messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Differentiate with respect to $x$: $f(x) = (5x + 5)\\sin(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (5x + 5)\\sin(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) ... | {
"type": "calculus",
"seed": 1337,
"index": 5400
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Compute the determinant: $A=\\begin{pmatrix}6&-9\\\\5&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}6&-9\\\\\\5&-2\\end{pmatrix} $\n\nUse $\\det(A)... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5401
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Compute $(-111+70) \\bmod 4$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-111+70) \\bmod 4 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5402
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Evaluate: ((164 + -56/4) * 10) + 8^3 - log_3(729) + (244 mod 26) + round(-27/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((164 + -56/4) * 10) + 8^3 - log_3(729) + (244 mod 26) + round(-27/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 5403
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. 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 ... | {
"type": "trigonometry",
"seed": 1337,
"index": 5404
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Solve for $x$ (in radians): sin(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 0 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(0) = 0 $\n\nThe ge... | {
"type": "trigonometry",
"seed": 1337,
"index": 5405
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Evaluate: ((153 + 429/11) * 3) + 5^4 - log_8(262144) + (-252 mod 18) + round(-71/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((153 + 429/11) * 3) + 5^4 - log_8(262144) + (-252 mod 18) + round(-71/... | {
"type": "arithmetic",
"seed": 1337,
"index": 5406
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Compute the determinant: $A=\\begin{pmatrix}0&-4\\\\5&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}0&-4\\\\\\5&-9\\end{pmatrix} $\n\nUse $\\det(A)=ad... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5407
} |
[
{
"role": "user",
"content": "Please calculate this equation. 23x - 120 + 177x^2 = -34"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 23x - 120 + 177x^2 = -34 $\n\nMove all terms to the left (standard form):\n$ 177x^2 + 23x + -86 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5408
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Differentiate with respect to $x$: $f(x) = 6\\sin(9x) + 5\\cos(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 6\\sin(9x) + 5\\cos(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) = ... | {
"type": "calculus",
"seed": 1337,
"index": 5409
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 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 $a,b\\in\\math... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5410
} |
[
{
"role": "user",
"content": "Work out the result of this equation. 12 - 15 - 67x = -73x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 12 - 15 - 67x = -73x^2 $\n\nMove all terms to the left (standard form):\n$ 73x^2 + -67x + -3 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5411
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:... | {
"type": "optimization",
"seed": 1337,
"index": 5412
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Prove that $f(x,y)=\\frac12(2x^2+8y^2)+1x+-4y+7$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(2x^2+8y^2)+1x+-4y+7 $\n\n$ \\frac{\\partial^2 f}{... | {
"type": "optimization",
"seed": 1337,
"index": 5413
} |
[
{
"role": "user",
"content": "Please calculate this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}9&4\\\\\\3&6\\end{pmatrix},\\quad b=\\begin{pmatrix}-50\\\\\\-12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}9&4\\\\\\3&6\\end{pmatrix} ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5414
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. -6x^2 + 63 + 128 = -35x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -6x^2 + 63 + 128 = -35x $\n\nMove all terms to the left (standard form):\n$ -6x^2 + 35x + 191 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5415
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Evaluate: ((139 + -216/12) * 10) + 5^4 - log_9(9) + (268 mod 27) + ceil(147/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((139 + -216/12) * 10) + 5^4 - log_9(9) + (268 mod 27) + ceil(147/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 5416
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. 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 = \\arct... | {
"type": "trigonometry",
"seed": 1337,
"index": 5417
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Compute $(-161+41) \\bmod 14$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-161+41) \\bmod 14 $\n\nUse the rule that addition is compatible with reduction... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5418
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value)... | {
"type": "trigonometry",
"seed": 1337,
"index": 5419
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Find the modular inverse of 9 modulo 34, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $9\\cdot a^{-1} \\equiv 1 \\pmod{34}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5420
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. 36x - 132 + 121x^2 = -41"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 36x - 132 + 121x^2 = -41 $\n\nMove all terms to the left (standard form):\n$ 121x^2 + 36x + -91 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5421
} |
[
{
"role": "user",
"content": "Please solve this math problem. Evaluate: ((-154 + 27/3) * 1) + 4^2 - log_10(10000) + (414 mod 13) + ceil(68/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-154 + 27/3) * 1) + 4^2 - log_10(10000) + (414 mod 13) + ceil(68/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 5422
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. 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": 5423
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 10x + 188x^2 + 49 = -179"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10x + 188x^2 + 49 = -179 $\n\nMove all terms to the left (standard form):\n$ 188x^2 + 10x + 228 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5424
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-8&7\\\\1&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -8 & 7 \\\\ 1 & 4 \\end{pmatrix} $\n\nCompute the d... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5425
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. -25 + 81 - 19x^2 = 117x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -25 + 81 - 19x^2 = 117x $\n\nMove all terms to the left (standard form):\n$ -19x^2 + -117x + 56 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5426
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. 23 - 81x - 128 = -109x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 23 - 81x - 128 = -109x^2 $\n\nMove all terms to the left (standard form):\n$ 109x^2 + -81x + -105 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5427
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Compute the indefinite integral: $\\int 2x^3 + -9x^2 + 4x + 6\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 2x^3 + -9x^2 + 4x + 6\\,dx $\n\nUse standard antiderivatives (and integration... | {
"type": "calculus",
"seed": 1337,
"index": 5428
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Compute the indefinite integral: $\\int -3\\sin(1x) + -2\\cos(1x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3\\sin(1x) + -2\\cos(1x)\\,dx $\n\nUse standard antiderivatives (and in... | {
"type": "calculus",
"seed": 1337,
"index": 5429
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Compute the determinant: $A=\\begin{pmatrix}-1&0\\\\5&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-1&0\\\\\\5&9\\end{pmatrix} $\n\nUse $\\det(A)=a... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5430
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-5&-3\\\\\\8&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}-36\\\\\\40\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-5&-3\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5431
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Differentiate with respect to $x$: $f(x) = (1x + 8)e^{3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (1x + 8)e^{3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{1e... | {
"type": "calculus",
"seed": 1337,
"index": 5432
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Evaluate: ((127 + 430/10) * 6) + 7^3 - log_3(81) + (96 mod 24) + floor(-65/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((127 + 430/10) * 6) + 7^3 - log_3(81) + (96 mod 24) + floor(-65/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 5433
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ ... | {
"type": "trigonometry",
"seed": 1337,
"index": 5434
} |
[
{
"role": "user",
"content": "Solve the following math 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$ \\alpha = \... | {
"type": "trigonometry",
"seed": 1337,
"index": 5435
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Differentiate with respect to $x$: $f(x) = (1x + -9)e^{2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (1x + -9)e^{2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed... | {
"type": "calculus",
"seed": 1337,
"index": 5436
} |
[
{
"role": "user",
"content": "Solve the following math equation. Compute the indefinite integral: $\\int -7e^{2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -7e^{2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int... | {
"type": "calculus",
"seed": 1337,
"index": 5437
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. -39x + 24x^2 + 124 = 126"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -39x + 24x^2 + 124 = 126 $\n\nMove all terms to the left (standard form):\n$ 24x^2 + -39x + -2 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5438
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Find the modular inverse of 9 modulo 10, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $9\\cdot a^{-1} \\equiv 1 \\pmod{10}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5439
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 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).\... | {
"type": "trigonometry",
"seed": 1337,
"index": 5440
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Evaluate: ((-68 + -540/12) * 4) + 4^3 - log_10(10000) + (199 mod 17) + ceil(175/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-68 + -540/12) * 4) + 4^3 - log_10(10000) + (199 mod 17) + ceil(175/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 5441
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. 449 + 205x = -419"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 449 + 205x = -419 $\n\nMove all terms to the left (standard form):\n$ 205x + 868 = 0 $\n\nIsolate the $x$ term:\n$ 205x = -868 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 5442
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 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}{\... | {
"type": "optimization",
"seed": 1337,
"index": 5443
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Evaluate: ((-20 + -385/11) * 13) + 2^3 - log_4(256) + (13 mod 5) + round(83/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-20 + -385/11) * 13) + 2^3 - log_4(256) + (13 mod 5) + round(83/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 5444
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. 36 + 178x^2 + 80 = 169x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 36 + 178x^2 + 80 = 169x $\n\nMove all terms to the left (standard form):\n$ 178x^2 + -169x + 116 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5445
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Evaluate: ((-48 + -48/3) * 11) + 7^3 - log_9(59049) + (-148 mod 6) + round(-168/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-48 + -48/3) * 11) + 7^3 - log_9(59049) + (-148 mod 6) + round(-168/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 5446
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. 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$ \\alph... | {
"type": "trigonometry",
"seed": 1337,
"index": 5447
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. 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 $\n\nThe general... | {
"type": "trigonometry",
"seed": 1337,
"index": 5448
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Evaluate: ((-14 + 165/11) * 14) + 8^4 - log_8(32768) + (290 mod 27) + round(106/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-14 + 165/11) * 14) + 8^4 - log_8(32768) + (290 mod 27) + round(106/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 5449
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}1&-8\\\\2&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 1 & -8 \\\\ 2 & 2 \\end{pmatrix} $\n\nCompute the... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5450
} |
[
{
"role": "user",
"content": "solve: Prove that $f(x)=1x^2+2x+-1$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+2x+-1$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 2x + 2 $\n$ f''(x) = 2 $\n\nSince... | {
"type": "optimization",
"seed": 1337,
"index": 5451
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Differentiate with respect to $x$: $f(x) = (1x + -4)e^{3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (1x + -4)e^{3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{1e^{3x} ... | {
"type": "calculus",
"seed": 1337,
"index": 5452
} |
[
{
"role": "user",
"content": "solve: Differentiate with respect to $x$: $f(x) = (-1x + -5)e^{2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-1x + -5)e^{2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-1e^{2x} + (-1x + -5)\\cdot 2e^{2x}}... | {
"type": "calculus",
"seed": 1337,
"index": 5453
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Prove that $f(x)=7x^2+-3x+3$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+-3x+3$.\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": 5454
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? 23 - 138x - 183x^2 = -91"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 23 - 138x - 183x^2 = -91 $\n\nMove all terms to the left (standard form):\n$ -183x^2 + -138x + 114 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5455
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 5456
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Differentiate with respect to $x$: $f(x) = -1x^3 + 2x^2 + 11x + 11$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1x^3 + 2x^2 + 11x + 11 $\n\nApply the standard differentiation rules:\n$... | {
"type": "calculus",
"seed": 1337,
"index": 5457
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Prove that $f(x,y)=\\frac12(2x^2+5y^2)+3x+-1y+-4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(2x^2+5y^2)+3x+-1y+-4 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 5458
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. 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 val... | {
"type": "trigonometry",
"seed": 1337,
"index": 5459
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Evaluate: ((-158 + -33/11) * 5) + 5^3 - log_2(32) + (-162 mod 3) + ceil(-62/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-158 + -33/11) * 5) + 5^3 - log_2(32) + (-162 mod 3) + ceil(-62/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 5460
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Evaluate: ((-34 + 370/10) * 5) + 7^4 - log_2(64) + (-414 mod 12) + round(-47/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-34 + 370/10) * 5) + 7^4 - log_2(64) + (-414 mod 12) + round(-47/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 5461
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Evaluate: ((-183 + -180/20) * 15) + 5^3 - log_8(8) + (428 mod 19) + round(73/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-183 + -180/20) * 15) + 5^3 - log_8(8) + (428 mod 19) + round(73/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 5462
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Differentiate with respect to $x$: $f(x) = (3x + -4)e^{5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (3x + -4)e^{5x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\b... | {
"type": "calculus",
"seed": 1337,
"index": 5463
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Solve for $x$ (in radians): cos(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(-\\... | {
"type": "trigonometry",
"seed": 1337,
"index": 5464
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Compute the indefinite integral: $\\int -2\\sin(3x) + 4\\cos(9x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -2\\sin(3x) + 4\\cos(9x)\\,dx $\n\nUse standard antiderivatives (and inte... | {
"type": "calculus",
"seed": 1337,
"index": 5465
} |
[
{
"role": "user",
"content": "Compute 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:\n$ ... | {
"type": "optimization",
"seed": 1337,
"index": 5466
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. -26x - 24 - 50 = 89x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -26x - 24 - 50 = 89x^2 $\n\nMove all terms to the left (standard form):\n$ -89x^2 + -26x + -74 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5467
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Solve for $x$ (in radians): cos(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -1 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(-1) = 3.14159 $\n\nThe ... | {
"type": "trigonometry",
"seed": 1337,
"index": 5468
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Evaluate: ((184 + -186/6) * 2) + 4^5 - log_10(100) + (328 mod 7) + ceil(-95/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((184 + -186/6) * 2) + 4^5 - log_10(100) + (328 mod 7) + ceil(-95/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 5469
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Evaluate: ((-31 + 495/11) * 20) + 7^3 - log_5(625) + (48 mod 26) + floor(-123/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-31 + 495/11) * 20) + 7^3 - log_5(625) + (48 mod 26) + floor(-12... | {
"type": "arithmetic",
"seed": 1337,
"index": 5470
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given 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": 5471
} |
[
{
"role": "user",
"content": "Can you compute this equation? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-5&-2\\\\\\1&-7\\end{pmatrix},\\quad b=\\begin{pmatrix}-41\\\\\\-14\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-5&-2\\\\\\1&-7\\end{pmat... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5472
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. 20x^2 - 48x - 128 = 14"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 20x^2 - 48x - 128 = 14 $\n\nMove all terms to the left (standard form):\n$ 20x^2 + -48x + -142 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5473
} |
[
{
"role": "user",
"content": "Please solve this math problem. -28 + 22x^2 - 171 = -43x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -28 + 22x^2 - 171 = -43x $\n\nMove all terms to the left (standard form):\n$ 22x^2 + 43x + -199 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5474
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. -275 - 395 = -49x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -275 - 395 = -49x $\n\nMove all terms to the left (standard form):\n$ 49x + -670 = 0 $\n\nIsolate the $x$ term:\n$ 49x = 670 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 5475
} |
[
{
"role": "user",
"content": "solve: \n\n Evaluate: ((164 + -187/17) * 4) + 10^3 - log_9(81) + (475 mod 8) + round(197/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((164 + -187/17) * 4) + 10^3 - log_9(81) + (475 mod 8) + round(197/2) $\n\nCompute each component:\n$ -187/... | {
"type": "arithmetic",
"seed": 1337,
"index": 5476
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute the determinant: $A=\\begin{pmatrix}-8&9\\\\3&0\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-8&9\\\\\\3&0\\end{pmatrix} $\n\nUse $\\det(A)=ad-... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5477
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}4&-8\\\\\\0&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}-24\\\\\\-24\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}4&-8\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5478
} |
[
{
"role": "user",
"content": "Please calculate this equation. 33 + 177 - 150x = 175x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 33 + 177 - 150x = 175x^2 $\n\nMove all terms to the left (standard form):\n$ -175x^2 + -150x + 210 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5479
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Differentiate with respect to $x$: $f(x) = -5x^3 + -9x^2 + 2x + 14$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -5x^3 + -9x^2 + 2x + 14 $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 5480
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. 36 + 177x - 166x^2 = 62"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 36 + 177x - 166x^2 = 62 $\n\nMove all terms to the left (standard form):\n$ -166x^2 + 177x + -26 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5481
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Evaluate: ((151 + -247/19) * 14) + 11^2 - log_8(512) + (-324 mod 13) + ceil(63/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((151 + -247/19) * 14) + 11^2 - log_8(512) + (-324 mod 13) + ceil... | {
"type": "arithmetic",
"seed": 1337,
"index": 5482
} |
[
{
"role": "user",
"content": "Evaluate the following 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": 5483
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Evaluate: ((166 + 300/25) * 16) + 9^3 - log_8(32768) + (-138 mod 4) + floor(-9/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((166 + 300/25) * 16) + 9^3 - log_8(32768) + (-138 mod 4) + floor... | {
"type": "arithmetic",
"seed": 1337,
"index": 5484
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. 936 - 471 = -223x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 936 - 471 = -223x $\n\nMove all terms to the left (standard form):\n$ 223x + 465 = 0 $\n\nIsolate the $x$ term:\n$ 223x = -465 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 5485
} |
[
{
"role": "user",
"content": "Please solve this math problem. 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 $\n\nThe general so... | {
"type": "trigonometry",
"seed": 1337,
"index": 5486
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((114 + 90/9) * 19) + 12^4 - log_10(1000000) + (-385 mod 26) + ceil(-13/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((114 + 90/9) * 19) + 12^4 - log_10(1000000) + (-385 mod 26... | {
"type": "arithmetic",
"seed": 1337,
"index": 5487
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Evaluate: ((65 + 336/12) * 1) + 11^4 - log_4(256) + (307 mod 17) + floor(-4/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((65 + 336/12) * 1) + 11^4 - log_4(256) + (307 mod 17) + floor(-4/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 5488
} |
[
{
"role": "user",
"content": "Solve the following math equation. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha =... | {
"type": "trigonometry",
"seed": 1337,
"index": 5489
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. 328x - 452 = 173"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 328x - 452 = 173 $\n\nMove all terms to the left (standard form):\n$ 328x + -625 = 0 $\n\nIsolate the $x$ term:\n$ 328x = 625 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 5490
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. -337 + 160x = -749"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -337 + 160x = -749 $\n\nMove all terms to the left (standard form):\n$ 160x + 412 = 0 $\n\nIsolate the $x$ term:\n$ 160x = -412 $\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 5491
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Differentiate with respect to $x$: $f(x) = (5x + 2)e^{6x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (5x + 2)e^{6x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{... | {
"type": "calculus",
"seed": 1337,
"index": 5492
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. -17 + 144 + 47x = 23x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -17 + 144 + 47x = 23x^2 $\n\nMove all terms to the left (standard form):\n$ -23x^2 + 47x + 127 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5493
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}4&2&5\\\\\\2&-1&3\\\\\\-5&5&4\\end{pmatrix},\\quad b=\\begin{pmatrix}6\\\\\\12\\\\\\-17\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5494
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Compute the determinant: $A=\\begin{pmatrix}8&-1\\\\0&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}8&-1\\\\\\0&-7\\end{pmatrix} $\n\nUs... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5495
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Evaluate: ((89 + 224/14) * 8) + 4^3 - log_5(625) + (390 mod 7) + ceil(85/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((89 + 224/14) * 8) + 4^3 - log_5(625) + (390 mod 7) + ceil(85/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 5496
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Differentiate with respect to $x$: $f(x) = \\ln(9x + 4)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(9x + 4) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{9}... | {
"type": "calculus",
"seed": 1337,
"index": 5497
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Compute the determinant: $A=\\begin{pmatrix}8&-3\\\\-1&5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}8&-3\\\\\\-1&5\\end{pmatrix} $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5498
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Prove that $f(x)=7x^2+9x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+9x+0$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 14x... | {
"type": "optimization",
"seed": 1337,
"index": 5499
} |
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