messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Can you evaluate this math equation? 835 + 174x = 627"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 835 + 174x = 627 $\n\nMove all terms to the left (standard form):\n$ 174x + 208 = 0 $\n\nIsolate the $x$ term:\n$ 174x = -208 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 5300
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Solve for $x$ (in radians): cos(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arcc... | {
"type": "trigonometry",
"seed": 1337,
"index": 5301
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 5302
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Compute the determinant: $A=\\begin{pmatrix}-3&-6\\\\-1&5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-3&-6\\\\\\-1&5\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5303
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 327x + 253 = 202"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 327x + 253 = 202 $\n\nMove all terms to the left (standard form):\n$ 327x + 51 = 0 $\n\nIsolate the $x$ term:\n$ 327x = -51 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 5304
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? 19x^2 + 0 - 19 = 64x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 19x^2 + 0 - 19 = 64x $\n\nMove all terms to the left (standard form):\n$ 19x^2 + -64x + -19 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5305
} |
[
{
"role": "user",
"content": "Can you solve the equation below? 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 $\n\nThe general solutio... | {
"type": "trigonometry",
"seed": 1337,
"index": 5306
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. -923 - 109 = 876x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -923 - 109 = 876x $\n\nMove all terms to the left (standard form):\n$ -876x + -1032 = 0 $\n\nIsolate the $x$ term:\n$ -876x = 1032 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 5307
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 10x - 186x^2 - 129 = -105"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10x - 186x^2 - 129 = -105 $\n\nMove all terms to the left (standard form):\n$ -186x^2 + 10x + -24 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5308
} |
[
{
"role": "user",
"content": "Please calculate and resolve this 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": 5309
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Evaluate: ((-164 + 140/7) * 17) + 4^5 - log_3(729) + (-423 mod 28) + floor(175/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-164 + 140/7) * 17) + 4^5 - log_3(729) + (-423 mod 28) + floor(175/... | {
"type": "arithmetic",
"seed": 1337,
"index": 5310
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. 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$ \\al... | {
"type": "trigonometry",
"seed": 1337,
"index": 5311
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Evaluate: ((-65 + -1250/25) * 3) + 9^4 - log_9(6561) + (-229 mod 12) + ceil(48/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-65 + -1250/25) * 3) + 9^4 - log_9(6561) + (-229 mod 12) + ceil(48/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 5312
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Find the modular inverse of 5 modulo 17, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{17}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5313
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Evaluate: ((-59 + 141/3) * 5) + 3^4 - log_7(117649) + (61 mod 3) + floor(-41/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-59 + 141/3) * 5) + 3^4 - log_7(117649) + (61 mod 3) + floor(-41/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 5314
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Differentiate with respect to $x$: $f(x) = (5x + 2)\\sin(6x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (5x + 2)\\sin(6x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxe... | {
"type": "calculus",
"seed": 1337,
"index": 5315
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Evaluate: ((-123 + -481/13) * 8) + 11^5 - log_10(1000000) + (-282 mod 16) + round(34/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-123 + -481/13) * 8) + 11^5 - log_10(1000000) + (-282 mod 16) +... | {
"type": "arithmetic",
"seed": 1337,
"index": 5316
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Evaluate: ((-146 + -130/13) * 19) + 2^3 - log_8(32768) + (-339 mod 12) + round(138/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-146 + -130/13) * 19) + 2^3 - log_8(32768) + (-339 mod 12) + r... | {
"type": "arithmetic",
"seed": 1337,
"index": 5317
} |
[
{
"role": "user",
"content": "Determine the solution of the given 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": 5318
} |
[
{
"role": "user",
"content": "solve: \n\n 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$ \\alpha = \\arctan(\\frac{\\sqrt{3... | {
"type": "trigonometry",
"seed": 1337,
"index": 5319
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&5&-3\\\\\\-3&2&0\\\\\\-3&-3&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}-2\\\\\\14\\\\\\-22\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5320
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 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 $a,b\\in\\mathbb{Z}_n$, then $(a+... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5321
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Differentiate with respect to $x$: $f(x) = 3e^{4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3e^{4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{12e^{4x}} $"
... | {
"type": "calculus",
"seed": 1337,
"index": 5322
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 842x - 788 = 799"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 842x - 788 = 799 $\n\nMove all terms to the left (standard form):\n$ 842x + -1587 = 0 $\n\nIsolate the $x$ term:\n$ 842x = 1587 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 5323
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? 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... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5324
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Prove that $f(x)=6x^2+-9x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=6x^2+-9x+0$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'... | {
"type": "optimization",
"seed": 1337,
"index": 5325
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. -243 + 584x = 864"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -243 + 584x = 864 $\n\nMove all terms to the left (standard form):\n$ 584x + -1107 = 0 $\n\nIsolate the $x$ term:\n$ 584x = 1107 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 5326
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. 42x + 142 - 82 = -110x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 42x + 142 - 82 = -110x^2 $\n\nMove all terms to the left (standard form):\n$ 110x^2 + 42x + 60 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5327
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\... | {
"type": "trigonometry",
"seed": 1337,
"index": 5328
} |
[
{
"role": "user",
"content": "Please work out this equation. 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 $\n\nThe general solutions ... | {
"type": "trigonometry",
"seed": 1337,
"index": 5329
} |
[
{
"role": "user",
"content": "Please calculate this equation. x + 61 - 200 = -137x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ x + 61 - 200 = -137x^2 $\n\nMove all terms to the left (standard form):\n$ 137x^2 + 1x + -139 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5330
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Compute $(-151+-90) \\bmod 25$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-151+-90) \\bmod 25 $\n\nUse the rule that addition is compatible with reducti... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5331
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Compute the indefinite integral: $\\int 5x^3 + 2x^2 + -11x + -12\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 5x^3 + 2x^2 + -11x + -12\\,dx $\n\nUse standard antiderivatives (and integ... | {
"type": "calculus",
"seed": 1337,
"index": 5332
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Compute the indefinite integral: $\\int 6\\sin(5x) + 9\\cos(9x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 6\\sin(5x) + 9\\cos(9x)\\,dx $\n\nUse standard antiderivative... | {
"type": "calculus",
"seed": 1337,
"index": 5333
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Evaluate: ((188 + 675/15) * 15) + 10^3 - log_6(6) + (-381 mod 29) + floor(-29/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((188 + 675/15) * 15) + 10^3 - log_6(6) + (-381 mod 29) + floor(-29/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 5334
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((-149 + 192/12) * 20) + 7^4 - log_7(49) + (-480 mod 7) + ceil(192/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-149 + 192/12) * 20) + 7^4 - log_7(49) + (-480 mod 7) + ceil(192/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 5335
} |
[
{
"role": "user",
"content": "solve: 888 - 156x = -268"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 888 - 156x = -268 $\n\nMove all terms to the left (standard form):\n$ -156x + 1156 = 0 $\n\nIsolate the $x$ term:\n$ -156x = -1156 $\n\nDivide both sides by the coefficient of $x... | {
"type": "linear_equation",
"seed": 1337,
"index": 5336
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-3&-1\\\\\\-7&5\\end{pmatrix},\\quad b=\\begin{pmatrix}-1\\\\\\5\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-3&-1\\\\\\-7&... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5337
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Compute the indefinite integral: $\\int -6e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -6e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n... | {
"type": "calculus",
"seed": 1337,
"index": 5338
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. -12x + 98x^2 + 52 = -23"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -12x + 98x^2 + 52 = -23 $\n\nMove all terms to the left (standard form):\n$ 98x^2 + -12x + 75 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5339
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Evaluate: ((-164 + -352/22) * 13) + 8^4 - log_9(531441) + (305 mod 13) + ceil(166/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-164 + -352/22) * 13) + 8^4 - log_9(531441) + (305 mod 13) + ceil(166/... | {
"type": "arithmetic",
"seed": 1337,
"index": 5340
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. -387x - 397 = 766"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -387x - 397 = 766 $\n\nMove all terms to the left (standard form):\n$ -387x + -1163 = 0 $\n\nIsolate the $x$ term:\n$ -387x = 1163 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 5341
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Differentiate with respect to $x$: $f(x) = -1e^{-2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1e^{-2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{2e^{-2x}} $"
}... | {
"type": "calculus",
"seed": 1337,
"index": 5342
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Prove that $f(x)=1x^2+-6x+-2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+-6x+-2$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$... | {
"type": "optimization",
"seed": 1337,
"index": 5343
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((-120 + -172/4) * 15) + 4^2 - log_10(100) + (187 mod 2) + ceil(133/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-120 + -172/4) * 15) + 4^2 - log_10(100) + (187 mod 2) + ceil(133/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 5344
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Compute the indefinite integral: $\\int (-1x + 9)\\sin(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-1x + 9)\\sin(2x)\\,dx $\n\nUse standard antiderivatives (and integration by pa... | {
"type": "calculus",
"seed": 1337,
"index": 5345
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical 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} & \\... | {
"type": "optimization",
"seed": 1337,
"index": 5346
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Solve for $x$ (in radians): cos(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(-... | {
"type": "trigonometry",
"seed": 1337,
"index": 5347
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-3&5\\\\\\-8&7\\end{pmatrix},\\quad b=\\begin{pmatrix}51\\\\\\98\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-3&5\\\\\\-8&7\\end{pma... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5348
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. -420 + 215x = 805"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -420 + 215x = 805 $\n\nMove all terms to the left (standard form):\n$ 215x + -1225 = 0 $\n\nIsolate the $x$ term:\n$ 215x = 1225 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 5349
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Differentiate with respect to $x$: $f(x) = -3\\sin(8x) + 0\\cos(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3\\sin(8x) + 0\\cos(4x) $\n\nApply the standard differentiation rules:... | {
"type": "calculus",
"seed": 1337,
"index": 5350
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. -21x + 84 + 28x^2 = -103"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -21x + 84 + 28x^2 = -103 $\n\nMove all terms to the left (standard form):\n$ 28x^2 + -21x + 187 = 0 $\n\nApply the quadratic... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5351
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. 10 + 117x^2 + 68 = 150x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10 + 117x^2 + 68 = 150x $\n\nMove all terms to the left (standard form):\n$ 117x^2 + -150x + 78 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5352
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Differentiate with respect to $x$: $f(x) = \\ln(4x + -6)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(4x + -6) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{... | {
"type": "calculus",
"seed": 1337,
"index": 5353
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. -323 - 208 = 282x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -323 - 208 = 282x $\n\nMove all terms to the left (standard form):\n$ -282x + -531 = 0 $\n\nIsolate the $x$ term:\n$ -282x = 531 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 5354
} |
[
{
"role": "user",
"content": "Please solve this math problem. -11x - 131x^2 - 110 = 24"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -11x - 131x^2 - 110 = 24 $\n\nMove all terms to the left (standard form):\n$ -131x^2 + -11x + -134 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5355
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Find the modular inverse of 2 modulo 7, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $2\\cdot a^{-1} \\equiv 1 \\pmod{7}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees int... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5356
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 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 $a,b\\in\\mathbb{Z}_n$, then... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5357
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Evaluate: ((93 + -77/11) * 5) + 8^4 - log_6(1296) + (-475 mod 9) + floor(-133/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((93 + -77/11) * 5) + 8^4 - log_6(1296) + (-475 mod 9) + floor(-133/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 5358
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. -572 - 816 = 743x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -572 - 816 = 743x $\n\nMove all terms to the left (standard form):\n$ -743x + -1388 = 0 $\n\nIsolate the $x$ term:\n$ -743x = 1388 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 5359
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. -39x + 97 - 120x^2 = -7"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -39x + 97 - 120x^2 = -7 $\n\nMove all terms to the left (standard form):\n$ -120x^2 + -39x + 104 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5360
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal va... | {
"type": "trigonometry",
"seed": 1337,
"index": 5361
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. 9x^2 - 90x - 26 = -185"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 9x^2 - 90x - 26 = -185 $\n\nMove all terms to the left (standard form):\n$ 9x^2 + -90x + 159 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5362
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}6&1\\\\\\7&1\\end{pmatrix},\\quad b=\\begin{pmatrix}43\\\\\\51\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}6&1\\\\\\7&1\\end{p... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5363
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Compute the indefinite integral: $\\int \\ln(8x + 0)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(8x + 0)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\... | {
"type": "calculus",
"seed": 1337,
"index": 5364
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}1&0\\\\\\4&8\\end{pmatrix},\\quad b=\\begin{pmatrix}1\\\\\\-4\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}1&0\\\\\\4&8\\end{... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5365
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Differentiate with respect to $x$: $f(x) = 8e^{3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 8e^{3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{24e^{3x}} $"
}
... | {
"type": "calculus",
"seed": 1337,
"index": 5366
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Solve for $x$ (in radians): tan(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(1) = 0.785398 $\n\nThe ge... | {
"type": "trigonometry",
"seed": 1337,
"index": 5367
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. 443 + 929 = 368x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 443 + 929 = 368x $\n\nMove all terms to the left (standard form):\n$ -368x + 1372 = 0 $\n\nIsolate the $x$ term:\n$ -368x = -1372 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 5368
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Differentiate with respect to $x$: $f(x) = 2x^3 + -1x^2 + 11x + 13$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2x^3 + -1x^2 + 11x + 13 $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed... | {
"type": "calculus",
"seed": 1337,
"index": 5369
} |
[
{
"role": "user",
"content": "solve: \n\n Evaluate: ((-22 + -210/10) * 8) + 3^2 - log_3(729) + (231 mod 8) + ceil(148/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-22 + -210/10) * 8) + 3^2 - log_3(729) + (231 mod 8) + ceil(148/2) $\n\nCompute each component:\n$ -210/10... | {
"type": "arithmetic",
"seed": 1337,
"index": 5370
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. -10x^2 + 125 + 176x = -98"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -10x^2 + 125 + 176x = -98 $\n\nMove all terms to the left (standard form):\n$ -10x^2 + 176x + 223 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5371
} |
[
{
"role": "user",
"content": "solve -3x^2 - 147 + 31 = 194x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -3x^2 - 147 + 31 = 194x $\n\nMove all terms to the left (standard form):\n$ -3x^2 + -194x + -116 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5372
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Find the modular inverse of 7 modulo 24, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{24}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5373
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ ... | {
"type": "trigonometry",
"seed": 1337,
"index": 5374
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-6&6\\\\\\7&-9\\end{pmatrix},\\quad b=\\begin{pmatrix}66\\\\\\-93\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-6&6\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5375
} |
[
{
"role": "user",
"content": "Calculate the answer for 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 gene... | {
"type": "trigonometry",
"seed": 1337,
"index": 5376
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-7&-9\\\\3&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -7 & -9 \\\\ 3 & -7 \\end{pmatrix} $\n\nCompute the ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5377
} |
[
{
"role": "user",
"content": "Please calculate this equation. Compute $(80+-103) \\bmod 21$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (80+-103) \\bmod 21 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5378
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Differentiate with respect to $x$: $f(x) = 9\\sin(9x) + -9\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 9\\sin(9x) + -9\\cos(7x) $\n\nApply the standard differentiation rules:... | {
"type": "calculus",
"seed": 1337,
"index": 5379
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Find $A^{-1}$ for $A=\\begin{pmatrix}7&-2\\\\3&7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 7 & -2 \\\\ 3 & 7 \\end{pmatrix} $\n\nCompute the deter... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5380
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. -21x^2 + 18 + 44 = -156x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -21x^2 + 18 + 44 = -156x $\n\nMove all terms to the left (standard form):\n$ -21x^2 + 156x + 62 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5381
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 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$ \\alpha = ... | {
"type": "trigonometry",
"seed": 1337,
"index": 5382
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Evaluate: ((41 + -820/20) * 2) + 8^2 - log_4(16) + (311 mod 11) + floor(26/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((41 + -820/20) * 2) + 8^2 - log_4(16) + (311 mod 11) + floor(26/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 5383
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. 423 + 679 = 599x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 423 + 679 = 599x $\n\nMove all terms to the left (standard form):\n$ -599x + 1102 = 0 $\n\nIsolate the $x$ term:\n$ -599x = -1102 $\n\... | {
"type": "linear_equation",
"seed": 1337,
"index": 5384
} |
[
{
"role": "user",
"content": "Find the solution to the following 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": 5385
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Find the modular inverse of 24 modulo 25, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $24\\cdot a^{-1} \\equiv 1 \\pmod{25}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantee... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5386
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. -712x + 141 = 340"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -712x + 141 = 340 $\n\nMove all terms to the left (standard form):\n$ -712x + -199 = 0 $\n\nIsolate the $x$ term:\n$ -712x = 199 $\n\... | {
"type": "linear_equation",
"seed": 1337,
"index": 5387
} |
[
{
"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": 5388
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. 237 + 972 = 491x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 237 + 972 = 491x $\n\nMove all terms to the left (standard form):\n$ -491x + 1209 = 0 $\n\nIsolate the $x$ term:\n$ -491x = -1209 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 5389
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\... | {
"type": "trigonometry",
"seed": 1337,
"index": 5390
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. -990 - 681 = -460x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -990 - 681 = -460x $\n\nMove all terms to the left (standard form):\n$ 460x + -1671 = 0 $\n\nIsolate the $x$ term:\n$ 460x = 1671 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 5391
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Evaluate: ((-48 + 225/9) * 12) + 10^5 - log_2(32) + (215 mod 14) + ceil(69/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-48 + 225/9) * 12) + 10^5 - log_2(32) + (215 mod 14) + ceil(69/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 5392
} |
[
{
"role": "user",
"content": "Please find and report 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\... | {
"type": "trigonometry",
"seed": 1337,
"index": 5393
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Prove that $(\\mathbb{Z}_24, +)$ is a group under addition modulo 24."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_24=\\{0,1,\\dots,23\\}$ with operation $+$ modulo $24$.\n\n**Closure:** If $a,b\\in\\mathbb{Z... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5394
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-9&-1\\\\\\9&-6\\end{pmatrix},\\quad b=\\begin{pmatrix}-60\\\\\\18\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-9&-1\\\\\\9&-6\\end{... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5395
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Compute the determinant: $A=\\begin{pmatrix}-7&-2\\\\-5&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-7&-2\\\\\\-5&9\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5396
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Evaluate: ((98 + 152/4) * 17) + 5^2 - log_10(1000) + (-243 mod 15) + floor(-38/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((98 + 152/4) * 17) + 5^2 - log_10(1000) + (-243 mod 15) + floor(-38/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 5397
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. -830 - 632 = 957x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -830 - 632 = 957x $\n\nMove all terms to the left (standard form):\n$ -957x + -1462 = 0 $\n\nIsolate the $x$ term:\n$ -957x = 1462 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 5398
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Differentiate with respect to $x$: $f(x) = \\ln(3x + 0)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(3x + 0) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{... | {
"type": "calculus",
"seed": 1337,
"index": 5399
} |
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