messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Compute the determinant: $A=\\begin{pmatrix}-9&0\\\\0&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-9&0\\\\\\0&3\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1300
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Compute the determinant: $A=\\begin{pmatrix}-5&9\\\\0&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-5&9\\\\\\0&2\\end{pmatrix} $\n\nUse $\\d... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1301
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Evaluate: ((1 + 55/5) * 11) + 6^2 - log_7(343) + (28 mod 25) + ceil(152/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((1 + 55/5) * 11) + 6^2 - log_7(343) + (28 mod 25) + ceil(152/2) $\n\nCompute each compon... | {
"type": "arithmetic",
"seed": 1337,
"index": 1302
} |
[
{
"role": "user",
"content": "Work out the result of 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 $\n\nThe ge... | {
"type": "trigonometry",
"seed": 1337,
"index": 1303
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. -12x^2 - 95 + 191x = -67"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -12x^2 - 95 + 191x = -67 $\n\nMove all terms to the left (standard form):\n$ -12x^2 + 191x + -28 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1304
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. -594 - 636x = 342"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -594 - 636x = 342 $\n\nMove all terms to the left (standard form):\n$ -636x + -936 = 0 $\n\nIsolate the $x$ term:\n$ -636x = 936 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1305
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 22x^2 - 183x + 30 = -68"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 22x^2 - 183x + 30 = -68 $\n\nMove all terms to the left (standard form):\n$ 22x^2 + -183x + 98 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1306
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Prove that $(\\mathbb{Z}_25, +)$ is a group under addition modulo 25."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_25=\\{0,1,\\dots,24\\}$ with operation $+$ modulo $25$.\n\n**Closure:** If $a,b\\in\\mathbb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1307
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Evaluate: ((192 + -189/9) * 12) + 9^4 - log_2(2) + (-25 mod 13) + floor(49/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((192 + -189/9) * 12) + 9^4 - log_2(2) + (-25 mod 13) + floor(49/2) $\n\nCompute each component:\n$ -189/... | {
"type": "arithmetic",
"seed": 1337,
"index": 1308
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 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 $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1309
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. 10 + 15 - 137x^2 = 167x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10 + 15 - 137x^2 = 167x $\n\nMove all terms to the left (standard form):\n$ -137x^2 + -167x + 25 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1310
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Find the modular inverse of 5 modulo 6, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{6}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees in... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1311
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. -27 - 87 - 196x^2 = -121x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -27 - 87 - 196x^2 = -121x $\n\nMove all terms to the left (standard form):\n$ -196x^2 + 121x + -114 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1312
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. -36x + 74 - 144 = 42x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -36x + 74 - 144 = 42x^2 $\n\nMove all terms to the left (standard form):\n$ -42x^2 + -36x + -70 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1313
} |
[
{
"role": "user",
"content": "Please calculate this equation. Compute the indefinite integral: $\\int (-1x + 7)\\sin(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-1x + 7)\\sin(2x)\\,dx $\n\nUse standard antiderivatives (and integration by parts if ... | {
"type": "calculus",
"seed": 1337,
"index": 1314
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. 50x^2 + 180 + 96 = -62x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 50x^2 + 180 + 96 = -62x $\n\nMove all terms to the left (standard form):\n$ 50x^2 + 62x + 276 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1315
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}8&-5\\\\\\8&4\\end{pmatrix},\\quad b=\\begin{pmatrix}28\\\\\\64\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}8&-5\\\\\\8&4\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1316
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. 26 + 87x^2 - 158 = -139x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 26 + 87x^2 - 158 = -139x $\n\nMove all terms to the left (standard form):\n$ 87x^2 + 139x + -132 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1317
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 1318
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. 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 $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1319
} |
[
{
"role": "user",
"content": "Please calculate this equation. 23 + 108x - 14 = 95x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 23 + 108x - 14 = 95x^2 $\n\nMove all terms to the left (standard form):\n$ -95x^2 + 108x + 9 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1320
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. -40x^2 + 10x + 65 = -166"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -40x^2 + 10x + 65 = -166 $\n\nMove all terms to the left (standard form):\n$ -40x^2 + 10x + 231 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1321
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. - - 12x - 52 = -188x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ - - 12x - 52 = -188x^2 $\n\nMove all terms to the left (standard form):\n$ 188x^2 + -12x + -52 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1322
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. -114 + 16x = 350"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -114 + 16x = 350 $\n\nMove all terms to the left (standard form):\n$ 16x + -464 = 0 $\n\nIsolate the $x$ term:\n$ 16x = 464 $\n\nDivide both sides by th... | {
"type": "linear_equation",
"seed": 1337,
"index": 1323
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Compute the indefinite integral: $\\int 9e^{-2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 9e^{-2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if n... | {
"type": "calculus",
"seed": 1337,
"index": 1324
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. 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": 1325
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Compute $(-175+-11) \\bmod 18$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-175+-11) \\bmod 18 $\n\nUse the rule that addition is compatible with reduction mo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1326
} |
[
{
"role": "user",
"content": "Please work out this equation. Compute the determinant: $A=\\begin{pmatrix}-1&5\\\\-5&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-1&5\\\\\\-5&2\\end{pmatrix} $\n\nUse $\\det(A)=ad... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1327
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Find the modular inverse of 9 modulo 31, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $9\\cdot a^{-1} \\equiv 1 \\pmod{31}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1328
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, henc... | {
"type": "optimization",
"seed": 1337,
"index": 1329
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Compute $(36+80) \\bmod 20$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (36+80) \\bmod 20 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\n... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1330
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Differentiate with respect to $x$: $f(x) = 4x^3 + 0x^2 + 4x + 3$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4x^3 + 0x^2 + 4x + 3 $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{12... | {
"type": "calculus",
"seed": 1337,
"index": 1331
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n -936 + 556x = 14"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -936 + 556x = 14 $\n\nMove all terms to the left (standard form):\n$ 556x + -950 = 0 $\n\nIsolate the $x$ term:\n$ 556x = 950 $\n\nD... | {
"type": "linear_equation",
"seed": 1337,
"index": 1332
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Compute the indefinite integral: $\\int -1\\sin(3x) + -9\\cos(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -1\\sin(3x) + -9\\cos(5x)\\,dx $\n\nUse standard antiderivatives... | {
"type": "calculus",
"seed": 1337,
"index": 1333
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Evaluate: ((97 + -1034/22) * 20) + 4^2 - log_3(81) + (485 mod 29) + floor(-127/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((97 + -1034/22) * 20) + 4^2 - log_3(81) + (485 mod 29) + floor(-127/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1334
} |
[
{
"role": "user",
"content": "Solve the following math equation. Prove that $f(x)=4x^2+0x+6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+0x+6$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 8x + 0 $... | {
"type": "optimization",
"seed": 1337,
"index": 1335
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Differentiate with respect to $x$: $f(x) = -2e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -2e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-2e^{1x}} $"
... | {
"type": "calculus",
"seed": 1337,
"index": 1336
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Prove that $f(x)=6x^2+8x+6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=6x^2+8x+6$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 1... | {
"type": "optimization",
"seed": 1337,
"index": 1337
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: -980x - 212 = -965"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -980x - 212 = -965 $\n\nMove all terms to the left (standard form):\n$ -980x + 753 = 0 $\n\nIsolate the $x$ term:\n$ -980x = -753 $\n\nDivide both sides by the coefficie... | {
"type": "linear_equation",
"seed": 1337,
"index": 1338
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Prove that $f(x)=2x^2+8x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+8x+0$.\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": 1339
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Evaluate: ((49 + -184/4) * 2) + 3^3 - log_10(10) + (-23 mod 26) + floor(115/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((49 + -184/4) * 2) + 3^3 - log_10(10) + (-23 mod 26) + floor(115/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 1340
} |
[
{
"role": "user",
"content": "Solve the following math equation. Prove that $f(x,y)=\\frac12(7x^2+1y^2)+1x+-5y+-10$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+1y^2)+1x+-5y+-10 $\n\n$ \\frac{\\partial^2 f}{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 1341
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. -571 - 941 = -648x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -571 - 941 = -648x $\n\nMove all terms to the left (standard form):\n$ 648x + -1512 = 0 $\n\nIsolate the $x$ term:\n$ 648x = 1512 $... | {
"type": "linear_equation",
"seed": 1337,
"index": 1342
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Evaluate: ((81 + 168/7) * 12) + 7^4 - log_6(36) + (52 mod 8) + ceil(12/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((81 + 168/7) * 12) + 7^4 - log_6(36) + (52 mod 8) + ceil(12/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 1343
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Compute $(132+142) \\bmod 9$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (132+142) \\bmod 9 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1344
} |
[
{
"role": "user",
"content": "Can you compute this equation? Solve for $x$ (in radians): sin(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(\\frac{1}{2}... | {
"type": "trigonometry",
"seed": 1337,
"index": 1345
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 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": 1346
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 1347
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Solve for $x$ (in radians): tan(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(\\frac{1}{2}... | {
"type": "trigonometry",
"seed": 1337,
"index": 1348
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Evaluate: ((16 + -276/6) * 16) + 4^5 - log_8(8) + (-392 mod 17) + floor(-199/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((16 + -276/6) * 16) + 4^5 - log_8(8) + (-392 mod 17) + floor(-199/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 1349
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Evaluate: ((16 + 264/11) * 13) + 8^4 - log_2(4) + (32 mod 19) + ceil(-124/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((16 + 264/11) * 13) + 8^4 - log_2(4) + (32 mod 19) + ceil(-124/2) $\n\nCompute each compo... | {
"type": "arithmetic",
"seed": 1337,
"index": 1350
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. 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 $\n\... | {
"type": "trigonometry",
"seed": 1337,
"index": 1351
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. -760 + 407 = -27x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -760 + 407 = -27x $\n\nMove all terms to the left (standard form):\n$ 27x + -353 = 0 $\n\nIsolate the $x$ term:\n$ 27x = 353 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 1352
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Differentiate with respect to $x$: $f(x) = 2x^3 + -7x^2 + 3x + 15$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2x^3 + -7x^2 + 3x + 15 $\n\nApply the standard differentiation rules:\n$ f'(x) = ... | {
"type": "calculus",
"seed": 1337,
"index": 1353
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Evaluate: ((81 + -434/14) * 3) + 9^5 - log_10(1000) + (416 mod 22) + round(-144/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((81 + -434/14) * 3) + 9^5 - log_10(1000) + (416 mod 22) + round(-144/... | {
"type": "arithmetic",
"seed": 1337,
"index": 1354
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. -608 - 212 = -761x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -608 - 212 = -761x $\n\nMove all terms to the left (standard form):\n$ 761x + -820 = 0 $\n\nIsolate the $x$ term:\n$ 761x = 820 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 1355
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Prove that $(\\mathbb{Z}_10, +)$ is a group under addition modulo 10."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_10=\\{0,1,\\dots,9\\}$ with operation $+$ modulo $10$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1356
} |
[
{
"role": "user",
"content": "solve: Compute the determinant: $A=\\begin{pmatrix}-4&4\\\\6&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&4\\\\\\6&3\\end{pmatrix} $\n\nUse $\\det(A)=ad-bc$: \n$ \\det(A) = (-4)... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1357
} |
[
{
"role": "user",
"content": "Please calculate this equation. 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 $a,b\\in\\mathbb{Z}_n$, then $(a+... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1358
} |
[
{
"role": "user",
"content": "Resolve the equation provided. -19 - 111x^2 - 133x = -149"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -19 - 111x^2 - 133x = -149 $\n\nMove all terms to the left (standard form):\n$ -111x^2 + -133x + 130 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1359
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Evaluate: ((-13 + 230/23) * 8) + 2^3 - log_5(125) + (469 mod 21) + ceil(189/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-13 + 230/23) * 8) + 2^3 - log_5(125) + (469 mod 21) + ceil(189/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 1360
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Differentiate with respect to $x$: $f(x) = -1\\sin(7x) + 1\\cos(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1\\sin(7x) + 1\\cos(4x) $\n\nApply the standard differentiation rules:\n$ f'(x) = ... | {
"type": "calculus",
"seed": 1337,
"index": 1361
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Prove that $f(x,y)=\\frac12(3x^2+4y^2)+-6x+1y+3$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+4y^2)+-6x+1y+3 $\n\n$ \\frac{\\partial^2 f}{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 1362
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 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$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 1363
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Differentiate with respect to $x$: $f(x) = \\ln(7x + -7)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(7x + -7) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac... | {
"type": "calculus",
"seed": 1337,
"index": 1364
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. -30 - 6x^2 + 179x = 97"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -30 - 6x^2 + 179x = 97 $\n\nMove all terms to the left (standard form):\n$ -6x^2 + 179x + -127 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1365
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Compute $(-79+119) \\bmod 5$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-79+119) \\bmod 5 $\n\nUse the rule that addition is compatible with reduction mod... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1366
} |
[
{
"role": "user",
"content": "Please solve this math problem. Find $A^{-1}$ for $A=\\begin{pmatrix}2&8\\\\-6&6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 2 & 8 \\\\ -6 & 6 \\end{pmatrix} $\n\nCompute the determinant: ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1367
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Differentiate with respect to $x$: $f(x) = \\ln(8x + 3)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(8x + 3) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{8... | {
"type": "calculus",
"seed": 1337,
"index": 1368
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Prove that $(\\mathbb{Z}_28, +)$ is a group under addition modulo 28."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_28=\\{0,1,\\dots,27\\}$ with operation $+$ modulo $28$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1369
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Find the modular inverse of 10 modulo 11, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $10\\cdot a^{-1} \\equiv 1 \\pmod{11}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarant... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1370
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Prove that $(\\mathbb{Z}_4, +)$ is a group under addition modulo 4."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_4=\\{0,1,\\dots,3\\}$ with operation $+$ modulo $4$.\n\n**Closure:** If $a,b\\in\\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1371
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 799x + 936 = 940"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 799x + 936 = 940 $\n\nMove all terms to the left (standard form):\n$ 799x + -4 = 0 $\n\nIsolate the $x$ term:\n$ 799x = 4 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 1372
} |
[
{
"role": "user",
"content": "Please solve this math problem. Compute $(-43+103) \\bmod 17$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-43+103) \\bmod 17 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1373
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Evaluate: ((-3 + -300/15) * 20) + 5^5 - log_5(625) + (-409 mod 9) + ceil(156/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-3 + -300/15) * 20) + 5^5 - log_5(625) + (-409 mod 9) + ceil(156/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 1374
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. 507 + 211x = 410"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 507 + 211x = 410 $\n\nMove all terms to the left (standard form):\n$ 211x + 97 = 0 $\n\nIsolate the $x$ term:\n$ 211x = -97 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 1375
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. -23 + 124x^2 - 177x = -128"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -23 + 124x^2 - 177x = -128 $\n\nMove all terms to the left (standard form):\n$ 124x^2 + -177x + 105 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1376
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 748 + 636 = 121x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 748 + 636 = 121x $\n\nMove all terms to the left (standard form):\n$ -121x + 1384 = 0 $\n\nIsolate the $x$ term:\n$ -121x = -1384 $\n\nDivide both sides by ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1377
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Evaluate: ((-6 + -23/23) * 3) + 9^3 - log_7(2401) + (229 mod 15) + round(95/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-6 + -23/23) * 3) + 9^3 - log_7(2401) + (229 mod 15) + round(95/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 1378
} |
[
{
"role": "user",
"content": "Evaluate and solve the given 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 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 1379
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Evaluate: ((-60 + 172/4) * 13) + 6^5 - log_3(3) + (-452 mod 18) + floor(-52/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-60 + 172/4) * 13) + 6^5 - log_3(3) + (-452 mod 18) + floor(-52/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 1380
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Differentiate with respect to $x$: $f(x) = 4\\sin(2x) + 9\\cos(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4\\sin(2x) + 9\\cos(4x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxe... | {
"type": "calculus",
"seed": 1337,
"index": 1381
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Compute the determinant: $A=\\begin{pmatrix}-1&1\\\\-3&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-1&1\\\\\\-3&-8\\end{pmatrix... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1382
} |
[
{
"role": "user",
"content": "Solve the following math equation. 320x + 683 = -799"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 320x + 683 = -799 $\n\nMove all terms to the left (standard form):\n$ 320x + 1482 = 0 $\n\nIsolate the $x$ term:\n$ 320x = -1482 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 1383
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\par... | {
"type": "optimization",
"seed": 1337,
"index": 1384
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. 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$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 1385
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 29x^2 - 34 - 163 = -17x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 29x^2 - 34 - 163 = -17x $\n\nMove all terms to the left (standard form):\n$ 29x^2 + 17x + -197 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1386
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Differentiate with respect to $x$: $f(x) = 2\\sin(6x) + -1\\cos(9x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2\\sin(6x) + -1\\cos(9x) $\n\nApply the standard differentiation ru... | {
"type": "calculus",
"seed": 1337,
"index": 1387
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. 36 - 34x^2 - 7 = 187x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 36 - 34x^2 - 7 = 187x $\n\nMove all terms to the left (standard form):\n$ -34x^2 + -187x + 29 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1388
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Evaluate: ((18 + -90/9) * 3) + 9^5 - log_4(64) + (-310 mod 26) + round(56/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((18 + -90/9) * 3) + 9^5 - log_4(64) + (-310 mod 26) + round(56/2) $\n\nCompute each comp... | {
"type": "arithmetic",
"seed": 1337,
"index": 1389
} |
[
{
"role": "user",
"content": "Please work out this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&3&-4\\\\\\-2&-3&2\\\\\\0&1&1\\end{pmatrix},\\quad b=\\begin{pmatrix}-6\\\\\\10\\\\\\-4\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by Gau... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1390
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 24x^2 + 95 - 128x = -200"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 24x^2 + 95 - 128x = -200 $\n\nMove all terms to the left (standard form):\n$ 24x^2 + -128x + 295 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1391
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. 15 - 93x + 95 = -18x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 15 - 93x + 95 = -18x^2 $\n\nMove all terms to the left (standard form):\n$ 18x^2 + -93x + 110 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1392
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 894 + 850x = 51"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 894 + 850x = 51 $\n\nMove all terms to the left (standard form):\n$ 850x + 843 = 0 $\n\nIsolate the $x$ term:\n$ 850x = -843 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 1393
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Compute the determinant: $A=\\begin{pmatrix}6&0\\\\9&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}6&0\\\\\\9&3\\end{pmatrix} $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1394
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 525 + 194 = 556x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 525 + 194 = 556x $\n\nMove all terms to the left (standard form):\n$ -556x + 719 = 0 $\n\nIsolate the $x$ term:\n$ -556x = -719 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1395
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. -97x + 575 = 119"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -97x + 575 = 119 $\n\nMove all terms to the left (standard form):\n$ -97x + 456 = 0 $\n\nIsolate the $x$ term:\n$ -97x = -456 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 1396
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Compute the indefinite integral: $\\int \\ln(6x + 5)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(6x + 5)\\,dx $\n\nUse standard antiderivatives (and integration by parts i... | {
"type": "calculus",
"seed": 1337,
"index": 1397
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Find $A^{-1}$ for $A=\\begin{pmatrix}-9&-9\\\\7&0\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -9 & -9 \\\\ 7 & 0 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1398
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Differentiate with respect to $x$: $f(x) = 8\\sin(2x) + -3\\cos(8x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 8\\sin(2x) + -3\\cos(8x) $\n\nApply the standard differentiation rules:\n$ f'(x)... | {
"type": "calculus",
"seed": 1337,
"index": 1399
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.