2 - log_4(256) + (142 mod 30) + floor(195/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-172 + 10/5) * 17) + 4^2 - log_4(256) + (142 mod 30) + floor(195/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 5228
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. -520 + 499x = -758"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -520 + 499x = -758 $\n\nMove all terms to the left (standard form):\n$ 499x + 238 = 0 $\n\nIsolate the $x$ term:\n$ 499x = -238 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 5229
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. -35x^2 + 142x - 51 = -160"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -35x^2 + 142x - 51 = -160 $\n\nMove all terms to the left (standard form):\n$ -35x^2 + 142x + 109 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5230
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Evaluate: ((-150 + 164/4) * 1) + 4^4 - log_7(117649) + (347 mod 25) + floor(-5/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-150 + 164/4) * 1) + 4^4 - log_7(117649) + (347 mod 25) + floor(-5/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 5231
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Find the modular inverse of 7 modulo 18, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{18}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarante... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5232
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Evaluate: ((73 + -160/10) * 15) + 2^2 - log_10(100) + (371 mod 24) + floor(26/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((73 + -160/10) * 15) + 2^2 - log_10(100) + (371 mod 24) + floor(26/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 5233
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. 11 - 150x^2 + 184x = -124"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 11 - 150x^2 + 184x = -124 $\n\nMove all terms to the left (standard form):\n$ -150x^2 + 184x + 135 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5234
} |
[
{
"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": 5235
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. 396 + 470x = -941"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 396 + 470x = -941 $\n\nMove all terms to the left (standard form):\n$ 470x + 1337 = 0 $\n\nIsolate the $x$ term:\n$ 470x = -1337 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 5236
} |
[
{
"role": "user",
"content": "Solve the equation shown below. -232x - 759 = -8"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -232x - 759 = -8 $\n\nMove all terms to the left (standard form):\n$ -232x + -751 = 0 $\n\nIsolate the $x$ term:\n$ -232x = 751 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 5237
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-4&-4&-3\\\\\\1&4&3\\\\\\-1&3&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}7\\\\\\-4\\\\\\4\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5238
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. 95 + 172 = 346x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 95 + 172 = 346x $\n\nMove all terms to the left (standard form):\n$ -346x + 267 = 0 $\n\nIsolate the $x$ term:\n$ -346x = -267 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 5239
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. -293 - 812x = -23"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -293 - 812x = -23 $\n\nMove all terms to the left (standard form):\n$ -812x + -270 = 0 $\n\nIsolate the $x$ term:\n$ -812x = 270 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 5240
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Prove that $f(x)=1x^2+1x+-10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+1x+-10$.\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": 5241
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&-5&4\\\\\\3&4&3\\\\\\3&5&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}15\\\\\\-2\\\\\\3\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5242
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 810x + 214 = 176"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 810x + 214 = 176 $\n\nMove all terms to the left (standard form):\n$ 810x + 38 = 0 $\n\nIsolate the $x$ term:\n$ 810x = -38 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 5243
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. 179x - 498 = 596"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 179x - 498 = 596 $\n\nMove all terms to the left (standard form):\n$ 179x + -1094 = 0 $\n\nIsolate the $x$ term:\n$ 179x = 1094 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 5244
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Evaluate: ((22 + 72/2) * 11) + 8^5 - log_4(256) + (15 mod 21) + round(-51/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((22 + 72/2) * 11) + 8^5 - log_4(256) + (15 mod 21) + round(-51/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 5245
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Compute the indefinite integral: $\\int 5\\sin(8x) + 7\\cos(8x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 5\\sin(8x) + 7\\cos(8x)\\,dx $\n\nUse standard antiderivatives (... | {
"type": "calculus",
"seed": 1337,
"index": 5246
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Evaluate: ((102 + 164/4) * 3) + 2^3 - log_9(729) + (-421 mod 10) + ceil(24/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((102 + 164/4) * 3) + 2^3 - log_9(729) + (-421 mod 10) + ceil(24/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 5247
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. 35x + 99 + 88x^2 = 7"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 35x + 99 + 88x^2 = 7 $\n\nMove all terms to the left (standard form):\n$ 88x^2 + 35x + 92 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5248
} |
[
{
"role": "user",
"content": "solve: \n\n Find $A^{-1}$ for $A=\\begin{pmatrix}8&-9\\\\-5&5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 8 & -9 \\\\ -5 & 5 \\end{pmatrix} $\n\nCompute the determinant: $\\det(A)=ad-bc$.\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5249
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Prove that $f(x,y)=\\frac12(9x^2+5y^2)+-2x+4y+-8$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+5y^2)+-2x+4y+-8 $\n\n$ \\frac{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 5250
} |
[
{
"role": "user",
"content": "solve: \n\n Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-3&4&-3\\\\\\4&-1&-3\\\\\\-2&-1&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}-2\\\\\\8\\\\\\4\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by Gaussian elimination... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5251
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. -18x^2 - 15 + 190 = 142x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -18x^2 - 15 + 190 = 142x $\n\nMove all terms to the left (standard form):\n$ -18x^2 + -142x + 175 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5252
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 11 + 96x^2 - 197x = -114"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 11 + 96x^2 - 197x = -114 $\n\nMove all terms to the left (standard form):\n$ 96x^2 + -197x + 125 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5253
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 600 + 329 = -601x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 600 + 329 = -601x $\n\nMove all terms to the left (standard form):\n$ 601x + 929 = 0 $\n\nIsolate the $x$ term:\n$ 601x = -929 $\n\nDivide both sides by... | {
"type": "linear_equation",
"seed": 1337,
"index": 5254
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Compute the indefinite integral: $\\int (6x + -3)\\sin(3x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (6x + -3)\\sin(3x)\\,dx $\n\nUse standard antiderivatives (and integration by parts i... | {
"type": "calculus",
"seed": 1337,
"index": 5255
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Evaluate: ((-105 + -700/20) * 20) + 12^5 - log_6(36) + (106 mod 25) + floor(-102/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-105 + -700/20) * 20) + 12^5 - log_6(36) + (106 mod 25) + floor(-102/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 5256
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. 858x + 395 = 766"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 858x + 395 = 766 $\n\nMove all terms to the left (standard form):\n$ 858x + -371 = 0 $\n\nIsolate the $x$ term:\n$ 858x = 371 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 5257
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? 40x^2 - 178 - 196x = -160"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 40x^2 - 178 - 196x = -160 $\n\nMove all terms to the left (standard form):\n$ 40x^2 + -196x + -18 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5258
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}0&9\\\\\\-5&-8\\end{pmatrix},\\quad b=\\begin{pmatrix}72\\\\\\-94\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}0&9\\\\\\-5&-8\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5259
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Find the modular inverse of 3 modulo 31, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $3\\cdot a^{-1} \\equiv 1 \\pmod{31}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integer... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5260
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Differentiate with respect to $x$: $f(x) = (1x + -4)e^{2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (1x + -4)e^{2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{1... | {
"type": "calculus",
"seed": 1337,
"index": 5261
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. -43 - 104x - 128x^2 = 194"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -43 - 104x - 128x^2 = 194 $\n\nMove all terms to the left (standard form):\n$ -128x^2 + -104x + -237 = 0 $\n\nApply the qua... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5262
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. 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 by parts if need... | {
"type": "calculus",
"seed": 1337,
"index": 5263
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Differentiate with respect to $x$: $f(x) = 4x^3 + -2x^2 + -9x + 3$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4x^3 + -2x^2 + -9x + 3 $\n\nApply the standard differentiation rules:\n$ f'(x) = \... | {
"type": "calculus",
"seed": 1337,
"index": 5264
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Evaluate: ((-2 + 483/23) * 5) + 8^2 - log_5(25) + (118 mod 5) + ceil(-187/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-2 + 483/23) * 5) + 8^2 - log_5(25) + (118 mod 5) + ceil(-187/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 5265
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}3&7\\\\\\1&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}31\\\\\\3\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}3&7\\\\\\1&-5\\end{pm... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5266
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((101 + 1034/22) * 10) + 3^5 - log_4(4096) + (-327 mod 16) + ceil(45/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((101 + 1034/22) * 10) + 3^5 - log_4(4096) + (-327 mod 16) + ceil(45/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 5267
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Evaluate: ((2 + -437/23) * 17) + 3^4 - log_10(100000) + (-500 mod 9) + round(-7/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((2 + -437/23) * 17) + 3^4 - log_10(100000) + (-500 mod 9) + round(-7/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 5268
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. -290 - 769 = -689x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -290 - 769 = -689x $\n\nMove all terms to the left (standard form):\n$ 689x + -1059 = 0 $\n\nIsolate the $x$ term:\n$ 689x = 1059 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 5269
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Compute the indefinite integral: $\\int (-1x + 9)\\sin(1x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-1x + 9)\\sin(1x)\\,dx $\n\nUse standard antiderivatives (and integra... | {
"type": "calculus",
"seed": 1337,
"index": 5270
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Compute the indefinite integral: $\\int 2e^{-4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 2e^{-4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if need... | {
"type": "calculus",
"seed": 1337,
"index": 5271
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Prove that $f(x,y)=\\frac12(4x^2+5y^2)+2x+5y+-2$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+5y^2)+2x+5y+-2 $\n\n$ \\frac{\\partia... | {
"type": "optimization",
"seed": 1337,
"index": 5272
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. 19 + 85x + 86 = 54x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 19 + 85x + 86 = 54x^2 $\n\nMove all terms to the left (standard form):\n$ -54x^2 + 85x + 105 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5273
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. 350x + 273 = 350"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 350x + 273 = 350 $\n\nMove all terms to the left (standard form):\n$ 350x + -77 = 0 $\n\nIsolate the $x$ term:\n$ 350x = 77 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 5274
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. -232x - 599 = -8"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -232x - 599 = -8 $\n\nMove all terms to the left (standard form):\n$ -232x + -591 = 0 $\n\nIsolate the $x$ term:\n$ -232x = 591 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 5275
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Differentiate with respect to $x$: $f(x) = (-3x + 4)\\sin(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-3x + 4)\\sin(4x) $\n\nApply the standard differentiation rules:\n$ f'(x... | {
"type": "calculus",
"seed": 1337,
"index": 5276
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Prove that $(\\mathbb{Z}_16, +)$ is a group under addition modulo 16."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_16=\\{0,1,\\dots,15\\}$ with operation $+$ modulo $16$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5277
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 3x^2 - 84 + 193 = 122x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 3x^2 - 84 + 193 = 122x $\n\nMove all terms to the left (standard form):\n$ 3x^2 + -122x + 109 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5278
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. 579 - 838x = 210"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 579 - 838x = 210 $\n\nMove all terms to the left (standard form):\n$ -838x + 369 = 0 $\n\nIsolate the $x$ term:\n$ -838x = -369 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 5279
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Prove that $(\\mathbb{Z}_26, +)$ is a group under addition modulo 26."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_26=\\{0,1,\\dots,25\\}$ with operation $+$ modulo $26$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, t... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5280
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((144 + -690/23) * 1) + 8^2 - log_7(49) + (434 mod 23) + ceil(185/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((144 + -690/23) * 1) + 8^2 - log_7(49) + (434 mod 23) + ceil(185/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 5281
} |
[
{
"role": "user",
"content": "Can you find the solution to 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... | {
"type": "optimization",
"seed": 1337,
"index": 5282
} |
[
{
"role": "user",
"content": "Can you compute this equation? Compute $(-38+97) \\bmod 8$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-38+97) \\bmod 8 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\n$ (a... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5283
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Prove that $f(x)=4x^2+-9x+10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+-9x+10$.\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": 5284
} |
[
{
"role": "user",
"content": "Please compute the answer to 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... | {
"type": "optimization",
"seed": 1337,
"index": 5285
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Differentiate with respect to $x$: $f(x) = \\ln(1x + 5)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(1x + 5) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{1... | {
"type": "calculus",
"seed": 1337,
"index": 5286
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}7&6\\\\\\-3&8\\end{pmatrix},\\quad b=\\begin{pmatrix}4\\\\\\-44\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}7&6\\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5287
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Differentiate with respect to $x$: $f(x) = -3\\sin(8x) + 4\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3\\sin(8x) + 4\\cos(7x) $\n\nApply the standard differentiation rules:\n... | {
"type": "calculus",
"seed": 1337,
"index": 5288
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&2&5\\\\\\1&0&3\\\\\\2&-1&5\\end{pmatrix},\\quad b=\\begin{pmatrix}-15\\\\\\-11\\\\\\-19\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5289
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Find $A^{-1}$ for $A=\\begin{pmatrix}-7&2\\\\5&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -7 & 2 \\\\ 5 & -8 \\end{pmatrix} $\n\nCompute the det... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5290
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((102 + 18/3) * 14) + 7^2 - log_2(16) + (-421 mod 10) + ceil(-62/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((102 + 18/3) * 14) + 7^2 - log_2(16) + (-421 mod 10) + ceil(-62/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 5291
} |
[
{
"role": "user",
"content": "solve -794x - 300 = 253"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -794x - 300 = 253 $\n\nMove all terms to the left (standard form):\n$ -794x + -553 = 0 $\n\nIsolate the $x$ term:\n$ -794x = 553 $\n\nDivide both sides by the coefficient of $x$:\... | {
"type": "linear_equation",
"seed": 1337,
"index": 5292
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. -29x + 38 - 188 = 110x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -29x + 38 - 188 = 110x^2 $\n\nMove all terms to the left (standard form):\n$ -110x^2 + -29x + -150 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5293
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Evaluate: ((-163 + -420/12) * 11) + 12^5 - log_9(6561) + (116 mod 29) + ceil(-83/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-163 + -420/12) * 11) + 12^5 - log_9(6561) + (116 mod 29) + ceil(-83/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 5294
} |
[
{
"role": "user",
"content": "Determine the result 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": 5295
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}6&-9\\\\5&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 6 & -9 \\\\ 5 & -8 \\end{pmatrix} $\n\nCompute the ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5296
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. -501x + 87 = -725"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -501x + 87 = -725 $\n\nMove all terms to the left (standard form):\n$ -501x + 812 = 0 $\n\nIsolate the $x$ term:\n$ -501x = -812 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 5297
} |
[
{
"role": "user",
"content": "Find the final answer to 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 $\n\nThe gene... | {
"type": "trigonometry",
"seed": 1337,
"index": 5298
} |
[
{
"role": "user",
"content": "Solve this equation accurately. -92 + 117 = -588x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -92 + 117 = -588x $\n\nMove all terms to the left (standard form):\n$ 588x + 25 = 0 $\n\nIsolate the $x$ term:\n$ 588x = -25 $\n\nDivide both sides by the... | {
"type": "linear_equation",
"seed": 1337,
"index": 5299
} |
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