messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Please determine the value of this equation. Compute the indefinite integral: $\\int \\ln(6x + 9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(6x + 9)\\,dx $\n\nUse standard antiderivatives (and integration by parts if... | {
"type": "calculus",
"seed": 1337,
"index": 1000
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Solve for $x$ (in radians): cos(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 1001
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Evaluate: ((66 + 64/8) * 16) + 12^4 - log_7(7) + (-13 mod 18) + round(160/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((66 + 64/8) * 16) + 12^4 - log_7(7) + (-13 mod 18) + round(160/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 1002
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-3&3&2\\\\\\1&-1&1\\\\\\2&-4&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}1\\\\\\-7\\\\\\8\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1003
} |
[
{
"role": "user",
"content": "Solve this equation step by step. -46 - 175x + 106 = 106x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -46 - 175x + 106 = 106x^2 $\n\nMove all terms to the left (standard form):\n$ -106x^2 + -175x + 60 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1004
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Evaluate: ((181 + -1034/22) * 16) + 4^3 - log_8(262144) + (-388 mod 7) + round(104/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((181 + -1034/22) * 16) + 4^3 - log_8(262144) + (-388 mod 7) + round(104... | {
"type": "arithmetic",
"seed": 1337,
"index": 1005
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Find the modular inverse of 17 modulo 20, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $17\\cdot a^{-1} \\equiv 1 \\pmod{20}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1006
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Compute the indefinite integral: $\\int (4x + -8)\\sin(4x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (4x + -8)\\sin(4x)\\,dx $\n\nUse standard antiderivatives (and integration by p... | {
"type": "calculus",
"seed": 1337,
"index": 1007
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x^... | {
"type": "optimization",
"seed": 1337,
"index": 1008
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. -675 + 21 = 204x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -675 + 21 = 204x $\n\nMove all terms to the left (standard form):\n$ -204x + -654 = 0 $\n\nIsolate the $x$ term:\n$ -204x = 654 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 1009
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. -706x - 174 = 910"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -706x - 174 = 910 $\n\nMove all terms to the left (standard form):\n$ -706x + -1084 = 0 $\n\nIsolate the $x$ term:\n$ -706x = 1084 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 1010
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. 167 - 768x = -10"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 167 - 768x = -10 $\n\nMove all terms to the left (standard form):\n$ -768x + 177 = 0 $\n\nIsolate the $x$ term:\n$ -768x = -177 $\n\nD... | {
"type": "linear_equation",
"seed": 1337,
"index": 1011
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Find the modular inverse of 23 modulo 39, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $23\\cdot a^{-1} \\equiv 1 \\pmod{39}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantee... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1012
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. -31x^2 + 69 - 47 = 27x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -31x^2 + 69 - 47 = 27x $\n\nMove all terms to the left (standard form):\n$ -31x^2 + -27x + 22 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1013
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-9&-7\\\\\\-2&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-119\\\\\\-38\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-9&-7\\\\\\-2... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1014
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Differentiate with respect to $x$: $f(x) = 7e^{-4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 7e^{-4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-28e^{-4x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 1015
} |
[
{
"role": "user",
"content": "solve: Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(-\\frac{\\sqrt{2}... | {
"type": "trigonometry",
"seed": 1337,
"index": 1016
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. -26x^2 + 75 - 24 = 169x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -26x^2 + 75 - 24 = 169x $\n\nMove all terms to the left (standard form):\n$ -26x^2 + -169x + 51 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1017
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Find the modular inverse of 5 modulo 8, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{8}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantee... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1018
} |
[
{
"role": "user",
"content": "Resolve the equation provided. -6 - 72 + 156x = 95x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -6 - 72 + 156x = 95x^2 $\n\nMove all terms to the left (standard form):\n$ -95x^2 + 156x + -78 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1019
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. 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\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 1020
} |
[
{
"role": "user",
"content": "solve Compute the indefinite integral: $\\int -2e^{-2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -2e^{-2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int -2e^{-2x}\\,dx = \\boxed{... | {
"type": "calculus",
"seed": 1337,
"index": 1021
} |
[
{
"role": "user",
"content": "Find the numerical solution to 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 1022
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Compute the determinant: $A=\\begin{pmatrix}8&-1\\\\-8&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}8&-1\\\\\\-8&4\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1023
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Solve for $x$ (in radians): sin(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -1 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(-1) = -1.5708 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 1024
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Differentiate with respect to $x$: $f(x) = -5e^{4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -5e^{4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-20e^{4x}... | {
"type": "calculus",
"seed": 1337,
"index": 1025
} |
[
{
"role": "user",
"content": "Please calculate this equation. Differentiate with respect to $x$: $f(x) = (4x + 5)e^{5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (4x + 5)e^{5x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{4e^{5x} + (4x + ... | {
"type": "calculus",
"seed": 1337,
"index": 1026
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Find the modular inverse of 19 modulo 30, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $19\\cdot a^{-1} \\equiv 1 \\pmod{30}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1027
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Evaluate: ((-107 + -688/16) * 14) + 6^5 - log_10(10000) + (214 mod 4) + ceil(-167/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-107 + -688/16) * 14) + 6^5 - log_10(10000) + (214 mod 4) + ceil(-1... | {
"type": "arithmetic",
"seed": 1337,
"index": 1028
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 32 + 35x + 67x^2 = -68"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 32 + 35x + 67x^2 = -68 $\n\nMove all terms to the left (standard form):\n$ 67x^2 + 35x + 100 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1029
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n -630 + 758 = 281x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -630 + 758 = 281x $\n\nMove all terms to the left (standard form):\n$ -281x + 128 = 0 $\n\nIsolate the $x$ term:\n$ -281x = -128 $\... | {
"type": "linear_equation",
"seed": 1337,
"index": 1030
} |
[
{
"role": "user",
"content": "Can you compute this equation? Prove that $f(x)=10x^2+-5x+7$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+-5x+7$.\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": 1031
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Evaluate: ((33 + -375/15) * 8) + 6^5 - log_7(49) + (81 mod 30) + round(-74/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((33 + -375/15) * 8) + 6^5 - log_7(49) + (81 mod 30) + round(-74/2) $\n\nCompute each component:\n$ -375/... | {
"type": "arithmetic",
"seed": 1337,
"index": 1032
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&2&1\\\\\\4&4&3\\\\\\4&-4&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}0\\\\\\-2\\\\\\16\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1033
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Evaluate: ((-12 + -506/23) * 8) + 9^4 - log_6(36) + (389 mod 30) + ceil(-90/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-12 + -506/23) * 8) + 9^4 - log_6(36) + (389 mod 30) + ceil(-90/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 1034
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}6&-3\\\\\\-2&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}57\\\\\\26\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}6&-3\\\\\\-2&-... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1035
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Evaluate: ((-68 + -19/19) * 14) + 10^4 - log_7(117649) + (119 mod 23) + round(-162/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-68 + -19/19) * 14) + 10^4 - log_7(117649) + (119 mod 23) + round(-162/... | {
"type": "arithmetic",
"seed": 1337,
"index": 1036
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Evaluate: ((-144 + 544/17) * 17) + 5^5 - log_9(59049) + (-354 mod 18) + floor(149/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-144 + 544/17) * 17) + 5^5 - log_9(59049) + (-354 mod 18) + floor(... | {
"type": "arithmetic",
"seed": 1337,
"index": 1037
} |
[
{
"role": "user",
"content": "solve Evaluate: ((169 + -240/15) * 16) + 10^3 - log_7(343) + (-107 mod 5) + floor(-149/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((169 + -240/15) * 16) + 10^3 - log_7(343) + (-107 mod 5) + floor(-149/2) $\n\nCompute each component:\n$ -2... | {
"type": "arithmetic",
"seed": 1337,
"index": 1038
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. 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\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1039
} |
[
{
"role": "user",
"content": "Calculate the result of the given 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$ \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 1040
} |
[
{
"role": "user",
"content": "Compute and determine the solution to 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 valu... | {
"type": "trigonometry",
"seed": 1337,
"index": 1041
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in 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 $f'(x)=... | {
"type": "optimization",
"seed": 1337,
"index": 1042
} |
[
{
"role": "user",
"content": "Solve the following math equation. 12 - 188x^2 + 171x = -168"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 12 - 188x^2 + 171x = -168 $\n\nMove all terms to the left (standard form):\n$ -188x^2 + 171x + 180 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1043
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. -48 - 191x^2 + 33 = 66x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -48 - 191x^2 + 33 = 66x $\n\nMove all terms to the left (standard form):\n$ -191x^2 + -66x + -15 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1044
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, h... | {
"type": "optimization",
"seed": 1337,
"index": 1045
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. 31x^2 - 134 - 119x = 117"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 31x^2 - 134 - 119x = 117 $\n\nMove all terms to the left (standard form):\n$ 31x^2 + -119x + -251 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1046
} |
[
{
"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 $\n\... | {
"type": "trigonometry",
"seed": 1337,
"index": 1047
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. -820x - 353 = 729"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -820x - 353 = 729 $\n\nMove all terms to the left (standard form):\n$ -820x + -1082 = 0 $\n\nIsolate the $x$ term:\n$ -820x = 1082 $\... | {
"type": "linear_equation",
"seed": 1337,
"index": 1048
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((19 + -224/7) * 6) + 9^5 - log_9(59049) + (-422 mod 2) + round(106/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((19 + -224/7) * 6) + 9^5 - log_9(59049) + (-422 mod 2) + round(106/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1049
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 10 - 199x^2 - 78x = -65"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10 - 199x^2 - 78x = -65 $\n\nMove all terms to the left (standard form):\n$ -199x^2 + -78x + 75 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1050
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -18x^2 + 89x + 80 = 33"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -18x^2 + 89x + 80 = 33 $\n\nMove all terms to the left (standard form):\n$ -18x^2 + 89x + 47 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1051
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Compute $(152+-85) \\bmod 2$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (152+-85) \\bmod 2 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\n... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1052
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Compute the determinant: $A=\\begin{pmatrix}3&-1\\\\7&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&-1\\\\\\7&-8\\end{pmatrix} $\n\nUse $\\det(A)... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1053
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute the determinant: $A=\\begin{pmatrix}-1&9\\\\1&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-1&9\\\\\\1&-2\\end{pmatrix} $\n\nUse $\\det(A)=a... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1054
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. -648 + 262x = -756"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -648 + 262x = -756 $\n\nMove all terms to the left (standard form):\n$ 262x + 108 = 0 $\n\nIsolate the $x$ term:\n$ 262x = -108 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 1055
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Find the modular inverse of 13 modulo 22, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $13\\cdot a^{-1} \\equiv 1 \\pmod{22}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1056
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. -438 - 876 = 135x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -438 - 876 = 135x $\n\nMove all terms to the left (standard form):\n$ -135x + -1314 = 0 $\n\nIsolate the $x$ term:\n$ -135x = 1314 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1057
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. -752x - 312 = 749"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -752x - 312 = 749 $\n\nMove all terms to the left (standard form):\n$ -752x + -1061 = 0 $\n\nIsolate the $x$ term:\n$ -752x = 1061 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1058
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Solve for $x$ (in radians): tan(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha ... | {
"type": "trigonometry",
"seed": 1337,
"index": 1059
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((182 + 176/8) * 11) + 3^2 - log_5(625) + (-19 mod 16) + round(-190/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((182 + 176/8) * 11) + 3^2 - log_5(625) + (-19 mod 16) + round(-190/2) $\n\nCompute eac... | {
"type": "arithmetic",
"seed": 1337,
"index": 1060
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Compute the indefinite integral: $\\int 4\\sin(8x) + -7\\cos(5x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 4\\sin(8x) + -7\\cos(5x)\\,dx $\n\nUse standard antideriva... | {
"type": "calculus",
"seed": 1337,
"index": 1061
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? -18 - 76x - 145 = 168x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -18 - 76x - 145 = 168x^2 $\n\nMove all terms to the left (standard form):\n$ -168x^2 + -76x + -163 = 0 $\n\nApply the quadratic... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1062
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((159 + 170/17) * 14) + 6^5 - log_9(9) + (-323 mod 30) + ceil(-168/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((159 + 170/17) * 14) + 6^5 - log_9(9) + (-323 mod 30) + ceil(-168/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1063
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-4&3\\\\\\-2&6\\end{pmatrix},\\quad b=\\begin{pmatrix}41\\\\\\34\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-4&3... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1064
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Evaluate: ((-112 + -50/10) * 16) + 12^3 - log_6(6) + (-409 mod 24) + round(179/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-112 + -50/10) * 16) + 12^3 - log_6(6) + (-409 mod 24) + round(179/... | {
"type": "arithmetic",
"seed": 1337,
"index": 1065
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. 713 - 748x = 655"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 713 - 748x = 655 $\n\nMove all terms to the left (standard form):\n$ -748x + 58 = 0 $\n\nIsolate the $x$ term:\n$ -748x = -58 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1066
} |
[
{
"role": "user",
"content": "Please calculate this equation. -785x + 56 = 408"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -785x + 56 = 408 $\n\nMove all terms to the left (standard form):\n$ -785x + -352 = 0 $\n\nIsolate the $x$ term:\n$ -785x = 352 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 1067
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 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} & \\f... | {
"type": "optimization",
"seed": 1337,
"index": 1068
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Evaluate: ((122 + 391/23) * 5) + 10^2 - log_7(16807) + (481 mod 6) + ceil(-30/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((122 + 391/23) * 5) + 10^2 - log_7(16807) + (481 mod 6) + ceil(-30/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 1069
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. 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\\mathbb{Z... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1070
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-5&4\\\\\\-2&1\\end{pmatrix},\\quad b=\\begin{pmatrix}-5\\\\\\1\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-5&4\\\\\\-... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1071
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Compute the indefinite integral: $\\int -1e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -1e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n... | {
"type": "calculus",
"seed": 1337,
"index": 1072
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. -808 + 137 = 178x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -808 + 137 = 178x $\n\nMove all terms to the left (standard form):\n$ -178x + -671 = 0 $\n\nIsolate the $x$ term:\n$ -178x = 671 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1073
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Prove that $f(x)=10x^2+-10x+10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+-10x+10$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\... | {
"type": "optimization",
"seed": 1337,
"index": 1074
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal val... | {
"type": "trigonometry",
"seed": 1337,
"index": 1075
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Compute the indefinite integral: $\\int -4x^3 + -1x^2 + -6x + 11\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4x^3 + -1x^2 + -6x + 11\\,dx $\n\nUse standard antiderivatives (and... | {
"type": "calculus",
"seed": 1337,
"index": 1076
} |
[
{
"role": "user",
"content": "Please work out this equation. -991x - 958 = 492"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -991x - 958 = 492 $\n\nMove all terms to the left (standard form):\n$ -991x + -1450 = 0 $\n\nIsolate the $x$ term:\n$ -991x = 1450 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 1077
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, h... | {
"type": "optimization",
"seed": 1337,
"index": 1078
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Evaluate: ((-6 + 720/20) * 3) + 12^4 - log_6(216) + (384 mod 21) + round(71/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-6 + 720/20) * 3) + 12^4 - log_6(216) + (384 mod 21) + round(71/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 1079
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Differentiate with respect to $x$: $f(x) = -3\\sin(8x) + 9\\cos(8x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3\\sin(8x) + 9\\cos(8x) $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 1080
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. -17 - 157x^2 + 160x = 76"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -17 - 157x^2 + 160x = 76 $\n\nMove all terms to the left (standard form):\n$ -157x^2 + 160x + -93 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1081
} |
[
{
"role": "user",
"content": "Please find the value of this math 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}_... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1082
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Compute the indefinite integral: $\\int 3x^3 + -8x^2 + -9x + 16\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3x^3 + -8x^2 + -9x + 16\\,dx $\n\nUse standard antiderivatives (and i... | {
"type": "calculus",
"seed": 1337,
"index": 1083
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&-7\\\\\\7&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}-17\\\\\\25\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&-7\\\\\\7&-4\\en... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1084
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Solve for $x$ (in radians): tan(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = ... | {
"type": "trigonometry",
"seed": 1337,
"index": 1085
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. 19 + 148x^2 - 27 = 70x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 19 + 148x^2 - 27 = 70x $\n\nMove all terms to the left (standard form):\n$ 148x^2 + -70x + -8 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1086
} |
[
{
"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": 1087
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. 543x + 891 = 486"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 543x + 891 = 486 $\n\nMove all terms to the left (standard form):\n$ 543x + 405 = 0 $\n\nIsolate the $x$ term:\n$ 543x = -405 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 1088
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Solve for $x$ (in radians): cos(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 0 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(0) = 1.5708 $\n\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 1089
} |
[
{
"role": "user",
"content": "solve 14x^2 + 87x + 147 = 117"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 14x^2 + 87x + 147 = 117 $\n\nMove all terms to the left (standard form):\n$ 14x^2 + 87x + 30 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1090
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. -883 + 951x = 732"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -883 + 951x = 732 $\n\nMove all terms to the left (standard form):\n$ 951x + -1615 = 0 $\n\nIsolate the $x$ term:\n$ 951x = 1615 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 1091
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. 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": 1092
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Compute the indefinite integral: $\\int -2x^3 + 1x^2 + 1x + -16\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -2x^3 + 1x^2 + 1x + -16\\,dx $\n\nUse standard antiderivatives (an... | {
"type": "calculus",
"seed": 1337,
"index": 1093
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. -552 - 89x = -783"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -552 - 89x = -783 $\n\nMove all terms to the left (standard form):\n$ -89x + 231 = 0 $\n\nIsolate the $x$ term:\n$ -89x = -231 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1094
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. -146 - 349x = -691"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -146 - 349x = -691 $\n\nMove all terms to the left (standard form):\n$ -349x + 545 = 0 $\n\nIsolate the $x$ term:\n$ -349x = -545 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1095
} |
[
{
"role": "user",
"content": "Solve the equation shown below. 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": 1096
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Evaluate: ((-142 + -400/25) * 5) + 9^5 - log_4(16) + (-404 mod 18) + round(-10/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-142 + -400/25) * 5) + 9^5 - log_4(16) + (-404 mod 18) + roun... | {
"type": "arithmetic",
"seed": 1337,
"index": 1097
} |
[
{
"role": "user",
"content": "Can you compute this equation? Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 1098
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Differentiate with respect to $x$: $f(x) = 3x^3 + -8x^2 + -18x + -4$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3x^3 + -8x^2 + -18x + -4 $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 1099
} |
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