messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Can you find the solution to this equation? 17 - 167 + 135x = -69x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 17 - 167 + 135x = -69x^2 $\n\nMove all terms to the left (standard form):\n$ 69x^2 + 135x + -150 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2200
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Compute $(-41+-96) \\bmod 9$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-41+-96) \\bmod 9 $\n\nUse the rule that addition is compatible with reduction... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2201
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Solve for $x$ (in radians): cos(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha ... | {
"type": "trigonometry",
"seed": 1337,
"index": 2202
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Differentiate with respect to $x$: $f(x) = 4x^3 + 7x^2 + 2x + 20$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4x^3 + 7x^2 + 2x + 20 $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 2203
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Differentiate with respect to $x$: $f(x) = \\ln(4x + -5)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(4x + -5) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{4}{4x + -... | {
"type": "calculus",
"seed": 1337,
"index": 2204
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Evaluate: ((-73 + -84/21) * 7) + 6^4 - log_9(59049) + (206 mod 2) + floor(-184/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-73 + -84/21) * 7) + 6^4 - log_9(59049) + (206 mod 2) + floor(-184/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2205
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Prove that $(\\mathbb{Z}_17, +)$ is a group under addition modulo 17."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_17=\\{0,1,\\dots,16\\}$ with operation $+$ modulo $17$.\n\n**Closure:** If $a,b\\in\\mathbb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2206
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Prove that $(\\mathbb{Z}_13, +)$ is a group under addition modulo 13."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_13=\\{0,1,\\dots,12\\}$ with operation $+$ modulo $13$.\n\n**Closure:** If $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2207
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. -23 + 183 + 13x^2 = -91x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -23 + 183 + 13x^2 = -91x $\n\nMove all terms to the left (standard form):\n$ 13x^2 + 91x + 160 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2208
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Evaluate: ((140 + 0/2) * 9) + 5^2 - log_4(16) + (-388 mod 10) + floor(132/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((140 + 0/2) * 9) + 5^2 - log_4(16) + (-388 mod 10) + floor(132/2) $\n\nCompute eac... | {
"type": "arithmetic",
"seed": 1337,
"index": 2209
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-1&-2&-2\\\\\\3&4&1\\\\\\-3&2&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-7\\\\\\4\\\\\\14\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2210
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Differentiate with respect to $x$: $f(x) = -1\\sin(5x) + 0\\cos(8x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1\\sin(5x) + 0\\cos(8x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-5\\cos(5x) ... | {
"type": "calculus",
"seed": 1337,
"index": 2211
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Compute the indefinite integral: $\\int (5x + 6)e^{1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (5x + 6)e^{1x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed... | {
"type": "calculus",
"seed": 1337,
"index": 2212
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. 16 - 132x - 172 = 57x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 16 - 132x - 172 = 57x^2 $\n\nMove all terms to the left (standard form):\n$ -57x^2 + -132x + -156 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2213
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Compute the determinant: $A=\\begin{pmatrix}3&3\\\\2&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&3\\\\\\2&1\\end{pmatrix} $\n\nUse... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2214
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 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}... | {
"type": "trigonometry",
"seed": 1337,
"index": 2215
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Evaluate: ((-75 + -153/17) * 4) + 12^5 - log_6(46656) + (-380 mod 25) + round(-152/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-75 + -153/17) * 4) + 12^5 - log_6(46656) + (-380 mod 25) + round(-152... | {
"type": "arithmetic",
"seed": 1337,
"index": 2216
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Prove that $f(x,y)=\\frac12(9x^2+4y^2)+-2x+4y+7$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+4y^2)+-2x+4y+7 $\n\n$ \\frac{\\partial^2 f}{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 2217
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&2&3\\\\\\2&4&3\\\\\\3&-1&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-11\\\\\\-9\\\\\\-1\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2218
} |
[
{
"role": "user",
"content": "Please determine 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 $f'(x)=0$, h... | {
"type": "optimization",
"seed": 1337,
"index": 2219
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. 92x + 286 = 719"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 92x + 286 = 719 $\n\nMove all terms to the left (standard form):\n$ 92x + -433 = 0 $\n\nIsolate the $x$ term:\n$ 92x = 433 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 2220
} |
[
{
"role": "user",
"content": "Please work out this equation. Differentiate with respect to $x$: $f(x) = \\ln(8x + 5)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(8x + 5) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{8}{8x + 5}} $"... | {
"type": "calculus",
"seed": 1337,
"index": 2221
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute the indefinite integral: $\\int \\ln(2x + -5)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(2x + -5)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n... | {
"type": "calculus",
"seed": 1337,
"index": 2222
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-9&-2\\\\-6&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -9 & -2 \\\\ -6 & 2 \\end{pmatrix} $\n\nCompute the ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2223
} |
[
{
"role": "user",
"content": "Evaluate the following equation. 416x + 665 = -95"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 416x + 665 = -95 $\n\nMove all terms to the left (standard form):\n$ 416x + 760 = 0 $\n\nIsolate the $x$ term:\n$ 416x = -760 $\n\nDivide both sides by th... | {
"type": "linear_equation",
"seed": 1337,
"index": 2224
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. 822x + 872 = -223"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 822x + 872 = -223 $\n\nMove all terms to the left (standard form):\n$ 822x + 1095 = 0 $\n\nIsolate the $x$ term:\n$ 822x = -1095 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2225
} |
[
{
"role": "user",
"content": "Please calculate this equation. Prove that $f(x)=1x^2+1x+-7$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+1x+-7$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 2x + 1 $\... | {
"type": "optimization",
"seed": 1337,
"index": 2226
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. 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\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2227
} |
[
{
"role": "user",
"content": "Compute the solution to 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{\\partia... | {
"type": "optimization",
"seed": 1337,
"index": 2228
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Find the modular inverse of 7 modulo 12, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{12}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integers... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2229
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n... | {
"type": "optimization",
"seed": 1337,
"index": 2230
} |
[
{
"role": "user",
"content": "Please work out this equation. Prove that $f(x)=10x^2+-6x+2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+-6x+2$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 20x + -6... | {
"type": "optimization",
"seed": 1337,
"index": 2231
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal ... | {
"type": "trigonometry",
"seed": 1337,
"index": 2232
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Compute $(-176+-23) \\bmod 22$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-176+-23) \\bmod 22 $\n\nUse the rule that addition is compatible with reduct... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2233
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. 38 - 194x + 25 = -127x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 38 - 194x + 25 = -127x^2 $\n\nMove all terms to the left (standard form):\n$ 127x^2 + -194x + 63 = 0 $\n\nApply the quadrat... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2234
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. -724 - 439 = 698x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -724 - 439 = 698x $\n\nMove all terms to the left (standard form):\n$ -698x + -1163 = 0 $\n\nIsolate the $x$ term:\n$ -698x = 1163 $\... | {
"type": "linear_equation",
"seed": 1337,
"index": 2235
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Compute the indefinite integral: $\\int 3e^{-1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3e^{-1x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if ... | {
"type": "calculus",
"seed": 1337,
"index": 2236
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\partial^2 f}{\\partial x\\par... | {
"type": "optimization",
"seed": 1337,
"index": 2237
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Evaluate: ((159 + 280/14) * 11) + 11^2 - log_2(64) + (65 mod 18) + ceil(-195/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((159 + 280/14) * 11) + 11^2 - log_2(64) + (65 mod 18) + ceil(-195/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 2238
} |
[
{
"role": "user",
"content": "Please solve this math problem. Find the modular inverse of 31 modulo 36, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $31\\cdot a^{-1} \\equiv 1 \\pmod{36}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integer... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2239
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Prove that $(\\mathbb{Z}_18, +)$ is a group under addition modulo 18."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_18=\\{0,1,\\dots,17\\}$ with operation $+$ modulo $18$.\n\n**Closure:** If $a,b\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2240
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, h... | {
"type": "optimization",
"seed": 1337,
"index": 2241
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Compute $(-119+175) \\bmod 15$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-119+175) \\bmod 15 $\n\nUse the rule that addition is compatible with reduction... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2242
} |
[
{
"role": "user",
"content": "Solve the following math equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}2&1\\\\\\-5&-9\\end{pmatrix},\\quad b=\\begin{pmatrix}-23\\\\\\90\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}2&1\\\\\\-5&-9\\end{pma... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2243
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Evaluate: ((108 + 36/2) * 17) + 4^2 - log_4(64) + (84 mod 20) + ceil(65/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((108 + 36/2) * 17) + 4^2 - log_4(64) + (84 mod 20) + ceil(65/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 2244
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Evaluate: ((72 + -272/16) * 9) + 11^4 - log_5(3125) + (-467 mod 23) + ceil(-73/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((72 + -272/16) * 9) + 11^4 - log_5(3125) + (-467 mod 23) + ceil(-73/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 2245
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Compute the indefinite integral: $\\int 3e^{-3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3e^{-3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed... | {
"type": "calculus",
"seed": 1337,
"index": 2246
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Evaluate: ((60 + 81/9) * 18) + 2^4 - log_3(729) + (-472 mod 21) + round(132/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((60 + 81/9) * 18) + 2^4 - log_3(729) + (-472 mod 21) + round(132/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 2247
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. -196x - 93 = -38"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -196x - 93 = -38 $\n\nMove all terms to the left (standard form):\n$ -196x + -55 = 0 $\n\nIsolate the $x$ term:\n$ -196x = 55 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 2248
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. 307x + 458 = -89"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 307x + 458 = -89 $\n\nMove all terms to the left (standard form):\n$ 307x + 547 = 0 $\n\nIsolate the $x$ term:\n$ 307x = -547 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2249
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. 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 $a,b\\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2250
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((-113 + 1080/24) * 4) + 3^4 - log_8(262144) + (-191 mod 8) + ceil(154/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-113 + 1080/24) * 4) + 3^4 - log_8(262144) + (-191 mod 8) + ceil(154/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 2251
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&-2&2\\\\\\3&-4&-2\\\\\\0&1&0\\end{pmatrix},\\quad b=\\begin{pmatrix}4\\\\\\3\\\\\\-2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2252
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(... | {
"type": "optimization",
"seed": 1337,
"index": 2253
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Evaluate: ((-33 + 52/2) * 15) + 5^5 - log_2(64) + (-39 mod 6) + ceil(-136/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-33 + 52/2) * 15) + 5^5 - log_2(64) + (-39 mod 6) + ceil(-136/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 2254
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 31 - 164x - 16x^2 = -98"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 31 - 164x - 16x^2 = -98 $\n\nMove all terms to the left (standard form):\n$ -16x^2 + -164x + 129 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2255
} |
[
{
"role": "user",
"content": "solve: \n\n Compute the indefinite integral: $\\int -6e^{2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -6e^{2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int -6e^{2x}\\,dx = \\boxe... | {
"type": "calculus",
"seed": 1337,
"index": 2256
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Solve for $x$ (in radians): tan(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alph... | {
"type": "trigonometry",
"seed": 1337,
"index": 2257
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Differentiate with respect to $x$: $f(x) = -3\\sin(8x) + 5\\cos(6x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3\\sin(8x) + 5\\cos(6x) $\n\nApply the standard differentiation ru... | {
"type": "calculus",
"seed": 1337,
"index": 2258
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. 298 + 502x = -959"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 298 + 502x = -959 $\n\nMove all terms to the left (standard form):\n$ 502x + 1257 = 0 $\n\nIsolate the $x$ term:\n$ 502x = -1257 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 2259
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Solve for $x$ (in radians): cos(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 0 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(0) = 1.5708 $\n\nThe gen... | {
"type": "trigonometry",
"seed": 1337,
"index": 2260
} |
[
{
"role": "user",
"content": "Please solve this math problem. Prove that $f(x)=7x^2+10x+3$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+10x+3$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 14x + 10 ... | {
"type": "optimization",
"seed": 1337,
"index": 2261
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Evaluate: ((-21 + 108/12) * 5) + 6^2 - log_2(8) + (400 mod 27) + floor(129/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-21 + 108/12) * 5) + 6^2 - log_2(8) + (400 mod 27) + floor(129/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2262
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. -50 + 95 - 72x = -27x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -50 + 95 - 72x = -27x^2 $\n\nMove all terms to the left (standard form):\n$ 27x^2 + -72x + 45 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2263
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Evaluate: ((125 + -20/5) * 10) + 6^4 - log_9(6561) + (-293 mod 26) + ceil(61/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((125 + -20/5) * 10) + 6^4 - log_9(6561) + (-293 mod 26) + ceil(61/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 2264
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Evaluate: ((77 + 60/2) * 12) + 6^4 - log_3(81) + (-199 mod 21) + floor(-173/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((77 + 60/2) * 12) + 6^4 - log_3(81) + (-199 mod 21) + floor(-173/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 2265
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x^2-... | {
"type": "optimization",
"seed": 1337,
"index": 2266
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Prove that $f(x,y)=\\frac12(9x^2+6y^2)+0x+-5y+7$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+6y^2)+0x+-5y+7 $\n\n$ \\frac{\\partial^2 ... | {
"type": "optimization",
"seed": 1337,
"index": 2267
} |
[
{
"role": "user",
"content": "Solve the following math equation. Prove that $(\\mathbb{Z}_12, +)$ is a group under addition modulo 12."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_12=\\{0,1,\\dots,11\\}$ with operation $+$ modulo $12$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, t... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2268
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? -26 - 19x - 195x^2 = -131"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -26 - 19x - 195x^2 = -131 $\n\nMove all terms to the left (standard form):\n$ -195x^2 + -19x + 105 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2269
} |
[
{
"role": "user",
"content": "Solve the following math equation. Differentiate with respect to $x$: $f(x) = 3\\sin(8x) + -1\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3\\sin(8x) + -1\\cos(7x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \... | {
"type": "calculus",
"seed": 1337,
"index": 2270
} |
[
{
"role": "user",
"content": "Evaluate the following equation. 36 + 3x + 49x^2 = -114"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 36 + 3x + 49x^2 = -114 $\n\nMove all terms to the left (standard form):\n$ 49x^2 + 3x + 150 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2271
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Find $A^{-1}$ for $A=\\begin{pmatrix}-5&9\\\\-4&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -5 & 9 \\\\ -4 & -7 \\end{pmatrix} $\n\nCompute... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2272
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-9&-6\\\\-4&5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -9 & -6 \\\\ -4 & 5 \\end{pmatrix} $\n\nCompute the ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2273
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Evaluate: ((-56 + -432/16) * 3) + 9^4 - log_10(1000000) + (-79 mod 22) + floor(89/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-56 + -432/16) * 3) + 9^4 - log_10(1000000) + (-79 mod 22)... | {
"type": "arithmetic",
"seed": 1337,
"index": 2274
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Differentiate with respect to $x$: $f(x) = -3x^3 + -4x^2 + -11x + -7$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3x^3 + -4x^2 + -11x + -7 $\n\nApply the standard differentiation rules:\n$ f'(... | {
"type": "calculus",
"seed": 1337,
"index": 2275
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Differentiate with respect to $x$: $f(x) = 1\\sin(9x) + 6\\cos(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1\\sin(9x) + 6\\cos(5x) $\n\nApply the standard differentiation rules:\n... | {
"type": "calculus",
"seed": 1337,
"index": 2276
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Compute the indefinite integral: $\\int -3x^3 + -6x^2 + 4x + 9\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3x^3 + -6x^2 + 4x + 9\\,dx $\n\nUse standard antiderivatives (and inte... | {
"type": "calculus",
"seed": 1337,
"index": 2277
} |
[
{
"role": "user",
"content": "solve: \n\n Find $A^{-1}$ for $A=\\begin{pmatrix}-5&2\\\\7&5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -5 & 2 \\\\ 7 & 5 \\end{pmatrix} $\n\nCompute the determinant: $\\det(A)=ad-bc$.\n$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2278
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Compute the indefinite integral: $\\int -4\\sin(9x) + 6\\cos(8x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4\\sin(9x) + 6\\cos(8x)\\,dx $\n\nUse standard antiderivatives (an... | {
"type": "calculus",
"seed": 1337,
"index": 2279
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. 724x + 106 = 658"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 724x + 106 = 658 $\n\nMove all terms to the left (standard form):\n$ 724x + -552 = 0 $\n\nIsolate the $x$ term:\n$ 724x = 552 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 2280
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. -23 + 78 + 82x^2 = 27x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -23 + 78 + 82x^2 = 27x $\n\nMove all terms to the left (standard form):\n$ 82x^2 + -27x + 55 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2281
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Find $A^{-1}$ for $A=\\begin{pmatrix}3&7\\\\-4&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 3 & 7 \\\\ -4 & -3 \\end{pmatrix} $\n\nCompute... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2282
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Evaluate: ((-74 + 828/18) * 3) + 6^4 - log_3(81) + (219 mod 2) + round(-94/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-74 + 828/18) * 3) + 6^4 - log_3(81) + (219 mod 2) + round(-94/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 2283
} |
[
{
"role": "user",
"content": "Compute the correct solution for 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\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2284
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Compute the determinant: $A=\\begin{pmatrix}-8&3\\\\-2&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-8&3\\\\\\-2&1\\end{pmatrix} $\n\nUse $\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2285
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Evaluate: ((55 + 816/24) * 12) + 2^3 - log_4(1024) + (-228 mod 21) + round(67/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((55 + 816/24) * 12) + 2^3 - log_4(1024) + (-228 mod 21) + round(67/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 2286
} |
[
{
"role": "user",
"content": "Calculate the answer for 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(-... | {
"type": "trigonometry",
"seed": 1337,
"index": 2287
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Prove that $(\\mathbb{Z}_11, +)$ is a group under addition modulo 11."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_11=\\{0,1,\\dots,10\\}$ with operation $+$ modulo $11$.\n\n**Closure:** If $a,b\\in\\math... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2288
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. 369x + 361 = 969"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 369x + 361 = 969 $\n\nMove all terms to the left (standard form):\n$ 369x + -608 = 0 $\n\nIsolate the $x$ term:\n$ 369x = 608 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 2289
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. -47 + 86x + 18 = -28x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -47 + 86x + 18 = -28x^2 $\n\nMove all terms to the left (standard form):\n$ 28x^2 + 86x + -29 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2290
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 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 = \\ar... | {
"type": "trigonometry",
"seed": 1337,
"index": 2291
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Evaluate: ((-84 + -558/18) * 10) + 8^2 - log_4(256) + (199 mod 8) + round(-19/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-84 + -558/18) * 10) + 8^2 - log_4(256) + (199 mod 8) + round(-19/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 2292
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x^... | {
"type": "optimization",
"seed": 1337,
"index": 2293
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Compute the indefinite integral: $\\int \\ln(9x + 1)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(9x + 1)\\,dx $\n\nUse standard antiderivatives (and integration by parts if need... | {
"type": "calculus",
"seed": 1337,
"index": 2294
} |
[
{
"role": "user",
"content": "Evaluate the following equation. 683x - 773 = -99"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 683x - 773 = -99 $\n\nMove all terms to the left (standard form):\n$ 683x + -674 = 0 $\n\nIsolate the $x$ term:\n$ 683x = 674 $\n\nDivide both sides by th... | {
"type": "linear_equation",
"seed": 1337,
"index": 2295
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. 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": 2296
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Compute $(155+-138) \\bmod 19$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (155+-138) \\bmod 19 $\n\nUse the rule that addition is compatible with reduction... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2297
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. -902x + 673 = -858"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -902x + 673 = -858 $\n\nMove all terms to the left (standard form):\n$ -902x + 1531 = 0 $\n\nIsolate the $x$ term:\n$ -902x = -1531 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2298
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&1\\\\\\-9&6\\end{pmatrix},\\quad b=\\begin{pmatrix}-15\\\\\\-12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&1\\\\\\-9&6\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2299
} |
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