messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((-190 + 64/2) * 6) + 12^3 - log_10(10) + (-76 mod 9) + floor(152/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-190 + 64/2) * 6) + 12^3 - log_10(10) + (-76 mod 9) + floor(152/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 700
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. -701x + 714 = -453"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -701x + 714 = -453 $\n\nMove all terms to the left (standard form):\n$ -701x + 1167 = 0 $\n\nIsolate the $x$ term:\n$ -701x = -1167 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 701
} |
[
{
"role": "user",
"content": "solve: \n\n Prove that $f(x,y)=\\frac12(6x^2+3y^2)+-4x+-4y+1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(6x^2+3y^2)+-4x+-4y+1 $\n\n$ \\frac{\\partial^2 f}{\\partial x^2} = 6,\\quad \\frac... | {
"type": "optimization",
"seed": 1337,
"index": 702
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. -410 - 466x = -533"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -410 - 466x = -533 $\n\nMove all terms to the left (standard form):\n$ -466x + 123 = 0 $\n\nIsolate the $x$ term:\n$ -466x = -123 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 703
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Compute the indefinite integral: $\\int -5\\sin(9x) + 1\\cos(3x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -5\\sin(9x) + 1\\cos(3x)\\,dx $\n\nUse standard antiderivatives (and inte... | {
"type": "calculus",
"seed": 1337,
"index": 704
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-6&4\\\\\\-8&2\\end{pmatrix},\\quad b=\\begin{pmatrix}60\\\\\\50\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-6&4\\\\\\-8&2\\e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 705
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. -633x + 213 = -440"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -633x + 213 = -440 $\n\nMove all terms to the left (standard form):\n$ -633x + 653 = 0 $\n\nIsolate the $x$ term:\n$ -633x = -653 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 706
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Prove that $f(x,y)=\\frac12(7x^2+1y^2)+-3x+2y+-1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+1y^2)+-3x+2y+-1 $\n\n$ \\frac{\\partial^2 f}{\\... | {
"type": "optimization",
"seed": 1337,
"index": 707
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Compute $(-109+192) \\bmod 16$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-109+192) \\bmod 16 $\n\nUse the rule that addition is compatible with redu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 708
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Differentiate with respect to $x$: $f(x) = 1x^3 + 6x^2 + 5x + 13$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1x^3 + 6x^2 + 5x + 13 $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{3x... | {
"type": "calculus",
"seed": 1337,
"index": 709
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Compute the indefinite integral: $\\int (4x + -8)e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (4x + -8)e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration by par... | {
"type": "calculus",
"seed": 1337,
"index": 710
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. 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 genera... | {
"type": "trigonometry",
"seed": 1337,
"index": 711
} |
[
{
"role": "user",
"content": "solve Compute the determinant: $A=\\begin{pmatrix}-2&-4\\\\6&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-2&-4\\\\\\6&8\\end{pmatrix} $\n\nUse $\\det(A)=ad-bc$: \n$ \\det(A) = (-2... | {
"type": "linear_algebra",
"seed": 1337,
"index": 712
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. 846x + 818 = 818"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 846x + 818 = 818 $\n\nMove all terms to the left (standard form):\n$ 846x + 0 = 0 $\n\nIsolate the $x$ term:\n$ 846x = 0 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 713
} |
[
{
"role": "user",
"content": "Solve the following math equation. Compute the indefinite integral: $\\int 2\\sin(5x) + 5\\cos(4x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 2\\sin(5x) + 5\\cos(4x)\\,dx $\n\nUse standard antiderivatives (and integration... | {
"type": "calculus",
"seed": 1337,
"index": 714
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-3&4&0\\\\\\0&4&1\\\\\\-4&-3&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}-28\\\\\\-12\\\\\\-24\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve... | {
"type": "linear_algebra",
"seed": 1337,
"index": 715
} |
[
{
"role": "user",
"content": "Solve the equation and calculate 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 $f'(x)=0$, henc... | {
"type": "optimization",
"seed": 1337,
"index": 716
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. -45x^2 + 91 + 188 = 27x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -45x^2 + 91 + 188 = 27x $\n\nMove all terms to the left (standard form):\n$ -45x^2 + -27x + 279 = 0 $\n\nApply the quadrat... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 717
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Compute the indefinite integral: $\\int (1x + 1)\\sin(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (1x + 1)\\sin(5x)\\,dx $\n\nUse standard antiderivatives (and integration by ... | {
"type": "calculus",
"seed": 1337,
"index": 718
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&1&4\\\\\\-3&4&-2\\\\\\-5&2&1\\end{pmatrix},\\quad b=\\begin{pmatrix}10\\\\\\8\\\\\\17\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 719
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Find the modular inverse of 11 modulo 18, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{18}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 720
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac... | {
"type": "optimization",
"seed": 1337,
"index": 721
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? 256 + 60 = 498x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 256 + 60 = 498x $\n\nMove all terms to the left (standard form):\n$ -498x + 316 = 0 $\n\nIsolate the $x$ term:\n$ -498x = -316 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 722
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Evaluate: ((12 + -91/13) * 18) + 3^2 - log_7(2401) + (96 mod 5) + floor(51/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((12 + -91/13) * 18) + 3^2 - log_7(2401) + (96 mod 5) + floor(51/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 723
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. 11x - 138x^2 - 195 = 140"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 11x - 138x^2 - 195 = 140 $\n\nMove all terms to the left (standard form):\n$ -138x^2 + 11x + -335 = 0 $\n\nApply the quad... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 724
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. 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$... | {
"type": "optimization",
"seed": 1337,
"index": 725
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. 812x - 133 = 436"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 812x - 133 = 436 $\n\nMove all terms to the left (standard form):\n$ 812x + -569 = 0 $\n\nIsolate the $x$ term:\n$ 812x = 569 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 726
} |
[
{
"role": "user",
"content": "Solve this equation step by step. -884x - 833 = -391"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -884x - 833 = -391 $\n\nMove all terms to the left (standard form):\n$ -884x + -442 = 0 $\n\nIsolate the $x$ term:\n$ -884x = 442 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 727
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Evaluate: ((-32 + -738/18) * 13) + 11^2 - log_2(64) + (-314 mod 20) + floor(21/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-32 + -738/18) * 13) + 11^2 - log_2(64) + (-314 mod 20) + floor... | {
"type": "arithmetic",
"seed": 1337,
"index": 728
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&4&2\\\\\\3&-2&-5\\\\\\2&2&3\\end{pmatrix},\\quad b=\\begin{pmatrix}10\\\\\\5\\\\\\9\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 729
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 34x^2 - 182 + 81x = 125"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 34x^2 - 182 + 81x = 125 $\n\nMove all terms to the left (standard form):\n$ 34x^2 + 81x + -307 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 730
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Compute the indefinite integral: $\\int \\ln(2x + 2)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(2x + 2)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):... | {
"type": "calculus",
"seed": 1337,
"index": 731
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}9&7\\\\\\1&6\\end{pmatrix},\\quad b=\\begin{pmatrix}-81\\\\\\-9\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}9&7\\\\\\1&6\\e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 732
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}4&2&1\\\\\\3&-3&-2\\\\\\-2&-3&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}17\\\\\\2\\\\\\-11\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax... | {
"type": "linear_algebra",
"seed": 1337,
"index": 733
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Find the modular inverse of 23 modulo 26, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $23\\cdot a^{-1} \\equiv 1 \\pmod{26}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identi... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 734
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Compute the indefinite integral: $\\int 7e^{1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 7e^{1x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n... | {
"type": "calculus",
"seed": 1337,
"index": 735
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 578x + 95 = -904"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 578x + 95 = -904 $\n\nMove all terms to the left (standard form):\n$ 578x + 999 = 0 $\n\nIsolate the $x$ term:\n$ 578x = -999 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 736
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Evaluate: ((-2 + 333/9) * 20) + 7^2 - log_10(1000) + (-348 mod 26) + round(-44/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-2 + 333/9) * 20) + 7^2 - log_10(1000) + (-348 mod 26) + round(-44/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 737
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Prove that $(\\mathbb{Z}_20, +)$ is a group under addition modulo 20."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_20=\\{0,1,\\dots,19\\}$ with operation $+$ modulo $20$.\n\n**Closure:** If $a,b\\in\\mathb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 738
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 7 - 80x - 178x^2 = 132"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 7 - 80x - 178x^2 = 132 $\n\nMove all terms to the left (standard form):\n$ -178x^2 + -80x + -125 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 739
} |
[
{
"role": "user",
"content": "Solve the following math equation. 23 - 63x + 176x^2 = 73"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 23 - 63x + 176x^2 = 73 $\n\nMove all terms to the left (standard form):\n$ 176x^2 + -63x + -50 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 740
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 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 = ... | {
"type": "trigonometry",
"seed": 1337,
"index": 741
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Compute the indefinite integral: $\\int (1x + 1)\\sin(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (1x + 1)\\sin(6x)\\,dx $\n\nUse standard antiderivatives (and integr... | {
"type": "calculus",
"seed": 1337,
"index": 742
} |
[
{
"role": "user",
"content": "Please solve this math problem. 27x + 44x^2 - 93 = 98"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 27x + 44x^2 - 93 = 98 $\n\nMove all terms to the left (standard form):\n$ 44x^2 + 27x + -191 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 743
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Compute the determinant: $A=\\begin{pmatrix}-1&-2\\\\9&7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-1&-2\\\\\\9&7\\end{pmatrix} $\n\nUse $\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 744
} |
[
{
"role": "user",
"content": "Please compute 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": 745
} |
[
{
"role": "user",
"content": "Calculate the solution to this math 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{\... | {
"type": "optimization",
"seed": 1337,
"index": 746
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. -21x - 24 - 132x^2 = -151"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -21x - 24 - 132x^2 = -151 $\n\nMove all terms to the left (standard form):\n$ -132x^2 + -21x + 127 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 747
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 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^2-1... | {
"type": "optimization",
"seed": 1337,
"index": 748
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Evaluate: ((92 + -100/4) * 11) + 6^5 - log_7(117649) + (-380 mod 28) + round(9/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((92 + -100/4) * 11) + 6^5 - log_7(117649) + (-380 mod 28) + round(9/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 749
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Prove that $(\\mathbb{Z}_26, +)$ is a group under addition modulo 26."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_26=\\{0,1,\\dots,25\\}$ with operation $+$ modulo $26$.\n\n**Closure:** If $a,b\\in\\m... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 750
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Find $A^{-1}$ for $A=\\begin{pmatrix}-6&-2\\\\-5&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -6 & -2 \\\\ -5 & 3 \\end{pmatrix} $\n\nCompute... | {
"type": "linear_algebra",
"seed": 1337,
"index": 751
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}1&6\\\\\\-6&6\\end{pmatrix},\\quad b=\\begin{pmatrix}-59\\\\\\-24\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}1&6\\\\\\-6&6\\end... | {
"type": "linear_algebra",
"seed": 1337,
"index": 752
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Prove that $f(x,y)=\\frac12(10x^2+10y^2)+4x+4y+-5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(10x^2+10y^2)+4x+4y+-5 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 753
} |
[
{
"role": "user",
"content": "Solve this equation step by step. -x - 12 + 165x^2 = -15"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -x - 12 + 165x^2 = -15 $\n\nMove all terms to the left (standard form):\n$ 165x^2 + -1x + 3 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 754
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Compute the indefinite integral: $\\int (5x + -2)\\sin(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (5x + -2)\\sin(5x)\\,dx $\n\nUse standard antiderivatives (and integration b... | {
"type": "calculus",
"seed": 1337,
"index": 755
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Differentiate with respect to $x$: $f(x) = 6e^{-3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 6e^{-3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-18e^{-3x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 756
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Compute the indefinite integral: $\\int -4x^3 + 0x^2 + 2x + 5\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4x^3 + 0x^2 + 2x + 5\\,dx $\n\nUse standard antiderivatives (and integ... | {
"type": "calculus",
"seed": 1337,
"index": 757
} |
[
{
"role": "user",
"content": "Solve the following math equation. 34x + 156 - 100 = 71x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 34x + 156 - 100 = 71x^2 $\n\nMove all terms to the left (standard form):\n$ -71x^2 + 34x + 56 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 758
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Compute $(-113+-10) \\bmod 13$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-113+-10) \\bmod 13 $\n\nUse the rule that addition is compatible with reduct... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 759
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Evaluate: ((-72 + -600/25) * 5) + 12^5 - log_10(100000) + (-129 mod 25) + ceil(77/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-72 + -600/25) * 5) + 12^5 - log_10(100000) + (-129 mod 25) + ceil... | {
"type": "arithmetic",
"seed": 1337,
"index": 760
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. -28 + 8x^2 - 72 = -81x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -28 + 8x^2 - 72 = -81x $\n\nMove all terms to the left (standard form):\n$ 8x^2 + 81x + -100 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 761
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. -4x - 53 + 47x^2 = -3"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -4x - 53 + 47x^2 = -3 $\n\nMove all terms to the left (standard form):\n$ 47x^2 + -4x + -50 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 762
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 842x + 187 = -464"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 842x + 187 = -464 $\n\nMove all terms to the left (standard form):\n$ 842x + 651 = 0 $\n\nIsolate the $x$ term:\n$ 842x = -651 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 763
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. -31x - 125x^2 + 152 = -51"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -31x - 125x^2 + 152 = -51 $\n\nMove all terms to the left (standard form):\n$ -125x^2 + -31x + 203 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 764
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}0&2&3\\\\\\-1&0&5\\\\\\0&-1&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-1\\\\\\-5\\\\\\2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 765
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. 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{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 766
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute $(-140+8) \\bmod 2$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-140+8) \\bmod 2 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\n$ (... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 767
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Compute $(4+-147) \\bmod 23$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (4+-147) \\bmod 23 $\n\nUse the rule that addition is compatible with reduction modul... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 768
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Prove that $(\\mathbb{Z}_20, +)$ is a group under addition modulo 20."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_20=\\{0,1,\\dots,19\\}$ with operation $+$ modulo $20$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 769
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Prove that $(\\mathbb{Z}_23, +)$ is a group under addition modulo 23."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_23=\\{0,1,\\dots,22\\}$ with operation $+$ modulo $23$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, then ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 770
} |
[
{
"role": "user",
"content": "Please evaluate and solve this 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 value).\n$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 771
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 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": 772
} |
[
{
"role": "user",
"content": "Please find and report 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} & ... | {
"type": "optimization",
"seed": 1337,
"index": 773
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((133 + -100/4) * 20) + 8^5 - log_8(4096) + (312 mod 19) + floor(193/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((133 + -100/4) * 20) + 8^5 - log_8(4096) + (312 mod 19) + floor(193/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 774
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. 33 + 17 - 125x^2 = 62x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 33 + 17 - 125x^2 = 62x $\n\nMove all terms to the left (standard form):\n$ -125x^2 + -62x + 50 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 775
} |
[
{
"role": "user",
"content": "Can you solve the equation below? 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 = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 776
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 43x - 23 - 36x^2 = 73"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 43x - 23 - 36x^2 = 73 $\n\nMove all terms to the left (standard form):\n$ -36x^2 + 43x + -96 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 777
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. 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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 778
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-4&3&-4\\\\\\5&3&-4\\\\\\3&-3&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}14\\\\\\-22\\\\\\-2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 779
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Prove that $f(x)=2x^2+2x+-3$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+2x+-3$.\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": 780
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Evaluate: ((-75 + -266/14) * 11) + 8^2 - log_6(46656) + (326 mod 21) + ceil(-181/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-75 + -266/14) * 11) + 8^2 - log_6(46656) + (326 mod 21) + ceil(-181... | {
"type": "arithmetic",
"seed": 1337,
"index": 781
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: 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 $a,b\\in\\mathbb{Z}_n$, then $(a+b)\\bmod n\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 782
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((-192 + -406/14) * 2) + 12^3 - log_5(625) + (-480 mod 2) + round(-157/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-192 + -406/14) * 2) + 12^3 - log_5(625) + (-480 mod 2) + round(-157/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 783
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 15x - 41x^2 + 24 = 145"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 15x - 41x^2 + 24 = 145 $\n\nMove all terms to the left (standard form):\n$ -41x^2 + 15x + -121 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 784
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Evaluate: ((92 + 144/24) * 12) + 8^2 - log_4(1024) + (-234 mod 12) + round(36/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((92 + 144/24) * 12) + 8^2 - log_4(1024) + (-234 mod 12) + round(36/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 785
} |
[
{
"role": "user",
"content": "Can you evaluate this math 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).\n$ \\alpha =... | {
"type": "trigonometry",
"seed": 1337,
"index": 786
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}6&5\\\\\\-3&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-4\\\\\\-2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}6&5\\\\\\-3&-2\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 787
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Evaluate: ((-155 + -280/8) * 1) + 11^3 - log_7(49) + (-132 mod 29) + ceil(-53/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-155 + -280/8) * 1) + 11^3 - log_7(49) + (-132 mod 29) + ceil(-53/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 788
} |
[
{
"role": "user",
"content": "Compute the correct solution for 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 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 789
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. -29x^2 + 31 + 81x = -24"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -29x^2 + 31 + 81x = -24 $\n\nMove all terms to the left (standard form):\n$ -29x^2 + 81x + 55 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 790
} |
[
{
"role": "user",
"content": "Please find the value of this math 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{\\... | {
"type": "optimization",
"seed": 1337,
"index": 791
} |
[
{
"role": "user",
"content": "Please find the solution of 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 792
} |
[
{
"role": "user",
"content": "solve: Differentiate with respect to $x$: $f(x) = 9\\sin(8x) + -7\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 9\\sin(8x) + -7\\cos(7x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{72\\cos(8x) - -49\\s... | {
"type": "calculus",
"seed": 1337,
"index": 793
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 794
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 291 + 636x = 76"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 291 + 636x = 76 $\n\nMove all terms to the left (standard form):\n$ 636x + 215 = 0 $\n\nIsolate the $x$ term:\n$ 636x = -215 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 795
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Differentiate with respect to $x$: $f(x) = (6x + -7)e^{2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (6x + -7)e^{2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\b... | {
"type": "calculus",
"seed": 1337,
"index": 796
} |
[
{
"role": "user",
"content": "Please find the value of this math 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{\\... | {
"type": "optimization",
"seed": 1337,
"index": 797
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Compute the determinant: $A=\\begin{pmatrix}3&-3\\\\9&-1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&-3\\\\\\9&-1\\end{pmatrix} $\n\nUse $\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 798
} |
[
{
"role": "user",
"content": "Compute the outcome of this 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$ \\alph... | {
"type": "trigonometry",
"seed": 1337,
"index": 799
} |
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