messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Please find the solution of this equation. Compute the indefinite integral: $\\int 6e^{-2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 6e^{-2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\... | {
"type": "calculus",
"seed": 1337,
"index": 1800
} |
[
{
"role": "user",
"content": "Solve the following math equation. -936 - 279x = 237"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -936 - 279x = 237 $\n\nMove all terms to the left (standard form):\n$ -279x + -1173 = 0 $\n\nIsolate the $x$ term:\n$ -279x = 1173 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 1801
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-4&0&-1\\\\\\2&1&-5\\\\\\-4&2&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-13\\\\\\22\\\\\\-27\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1802
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. -54 + 549x = 711"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -54 + 549x = 711 $\n\nMove all terms to the left (standard form):\n$ 549x + -765 = 0 $\n\nIsolate the $x$ term:\n$ 549x = 765 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1803
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Compute $(-105+-31) \\bmod 19$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-105+-31) \\bmod 19 $\n\nUse the rule that addition is compatible with reduction modul... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1804
} |
[
{
"role": "user",
"content": "solve: \n\n Differentiate with respect to $x$: $f(x) = (-3x + 2)e^{2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-3x + 2)e^{2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-3e^{2x} + (-3x + 2)\\cdot 2e^{2x}... | {
"type": "calculus",
"seed": 1337,
"index": 1805
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&1&1\\\\\\2&-2&1\\\\\\-3&-2&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}-16\\\\\\8\\\\\\-7\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1806
} |
[
{
"role": "user",
"content": "Provide the solution to the following 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": 1807
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}4&9\\\\\\9&2\\end{pmatrix},\\quad b=\\begin{pmatrix}47\\\\\\51\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}4&9\\\\\\9&2\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1808
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Find $A^{-1}$ for $A=\\begin{pmatrix}-7&5\\\\-2&5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -7 & 5 \\\\ -2 & 5 \\end{pmatrix} $\n\nCompute the det... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1809
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Prove that $(\\mathbb{Z}_11, +)$ is a group under addition modulo 11."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_11=\\{0,1,\\dots,10\\}$ with operation $+$ modulo $11$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1810
} |
[
{
"role": "user",
"content": "solve 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(-\\frac{1}{2}) = -0.463648 $\n\nTh... | {
"type": "trigonometry",
"seed": 1337,
"index": 1811
} |
[
{
"role": "user",
"content": "Please evaluate and compute 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 = \\arctan(... | {
"type": "trigonometry",
"seed": 1337,
"index": 1812
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Find the modular inverse of 4 modulo 29, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $4\\cdot a^{-1} \\equiv 1 \\pmod{29}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1813
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. 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": 1814
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Evaluate: ((82 + 475/19) * 18) + 12^4 - log_5(15625) + (-256 mod 21) + ceil(11/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((82 + 475/19) * 18) + 12^4 - log_5(15625) + (-256 mod 21) + ceil(11/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 1815
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Prove that $f(x)=4x^2+4x+4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+4x+4$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 8x ... | {
"type": "optimization",
"seed": 1337,
"index": 1816
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Evaluate: ((68 + 456/12) * 6) + 8^3 - log_4(64) + (-412 mod 25) + ceil(-182/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((68 + 456/12) * 6) + 8^3 - log_4(64) + (-412 mod 25) + ceil(-182/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 1817
} |
[
{
"role": "user",
"content": "Find the answer to the following 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{\\pa... | {
"type": "optimization",
"seed": 1337,
"index": 1818
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Differentiate with respect to $x$: $f(x) = (1x + 10)e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (1x + 10)e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\box... | {
"type": "calculus",
"seed": 1337,
"index": 1819
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. -34x^2 - 65 + 98x = 150"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -34x^2 - 65 + 98x = 150 $\n\nMove all terms to the left (standard form):\n$ -34x^2 + 98x + -215 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1820
} |
[
{
"role": "user",
"content": "Evaluate the following equation. -37 + 140 + 69x = -19x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -37 + 140 + 69x = -19x^2 $\n\nMove all terms to the left (standard form):\n$ 19x^2 + 69x + 103 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1821
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. 48x - 38 + 88 = -148x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 48x - 38 + 88 = -148x^2 $\n\nMove all terms to the left (standard form):\n$ 148x^2 + 48x + 50 = 0 $\n\nApply the quadratic... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1822
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. -415 + 515x = -144"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -415 + 515x = -144 $\n\nMove all terms to the left (standard form):\n$ 515x + -271 = 0 $\n\nIsolate the $x$ term:\n$ 515x = 271 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 1823
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Evaluate: ((62 + -481/13) * 6) + 5^3 - log_8(32768) + (336 mod 3) + floor(87/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((62 + -481/13) * 6) + 5^3 - log_8(32768) + (336 mod 3) + floor(87/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 1824
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 947x - 849 = 684"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 947x - 849 = 684 $\n\nMove all terms to the left (standard form):\n$ 947x + -1533 = 0 $\n\nIsolate the $x$ term:\n$ 947x = 1533 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 1825
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. 24 + 192 - 113x^2 = -93x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 24 + 192 - 113x^2 = -93x $\n\nMove all terms to the left (standard form):\n$ -113x^2 + 93x + 216 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1826
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Evaluate: ((28 + 920/23) * 14) + 7^3 - log_6(46656) + (-118 mod 24) + round(68/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((28 + 920/23) * 14) + 7^3 - log_6(46656) + (-118 mod 24) + round(68/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 1827
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-7&6\\\\\\3&-6\\end{pmatrix},\\quad b=\\begin{pmatrix}-30\\\\\\30\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-7&6\\\\\\3... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1828
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}0&-2&5\\\\\\-3&0&-5\\\\\\5&1&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}-9\\\\\\15\\\\\\0\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1829
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Evaluate: ((-97 + -1056/24) * 14) + 6^2 - log_6(6) + (196 mod 25) + floor(-52/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-97 + -1056/24) * 14) + 6^2 - log_6(6) + (196 mod 25) + floor(-52/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 1830
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. 608 - 158 = -133x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 608 - 158 = -133x $\n\nMove all terms to the left (standard form):\n$ 133x + 450 = 0 $\n\nIsolate the $x$ term:\n$ 133x = -450 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 1831
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Find the modular inverse of 19 modulo 33, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $19\\cdot a^{-1} \\equiv 1 \\pmod{33}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarant... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1832
} |
[
{
"role": "user",
"content": "solve: -40 - 799 = -288x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -40 - 799 = -288x $\n\nMove all terms to the left (standard form):\n$ 288x + -839 = 0 $\n\nIsolate the $x$ term:\n$ 288x = 839 $\n\nDivide both sides by the coefficient of $x$:\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 1833
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Find the modular inverse of 7 modulo 37, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{37}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantee... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1834
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&-5&5\\\\\\-2&3&5\\\\\\2&-4&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}-35\\\\\\1\\\\\\-4\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1835
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Compute the indefinite integral: $\\int 3\\sin(9x) + 4\\cos(4x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3\\sin(9x) + 4\\cos(4x)\\,dx $\n\nUse standard antiderivatives (and integr... | {
"type": "calculus",
"seed": 1337,
"index": 1836
} |
[
{
"role": "user",
"content": "solve: Compute $(168+-105) \\bmod 18$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (168+-105) \\bmod 18 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\n$ (a+b)\\bmod n = ((a... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1837
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Evaluate: ((81 + -54/18) * 14) + 9^2 - log_10(1000000) + (-356 mod 11) + ceil(-23/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((81 + -54/18) * 14) + 9^2 - log_10(1000000) + (-356 mod 11) + ceil(-23/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 1838
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-9&-1\\\\\\0&9\\end{pmatrix},\\quad b=\\begin{pmatrix}9\\\\\\81\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-9&-1\\\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1839
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. 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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 1840
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Compute $(-196+-110) \\bmod 14$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-196+-110) \\bmod 14 $\n\nUse the rule that addition is compatible with reduc... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1841
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Compute the indefinite integral: $\\int 3\\sin(6x) + -9\\cos(8x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3\\sin(6x) + -9\\cos(8x)\\,dx $\n\nUse standard antiderivatives (and integration... | {
"type": "calculus",
"seed": 1337,
"index": 1842
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. 5 + 59x + 111 = -193x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 5 + 59x + 111 = -193x^2 $\n\nMove all terms to the left (standard form):\n$ 193x^2 + 59x + 116 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1843
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Compute the indefinite integral: $\\int -3\\sin(2x) + 2\\cos(9x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3\\sin(2x) + 2\\cos(9x)\\,dx $\n\nUse standard antiderivatives (and... | {
"type": "calculus",
"seed": 1337,
"index": 1844
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Evaluate: ((147 + 756/21) * 17) + 5^2 - log_9(729) + (-214 mod 16) + ceil(-180/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((147 + 756/21) * 17) + 5^2 - log_9(729) + (-214 mod 16) + ceil(-180/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 1845
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Prove that $f(x)=3x^2+5x+2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=3x^2+5x+2$.\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": 1846
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. 235 + 834x = 61"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 235 + 834x = 61 $\n\nMove all terms to the left (standard form):\n$ 834x + 174 = 0 $\n\nIsolate the $x$ term:\n$ 834x = -174 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1847
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. -47 - 152x^2 - 22x = 154"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -47 - 152x^2 - 22x = 154 $\n\nMove all terms to the left (standard form):\n$ -152x^2 + -22x + -201 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1848
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. -215 - 230x = -689"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -215 - 230x = -689 $\n\nMove all terms to the left (standard form):\n$ -230x + 474 = 0 $\n\nIsolate the $x$ term:\n$ -230x = -474 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1849
} |
[
{
"role": "user",
"content": "Please determine the outcome of 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) = 0 $\n\nThe ge... | {
"type": "trigonometry",
"seed": 1337,
"index": 1850
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Prove that $(\\mathbb{Z}_17, +)$ is a group under addition modulo 17."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_17=\\{0,1,\\dots,16\\}$ with operation $+$ modulo $17$.\n\n**Closure:** If $a,b\\in\\mathb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1851
} |
[
{
"role": "user",
"content": "Can you compute this equation? Prove that $(\\mathbb{Z}_5, +)$ is a group under addition modulo 5."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_5=\\{0,1,\\dots,4\\}$ with operation $+$ modulo $5$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, then $(a+b... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1852
} |
[
{
"role": "user",
"content": "Calculate the answer 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{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 1853
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((80 + 575/25) * 12) + 3^3 - log_2(8) + (-53 mod 15) + round(-35/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((80 + 575/25) * 12) + 3^3 - log_2(8) + (-53 mod 15) + round(-35/2) $\n\nCompute each c... | {
"type": "arithmetic",
"seed": 1337,
"index": 1854
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&1&-1\\\\\\0&-2&-2\\\\\\2&-5&2\\end{pmatrix},\\quad b=\\begin{pmatrix}-5\\\\\\10\\\\\\-2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1855
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Evaluate: ((188 + -315/21) * 16) + 6^5 - log_7(49) + (-39 mod 30) + floor(124/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((188 + -315/21) * 16) + 6^5 - log_7(49) + (-39 mod 30) + floor(124/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 1856
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Compute the determinant: $A=\\begin{pmatrix}-5&-5\\\\-3&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-5&-5\\\\\\-3&4\\end{pmatrix}... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1857
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Prove that $f(x)=10x^2+5x+3$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+5x+3$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 20x + 5 $\... | {
"type": "optimization",
"seed": 1337,
"index": 1858
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=... | {
"type": "optimization",
"seed": 1337,
"index": 1859
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 1860
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. 24x^2 + 173 - 20x = 198"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 24x^2 + 173 - 20x = 198 $\n\nMove all terms to the left (standard form):\n$ 24x^2 + -20x + -25 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1861
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0... | {
"type": "optimization",
"seed": 1337,
"index": 1862
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. 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 $\n\nThe ... | {
"type": "trigonometry",
"seed": 1337,
"index": 1863
} |
[
{
"role": "user",
"content": "Solve the equation shown below. 439 - 727 = 794x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 439 - 727 = 794x $\n\nMove all terms to the left (standard form):\n$ -794x + -288 = 0 $\n\nIsolate the $x$ term:\n$ -794x = 288 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 1864
} |
[
{
"role": "user",
"content": "solve: \n\n Differentiate with respect to $x$: $f(x) = -6x^3 + -2x^2 + 10x + 7$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6x^3 + -2x^2 + 10x + 7 $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-18x^2 + -4x + 10}... | {
"type": "calculus",
"seed": 1337,
"index": 1865
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Compute the indefinite integral: $\\int -8\\sin(2x) + -1\\cos(4x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -8\\sin(2x) + -1\\cos(4x)\\,dx $\n\nUse standard antiderivatives ... | {
"type": "calculus",
"seed": 1337,
"index": 1866
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. -34x + 29 - 184 = -23x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -34x + 29 - 184 = -23x^2 $\n\nMove all terms to the left (standard form):\n$ 23x^2 + -34x + -155 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1867
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Prove that $f(x)=5x^2+0x+-8$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+0x+-8$.\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": 1868
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Compute $(79+-49) \\bmod 24$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (79+-49) \\bmod 24 $\n\nUse the rule that addition is compatible with reduction m... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1869
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Evaluate: ((195 + 850/17) * 15) + 8^2 - log_3(3) + (198 mod 16) + round(133/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((195 + 850/17) * 15) + 8^2 - log_3(3) + (198 mod 16) + round(133/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 1870
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Evaluate: ((-33 + -620/20) * 6) + 5^2 - log_4(64) + (-302 mod 6) + ceil(112/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-33 + -620/20) * 6) + 5^2 - log_4(64) + (-302 mod 6) + ceil(112/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1871
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Compute the indefinite integral: $\\int -2\\sin(1x) + 6\\cos(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -2\\sin(1x) + 6\\cos(6x)\\,dx $\n\nUse standard antiderivatives (and integratio... | {
"type": "calculus",
"seed": 1337,
"index": 1872
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-2&0\\\\-1&-1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -2 & 0 \\\\ -1 & -1 \\end{pmatrix} $\n\nCompute the det... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1873
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-4&5&3\\\\\\-5&5&1\\\\\\-3&-3&0\\end{pmatrix},\\quad b=\\begin{pmatrix}19\\\\\\14\\\\\\12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1874
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. 41 + 113x^2 - 17x = 121"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 41 + 113x^2 - 17x = 121 $\n\nMove all terms to the left (standard form):\n$ 113x^2 + -17x + -80 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1875
} |
[
{
"role": "user",
"content": "Work through and solve this equation. -11x - 186x^2 + 14 = 133"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -11x - 186x^2 + 14 = 133 $\n\nMove all terms to the left (standard form):\n$ -186x^2 + -11x + -119 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1876
} |
[
{
"role": "user",
"content": "Solve the following math equation. 43x^2 - 131x - 91 = -179"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 43x^2 - 131x - 91 = -179 $\n\nMove all terms to the left (standard form):\n$ 43x^2 + -131x + 88 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1877
} |
[
{
"role": "user",
"content": "Please work out this equation. 25 - 14x - 7x^2 = 4"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 25 - 14x - 7x^2 = 4 $\n\nMove all terms to the left (standard form):\n$ -7x^2 + -14x + 21 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1878
} |
[
{
"role": "user",
"content": "solve: -111x + 391 = 27"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -111x + 391 = 27 $\n\nMove all terms to the left (standard form):\n$ -111x + 364 = 0 $\n\nIsolate the $x$ term:\n$ -111x = -364 $\n\nDivide both sides by the coefficient of $x$:\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 1879
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Evaluate: ((-143 + 114/6) * 6) + 6^5 - log_6(7776) + (-316 mod 18) + ceil(51/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-143 + 114/6) * 6) + 6^5 - log_6(7776) + (-316 mod 18) + ceil(51/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 1880
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. -275 - 805x = -14"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -275 - 805x = -14 $\n\nMove all terms to the left (standard form):\n$ -805x + -261 = 0 $\n\nIsolate the $x$ term:\n$ -805x = 261 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 1881
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. -980 + 887x = -977"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -980 + 887x = -977 $\n\nMove all terms to the left (standard form):\n$ 887x + -3 = 0 $\n\nIsolate the $x$ term:\n$ 887x = 3 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 1882
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Find $A^{-1}$ for $A=\\begin{pmatrix}0&-3\\\\-7&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 0 & -3 \\\\ -7 & 4 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1883
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}4&0&4\\\\\\-3&-1&3\\\\\\-4&5&4\\end{pmatrix},\\quad b=\\begin{pmatrix}-4\\\\\\-7\\\\\\16\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1884
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Prove that $f(x)=8x^2+-6x+-5$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=8x^2+-6x+-5$.\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": 1885
} |
[
{
"role": "user",
"content": "Solve this equation accurately. -8 + 121x^2 + 63x = 177"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -8 + 121x^2 + 63x = 177 $\n\nMove all terms to the left (standard form):\n$ 121x^2 + 63x + -185 = 0 $\n\nApply the quadratic formula:\n$ x = \\fr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1886
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Prove that $f(x)=4x^2+-1x+-2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+-1x+-2$.\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": 1887
} |
[
{
"role": "user",
"content": "Can you determine the solution 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).\... | {
"type": "trigonometry",
"seed": 1337,
"index": 1888
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Find the modular inverse of 29 modulo 32, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $29\\cdot a^{-1} \\equiv 1 \\pmod{32}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1889
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, h... | {
"type": "optimization",
"seed": 1337,
"index": 1890
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Evaluate: ((-52 + 675/25) * 2) + 9^4 - log_8(262144) + (-375 mod 5) + round(153/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-52 + 675/25) * 2) + 9^4 - log_8(262144) + (-375 mod 5) + round(15... | {
"type": "arithmetic",
"seed": 1337,
"index": 1891
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. 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 $\n\... | {
"type": "trigonometry",
"seed": 1337,
"index": 1892
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. 15x^2 + 22x + 88 = 135"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 15x^2 + 22x + 88 = 135 $\n\nMove all terms to the left (standard form):\n$ 15x^2 + 22x + -47 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1893
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Find the modular inverse of 7 modulo 10, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{10}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees i... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1894
} |
[
{
"role": "user",
"content": "Solve the following mathematical 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:\... | {
"type": "optimization",
"seed": 1337,
"index": 1895
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Differentiate with respect to $x$: $f(x) = 2x^3 + -5x^2 + 18x + -2$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2x^3 + -5x^2 + 18x + -2 $\n\nApply the standard differentiation rules:\n$ f'(x)... | {
"type": "calculus",
"seed": 1337,
"index": 1896
} |
[
{
"role": "user",
"content": "solve: Prove that $f(x)=8x^2+2x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=8x^2+2x+0$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 16x + 2 $\n$ f''(x) = 16 $\n\nSince... | {
"type": "optimization",
"seed": 1337,
"index": 1897
} |
[
{
"role": "user",
"content": "Can you compute this equation? Differentiate with respect to $x$: $f(x) = -1e^{3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1e^{3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-3e^{3x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 1898
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Compute the indefinite integral: $\\int 3\\sin(6x) + -1\\cos(7x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3\\sin(6x) + -1\\cos(7x)\\,dx $\n\nUse standard antiderivati... | {
"type": "calculus",
"seed": 1337,
"index": 1899
} |
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