messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Solve the math equation and present the result. -147 + 994 = -628x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -147 + 994 = -628x $\n\nMove all terms to the left (standard form):\n$ 628x + 847 = 0 $\n\nIsolate the $x$ term:\n$ 628x = -847 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1700
} |
[
{
"role": "user",
"content": "Please calculate this equation. -26x + 116 + 116x^2 = -121"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -26x + 116 + 116x^2 = -121 $\n\nMove all terms to the left (standard form):\n$ 116x^2 + -26x + 237 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1701
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Differentiate with respect to $x$: $f(x) = -1\\sin(6x) + 3\\cos(8x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1\\sin(6x) + 3\\cos(8x) $\n\nApply the standard differentiation r... | {
"type": "calculus",
"seed": 1337,
"index": 1702
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Evaluate: ((12 + -21/7) * 19) + 5^4 - log_9(81) + (479 mod 24) + round(23/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((12 + -21/7) * 19) + 5^4 - log_9(81) + (479 mod 24) + round(23/2) $\n\nCompute each compo... | {
"type": "arithmetic",
"seed": 1337,
"index": 1703
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Differentiate with respect to $x$: $f(x) = 3x^3 + 5x^2 + 0x + 11$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3x^3 + 5x^2 + 0x + 11 $\n\nApply the standard differentiation rules:\... | {
"type": "calculus",
"seed": 1337,
"index": 1704
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Prove that $f(x,y)=\\frac12(10x^2+9y^2)+1x+4y+-5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(10x^2+9y^2)+1x+4y+-5 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 1705
} |
[
{
"role": "user",
"content": "Please compute the answer 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{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 1706
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Evaluate: ((125 + -6/3) * 9) + 3^2 - log_5(5) + (-346 mod 2) + ceil(139/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((125 + -6/3) * 9) + 3^2 - log_5(5) + (-346 mod 2) + ceil(139/2) $\n\nCompute each component:\n$ -6/3 = -2 $... | {
"type": "arithmetic",
"seed": 1337,
"index": 1707
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Prove that $f(x,y)=\\frac12(7x^2+6y^2)+-3x+0y+1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+6y^2)+-3x+0y+1 $\n\n$ \\frac{\\partial^2 f}{... | {
"type": "optimization",
"seed": 1337,
"index": 1708
} |
[
{
"role": "user",
"content": "Please solve this math problem. 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": 1709
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. -32 - 99x^2 - 22x = -124"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -32 - 99x^2 - 22x = -124 $\n\nMove all terms to the left (standard form):\n$ -99x^2 + -22x + 92 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1710
} |
[
{
"role": "user",
"content": "solve: \n\n Evaluate: ((141 + -117/13) * 2) + 7^3 - log_2(64) + (442 mod 4) + ceil(39/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((141 + -117/13) * 2) + 7^3 - log_2(64) + (442 mod 4) + ceil(39/2) $\n\nCompute each component:\n$ -117/13 = -... | {
"type": "arithmetic",
"seed": 1337,
"index": 1711
} |
[
{
"role": "user",
"content": "Work through and solve this equation. 573 + 432x = -503"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 573 + 432x = -503 $\n\nMove all terms to the left (standard form):\n$ 432x + 1076 = 0 $\n\nIsolate the $x$ term:\n$ 432x = -1076 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 1712
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. 16x^2 + 31x - 33 = -106"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 16x^2 + 31x - 33 = -106 $\n\nMove all terms to the left (standard form):\n$ 16x^2 + 31x + 73 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1713
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Differentiate with respect to $x$: $f(x) = 4\\sin(1x) + 3\\cos(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4\\sin(1x) + 3\\cos(1x) $\n\nApply the standard differentiation rules:\n$ f'(x) =... | {
"type": "calculus",
"seed": 1337,
"index": 1714
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Compute the indefinite integral: $\\int -5x^3 + 8x^2 + 7x + -2\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -5x^3 + 8x^2 + 7x + -2\\,dx $\n\nUse standard antiderivatives (... | {
"type": "calculus",
"seed": 1337,
"index": 1715
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Evaluate: ((-116 + 738/18) * 13) + 8^3 - log_10(100000) + (-124 mod 16) + round(-162/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-116 + 738/18) * 13) + 8^3 - log_10(100000) + (-124 mod 1... | {
"type": "arithmetic",
"seed": 1337,
"index": 1716
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 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": 1717
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. 11 - 10x^2 + 54 = 148x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 11 - 10x^2 + 54 = 148x $\n\nMove all terms to the left (standard form):\n$ -10x^2 + -148x + 65 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1718
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. 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{\\pa... | {
"type": "optimization",
"seed": 1337,
"index": 1719
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. -888x - 991 = -334"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -888x - 991 = -334 $\n\nMove all terms to the left (standard form):\n$ -888x + -657 = 0 $\n\nIsolate the $x$ term:\n$ -888x = 657 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 1720
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. 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\\in\\mathbb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1721
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Prove that $f(x,y)=\\frac12(4x^2+7y^2)+5x+-1y+-4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+7y^2)+5x+-1y+-4 $\n\n$ \\frac{\\partial^2 f... | {
"type": "optimization",
"seed": 1337,
"index": 1722
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Prove that $(\\mathbb{Z}_15, +)$ is a group under addition modulo 15."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_15=\\{0,1,\\dots,14\\}$ with operation $+$ modulo $15$.\n\n**Closure:** If $a,b\\in\\math... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1723
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. -275 + 353 = -895x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -275 + 353 = -895x $\n\nMove all terms to the left (standard form):\n$ 895x + 78 = 0 $\n\nIsolate the $x$ term:\n$ 895x = -78 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1724
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. 243x - 477 = 247"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 243x - 477 = 247 $\n\nMove all terms to the left (standard form):\n$ 243x + -724 = 0 $\n\nIsolate the $x$ term:\n$ 243x = 724 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1725
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. 20 - 46 + 92x^2 = 199x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 20 - 46 + 92x^2 = 199x $\n\nMove all terms to the left (standard form):\n$ 92x^2 + -199x + -26 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1726
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Compute the determinant: $A=\\begin{pmatrix}2&3\\\\3&-1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}2&3\\\\\\3&-1\\end{pmatrix} $\n\nUse... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1727
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Prove that $f(x)=10x^2+8x+2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+8x+2$.\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": 1728
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Find $A^{-1}$ for $A=\\begin{pmatrix}9&4\\\\1&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 9 & 4 \\\\ 1 & -4 \\end{pmatrix} $\n\nCompute the det... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1729
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Prove that $f(x,y)=\\frac12(4x^2+10y^2)+-2x+-2y+7$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+10y^2)+-2x+-2y+7 $\n\n$ \\frac{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 1730
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. -442 - 626x = 678"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -442 - 626x = 678 $\n\nMove all terms to the left (standard form):\n$ -626x + -1120 = 0 $\n\nIsolate the $x$ term:\n$ -626x = 1120 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1731
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Prove that $f(x,y)=\\frac12(4x^2+3y^2)+-4x+-4y+3$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+3y^2)+-4x+-4y+3 $\n\n$ \\frac{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 1732
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Evaluate: ((175 + 66/3) * 7) + 10^4 - log_4(4) + (160 mod 30) + round(-19/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((175 + 66/3) * 7) + 10^4 - log_4(4) + (160 mod 30) + round(-19/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 1733
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. -4 + 24x - 113x^2 = 16"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -4 + 24x - 113x^2 = 16 $\n\nMove all terms to the left (standard form):\n$ -113x^2 + 24x + -20 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1734
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. 37 + 125x + 131x^2 = 2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 37 + 125x + 131x^2 = 2 $\n\nMove all terms to the left (standard form):\n$ 131x^2 + 125x + 35 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1735
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. -600x - 524 = 888"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -600x - 524 = 888 $\n\nMove all terms to the left (standard form):\n$ -600x + -1412 = 0 $\n\nIsolate the $x$ term:\n$ -600x = 1412 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 1736
} |
[
{
"role": "user",
"content": "Evaluate the following equation. -315 + 170 = 793x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -315 + 170 = 793x $\n\nMove all terms to the left (standard form):\n$ -793x + -145 = 0 $\n\nIsolate the $x$ term:\n$ -793x = 145 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 1737
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}0&6\\\\-9&0\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 0 & 6 \\\\ -9 & 0 \\end{pmatrix} $\n\nCompute the d... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1738
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Compute the determinant: $A=\\begin{pmatrix}0&-9\\\\3&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}0&-9\\\\\\3&1\\end{pmatrix} $\n\nUse $\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1739
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Prove that $(\\mathbb{Z}_6, +)$ is a group under addition modulo 6."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_6=\\{0,1,\\dots,5\\}$ with operation $+$ modulo $6$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1740
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. 47 + 110x - 91x^2 = -163"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 47 + 110x - 91x^2 = -163 $\n\nMove all terms to the left (standard form):\n$ -91x^2 + 110x + 210 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1741
} |
[
{
"role": "user",
"content": "Compute the outcome of 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$ 4... | {
"type": "optimization",
"seed": 1337,
"index": 1742
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. -547 + 170 = 939x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -547 + 170 = 939x $\n\nMove all terms to the left (standard form):\n$ -939x + -377 = 0 $\n\nIsolate the $x$ term:\n$ -939x = 377 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 1743
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Prove that $(\\mathbb{Z}_9, +)$ is a group under addition modulo 9."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_9=\\{0,1,\\dots,8\\}$ with operation $+$ modulo $9$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, th... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1744
} |
[
{
"role": "user",
"content": "Work through and solve this equation. 23x^2 - 68 + 24x = 151"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 23x^2 - 68 + 24x = 151 $\n\nMove all terms to the left (standard form):\n$ 23x^2 + 24x + -219 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1745
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? 50x^2 - 93x - 96 = 38"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 50x^2 - 93x - 96 = 38 $\n\nMove all terms to the left (standard form):\n$ 50x^2 + -93x + -134 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1746
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Evaluate: ((119 + -168/8) * 19) + 8^4 - log_4(1024) + (64 mod 2) + floor(-133/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((119 + -168/8) * 19) + 8^4 - log_4(1024) + (64 mod 2) + floor(-133/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 1747
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Differentiate with respect to $x$: $f(x) = -6x^3 + 4x^2 + 10x + -14$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6x^3 + 4x^2 + 10x + -14 $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 1748
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Compute the determinant: $A=\\begin{pmatrix}7&-8\\\\-6&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}7&-8\\\\\\-6&8\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1749
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 259 - 692x = 479"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 259 - 692x = 479 $\n\nMove all terms to the left (standard form):\n$ -692x + -220 = 0 $\n\nIsolate the $x$ term:\n$ -692x = 220 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 1750
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Prove that $f(x)=1x^2+-6x+-10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+-6x+-10$.\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": 1751
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 15 + 23 + 124x = -11x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 15 + 23 + 124x = -11x^2 $\n\nMove all terms to the left (standard form):\n$ 11x^2 + 124x + 38 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1752
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Find the modular inverse of 18 modulo 35, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $18\\cdot a^{-1} \\equiv 1 \\pmod{35}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1753
} |
[
{
"role": "user",
"content": "Solve the equation and return 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 = \\arctan... | {
"type": "trigonometry",
"seed": 1337,
"index": 1754
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Evaluate: ((-129 + -108/6) * 4) + 5^5 - log_8(512) + (275 mod 28) + round(32/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-129 + -108/6) * 4) + 5^5 - log_8(512) + (275 mod 28) + round(32/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 1755
} |
[
{
"role": "user",
"content": "Can you solve the equation below? 843x + 354 = 777"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 843x + 354 = 777 $\n\nMove all terms to the left (standard form):\n$ 843x + -423 = 0 $\n\nIsolate the $x$ term:\n$ 843x = 423 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 1756
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. -309 - 207 = 264x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -309 - 207 = 264x $\n\nMove all terms to the left (standard form):\n$ -264x + -516 = 0 $\n\nIsolate the $x$ term:\n$ -264x = 516 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1757
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-1&9\\\\7&0\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -1 & 9 \\\\ 7 & 0 \\end{pmatrix} $\n\nCompute the determinan... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1758
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Evaluate: ((-10 + 460/20) * 19) + 10^4 - log_3(729) + (-404 mod 10) + round(-52/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-10 + 460/20) * 19) + 10^4 - log_3(729) + (-404 mod 10) + rou... | {
"type": "arithmetic",
"seed": 1337,
"index": 1759
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? -26x^2 + 122 + 24 = 158x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -26x^2 + 122 + 24 = 158x $\n\nMove all terms to the left (standard form):\n$ -26x^2 + -158x + 146 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1760
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. -536x - 122 = -475"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -536x - 122 = -475 $\n\nMove all terms to the left (standard form):\n$ -536x + 353 = 0 $\n\nIsolate the $x$ term:\n$ -536x = -353 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 1761
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Evaluate: ((-106 + -567/21) * 6) + 3^4 - log_4(16) + (-93 mod 2) + round(-7/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-106 + -567/21) * 6) + 3^4 - log_4(16) + (-93 mod 2) + round(-7/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 1762
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&1&-4\\\\\\1&5&-3\\\\\\-4&-3&4\\end{pmatrix},\\quad b=\\begin{pmatrix}-8\\\\\\-20\\\\\\14\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1763
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Evaluate: ((73 + -340/17) * 19) + 6^2 - log_5(25) + (133 mod 13) + round(-74/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((73 + -340/17) * 19) + 6^2 - log_5(25) + (133 mod 13) + round(-74/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 1764
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Differentiate with respect to $x$: $f(x) = \\ln(8x + 1)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(8x + 1) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{8}{8... | {
"type": "calculus",
"seed": 1337,
"index": 1765
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. -49x + 99x^2 + 177 = 63"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -49x + 99x^2 + 177 = 63 $\n\nMove all terms to the left (standard form):\n$ 99x^2 + -49x + 114 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1766
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. 38x^2 - 103 - 196 = -191x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 38x^2 - 103 - 196 = -191x $\n\nMove all terms to the left (standard form):\n$ 38x^2 + 191x + -299 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1767
} |
[
{
"role": "user",
"content": "Solve the following math 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 gener... | {
"type": "trigonometry",
"seed": 1337,
"index": 1768
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Differentiate with respect to $x$: $f(x) = (2x + 2)\\sin(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (2x + 2)\\sin(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\... | {
"type": "calculus",
"seed": 1337,
"index": 1769
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\... | {
"type": "optimization",
"seed": 1337,
"index": 1770
} |
[
{
"role": "user",
"content": "solve: \n\n 159 + 197x = -354"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 159 + 197x = -354 $\n\nMove all terms to the left (standard form):\n$ 197x + 513 = 0 $\n\nIsolate the $x$ term:\n$ 197x = -513 $\n\nDivide both sides by the coefficient of $x... | {
"type": "linear_equation",
"seed": 1337,
"index": 1771
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. -789x - 446 = 945"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -789x - 446 = 945 $\n\nMove all terms to the left (standard form):\n$ -789x + -1391 = 0 $\n\nIsolate the $x$ term:\n$ -789x = 1391 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1772
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Evaluate: ((197 + -280/14) * 4) + 10^2 - log_2(4) + (-17 mod 7) + floor(-63/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((197 + -280/14) * 4) + 10^2 - log_2(4) + (-17 mod 7) + floor(-63/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 1773
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Evaluate: ((-23 + -396/22) * 18) + 3^2 - log_3(27) + (70 mod 13) + floor(25/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-23 + -396/22) * 18) + 3^2 - log_3(27) + (70 mod 13) + floor(25/... | {
"type": "arithmetic",
"seed": 1337,
"index": 1774
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. -40 + 54 + 104x = 50x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -40 + 54 + 104x = 50x^2 $\n\nMove all terms to the left (standard form):\n$ -50x^2 + 104x + 14 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1775
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Compute the indefinite integral: $\\int -1x^3 + 4x^2 + 15x + -11\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -1x^3 + 4x^2 + 15x + -11\\,dx $\n\nUse standard antiderivatives (and int... | {
"type": "calculus",
"seed": 1337,
"index": 1776
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. -50x + 10 + 29 = -19x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -50x + 10 + 29 = -19x^2 $\n\nMove all terms to the left (standard form):\n$ 19x^2 + -50x + 39 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1777
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Compute the indefinite integral: $\\int -7\\sin(7x) + -2\\cos(1x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -7\\sin(7x) + -2\\cos(1x)\\,dx $\n\nUse standard antiderivatives... | {
"type": "calculus",
"seed": 1337,
"index": 1778
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Compute the indefinite integral: $\\int 7e^{1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 7e^{1x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\in... | {
"type": "calculus",
"seed": 1337,
"index": 1779
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Evaluate: ((-85 + -560/16) * 1) + 2^2 - log_2(4) + (-128 mod 7) + round(-136/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-85 + -560/16) * 1) + 2^2 - log_2(4) + (-128 mod 7) + round(-136/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 1780
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. 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$ \\al... | {
"type": "trigonometry",
"seed": 1337,
"index": 1781
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((27 + 686/14) * 10) + 2^3 - log_4(1024) + (385 mod 26) + round(-19/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((27 + 686/14) * 10) + 2^3 - log_4(1024) + (385 mod 26) + round(-19/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 1782
} |
[
{
"role": "user",
"content": "Work through and solve this equation. 33x^2 - 37 - 197x = 62"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 33x^2 - 37 - 197x = 62 $\n\nMove all terms to the left (standard form):\n$ 33x^2 + -197x + -99 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1783
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Compute the indefinite integral: $\\int -8\\sin(1x) + 0\\cos(8x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -8\\sin(1x) + 0\\cos(8x)\\,dx $\n\nUse standard antiderivatives (and ... | {
"type": "calculus",
"seed": 1337,
"index": 1784
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((-56 + 160/10) * 16) + 12^4 - log_5(15625) + (-31 mod 15) + round(81/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-56 + 160/10) * 16) + 12^4 - log_5(15625) + (-31 mod 15) + round(81/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 1785
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Compute $(44+-164) \\bmod 7$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (44+-164) \\bmod 7 $\n\nUse the rule that addition is compatible with reduction modulo $... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1786
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Find the modular inverse of 15 modulo 34, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $15\\cdot a^{-1} \\equiv 1 \\pmod{34}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identi... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1787
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Differentiate with respect to $x$: $f(x) = (-1x + -3)e^{3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-1x + -3)e^{3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-... | {
"type": "calculus",
"seed": 1337,
"index": 1788
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 1789
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? 257 + 123x = -811"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 257 + 123x = -811 $\n\nMove all terms to the left (standard form):\n$ 123x + 1068 = 0 $\n\nIsolate the $x$ term:\n$ 123x = -1068 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 1790
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Evaluate: ((116 + -432/9) * 15) + 12^2 - log_6(1296) + (-329 mod 23) + round(-19/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((116 + -432/9) * 15) + 12^2 - log_6(1296) + (-329 mod 23) + round(-19/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 1791
} |
[
{
"role": "user",
"content": "Find 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": 1792
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Differentiate with respect to $x$: $f(x) = -6x^3 + 9x^2 + 6x + 2$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6x^3 + 9x^2 + 6x + 2 $\n\nApply the standard differentiation rules:\n$ f'(... | {
"type": "calculus",
"seed": 1337,
"index": 1793
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Prove that $f(x)=8x^2+8x+2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=8x^2+8x+2$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 16x + 8 $\n$... | {
"type": "optimization",
"seed": 1337,
"index": 1794
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Find $A^{-1}$ for $A=\\begin{pmatrix}9&9\\\\-6&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 9 & 9 \\\\ -6 & 9 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1795
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Evaluate: ((-109 + 299/23) * 19) + 9^5 - log_10(100) + (354 mod 10) + floor(33/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-109 + 299/23) * 19) + 9^5 - log_10(100) + (354 mod 10) + floor(33... | {
"type": "arithmetic",
"seed": 1337,
"index": 1796
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Evaluate: ((106 + 144/6) * 9) + 11^2 - log_2(2) + (-424 mod 22) + ceil(81/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((106 + 144/6) * 9) + 11^2 - log_2(2) + (-424 mod 22) + ceil(81/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 1797
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Prove that $f(x,y)=\\frac12(7x^2+4y^2)+0x+-5y+-5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+4y^2)+0x+-5y+-5 $\n\n$ \\frac{\\partial^2 f}... | {
"type": "optimization",
"seed": 1337,
"index": 1798
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Evaluate: ((-45 + 736/23) * 3) + 6^3 - log_3(27) + (-294 mod 20) + floor(-25/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-45 + 736/23) * 3) + 6^3 - log_3(27) + (-294 mod 20) + floor(-... | {
"type": "arithmetic",
"seed": 1337,
"index": 1799
} |
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