messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Compute the final answer to this equation. Evaluate: ((-53 + 100/2) * 1) + 4^2 - log_10(1000) + (-308 mod 27) + round(7/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-53 + 100/2) * 1) + 4^2 - log_10(1000) + (-308 mod 27) + round(7/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 6700
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 6701
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Evaluate: ((-130 + 420/14) * 5) + 3^4 - log_5(3125) + (-352 mod 15) + ceil(132/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-130 + 420/14) * 5) + 3^4 - log_5(3125) + (-352 mod 15) + ceil(132/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 6702
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 925x - 277 = 976"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 925x - 277 = 976 $\n\nMove all terms to the left (standard form):\n$ 925x + -1253 = 0 $\n\nIsolate the $x$ term:\n$ 925x = 1253 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6703
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Differentiate with respect to $x$: $f(x) = 1\\sin(1x) + 0\\cos(6x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1\\sin(1x) + 0\\cos(6x) $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 6704
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Evaluate: ((73 + 192/24) * 4) + 12^3 - log_5(125) + (-11 mod 29) + floor(54/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((73 + 192/24) * 4) + 12^3 - log_5(125) + (-11 mod 29) + floor(54/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 6705
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Find the modular inverse of 13 modulo 20, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $13\\cdot a^{-1} \\equiv 1 \\pmod{20}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6706
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Differentiate with respect to $x$: $f(x) = -7e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -7e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-7e^{1x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 6707
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Evaluate: ((136 + 576/18) * 17) + 6^4 - log_4(256) + (-327 mod 7) + ceil(-156/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((136 + 576/18) * 17) + 6^4 - log_4(256) + (-327 mod 7) + ceil(-156/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6708
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Solve for $x$ (in radians): tan(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(1) = 0.785398 $\n\nThe ge... | {
"type": "trigonometry",
"seed": 1337,
"index": 6709
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&-3&2\\\\\\4&-5&-1\\\\\\-2&-5&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}2\\\\\\-1\\\\\\11\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6710
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Differentiate with respect to $x$: $f(x) = -6\\sin(3x) + -6\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6\\sin(3x) + -6\\cos(7x) $\n\nApply the standard differentiation rule... | {
"type": "calculus",
"seed": 1337,
"index": 6711
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \... | {
"type": "optimization",
"seed": 1337,
"index": 6712
} |
[
{
"role": "user",
"content": "Determine the value produced by 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$... | {
"type": "trigonometry",
"seed": 1337,
"index": 6713
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = ... | {
"type": "trigonometry",
"seed": 1337,
"index": 6714
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&-3&-1\\\\\\5&-1&-4\\\\\\-5&1&3\\end{pmatrix},\\quad b=\\begin{pmatrix}12\\\\\\15\\\\\\-12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6715
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 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$ \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 6716
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Prove that $f(x)=10x^2+-7x+2$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+-7x+2$.\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": 6717
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Find $A^{-1}$ for $A=\\begin{pmatrix}-9&-8\\\\6&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -9 & -8 \\\\ 6 & 2 \\end{pmatrix} $\n\nCompute the ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6718
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. 39 + 36x - 113 = -99x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 39 + 36x - 113 = -99x^2 $\n\nMove all terms to the left (standard form):\n$ 99x^2 + 36x + -74 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6719
} |
[
{
"role": "user",
"content": "Solve the equation shown below. 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 general ... | {
"type": "trigonometry",
"seed": 1337,
"index": 6720
} |
[
{
"role": "user",
"content": "Work out the result of 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{\\partial... | {
"type": "optimization",
"seed": 1337,
"index": 6721
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Compute the determinant: $A=\\begin{pmatrix}6&9\\\\0&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}6&9\\\\\\0&1\\end{pmatrix} $\n\nUse $\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6722
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. -929x + 249 = 936"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -929x + 249 = 936 $\n\nMove all terms to the left (standard form):\n$ -929x + -687 = 0 $\n\nIsolate the $x$ term:\n$ -929x = 687 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 6723
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Compute $(-116+114) \\bmod 14$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-116+114) \\bmod 14 $\n\nUse the rule that addition is compatible with reducti... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6724
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 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 in... | {
"type": "calculus",
"seed": 1337,
"index": 6725
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-4&-5\\\\0&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -4 & -5 \\\\ 0 & 2 \\end{pmatrix} $\n\nCompute the ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6726
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Find the modular inverse of 19 modulo 32, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $19\\cdot a^{-1} \\equiv 1 \\pmod{32}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity g... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6727
} |
[
{
"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": 6728
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Compute $(-192+-51) \\bmod 25$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-192+-51) \\bmod 25 $\n\nUse the rule that addition is compatible with reduction mo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6729
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute $(148+11) \\bmod 19$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (148+11) \\bmod 19 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\n$... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6730
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Compute the indefinite integral: $\\int 4x^3 + -6x^2 + -1x + -11\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 4x^3 + -6x^2 + -1x + -11\\,dx $\n\nUse standard antiderivati... | {
"type": "calculus",
"seed": 1337,
"index": 6731
} |
[
{
"role": "user",
"content": "Please work out this equation. Compute $(29+-65) \\bmod 12$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (29+-65) \\bmod 12 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\n$ ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6732
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Compute the indefinite integral: $\\int \\ln(1x + 3)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(1x + 3)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n... | {
"type": "calculus",
"seed": 1337,
"index": 6733
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Prove that $(\\mathbb{Z}_10, +)$ is a group under addition modulo 10."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_10=\\{0,1,\\dots,9\\}$ with operation $+$ modulo $10$.\n\n**Closure:** If $a,b\\in\\mathbb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6734
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Evaluate: ((-35 + 112/4) * 11) + 8^4 - log_5(25) + (-253 mod 15) + ceil(88/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-35 + 112/4) * 11) + 8^4 - log_5(25) + (-253 mod 15) + ceil(88/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 6735
} |
[
{
"role": "user",
"content": "Can you compute this equation? Compute the determinant: $A=\\begin{pmatrix}-4&-8\\\\3&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&-8\\\\\\3&9\\end{pmatrix} $\n\nUse $\\det(A)=ad... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6736
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\... | {
"type": "trigonometry",
"seed": 1337,
"index": 6737
} |
[
{
"role": "user",
"content": "Please calculate this equation. 308 + 615x = 827"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 308 + 615x = 827 $\n\nMove all terms to the left (standard form):\n$ 615x + -519 = 0 $\n\nIsolate the $x$ term:\n$ 615x = 519 $\n\nDivide both sides by the... | {
"type": "linear_equation",
"seed": 1337,
"index": 6738
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: -50 + 192x^2 - 146x = -35"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -50 + 192x^2 - 146x = -35 $\n\nMove all terms to the left (standard form):\n$ 192x^2 + -146x + -15 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6739
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}5&4\\\\\\-8&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}24\\\\\\-30\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}5&4\\\\\\-8&-... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6740
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Compute the determinant: $A=\\begin{pmatrix}-4&9\\\\5&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&9\\\\\\5&9\\end{pmatrix} $\n\nUse $\\d... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6741
} |
[
{
"role": "user",
"content": "Solve the equation shown below. 582 - 219x = -697"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 582 - 219x = -697 $\n\nMove all terms to the left (standard form):\n$ -219x + 1279 = 0 $\n\nIsolate the $x$ term:\n$ -219x = -1279 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6742
} |
[
{
"role": "user",
"content": "Calculate and solve 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{\\partial^2 ... | {
"type": "optimization",
"seed": 1337,
"index": 6743
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Find the modular inverse of 12 modulo 19, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $12\\cdot a^{-1} \\equiv 1 \\pmod{19}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identit... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6744
} |
[
{
"role": "user",
"content": "Please calculate and resolve 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": 6745
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -954 + 907x = -867"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -954 + 907x = -867 $\n\nMove all terms to the left (standard form):\n$ 907x + -87 = 0 $\n\nIsolate the $x$ term:\n$ 907x = 87 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 6746
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Prove that $f(x)=1x^2+2x+6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+2x+6$.\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": 6747
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. 20 - 175x^2 + 187 = -181x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 20 - 175x^2 + 187 = -181x $\n\nMove all terms to the left (standard form):\n$ -175x^2 + 181x + 207 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6748
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 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 $\n\nThe general s... | {
"type": "trigonometry",
"seed": 1337,
"index": 6749
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 39x - 157 + 52 = -50x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 39x - 157 + 52 = -50x^2 $\n\nMove all terms to the left (standard form):\n$ 50x^2 + 39x + -105 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6750
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Prove that $(\\mathbb{Z}_28, +)$ is a group under addition modulo 28."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_28=\\{0,1,\\dots,27\\}$ with operation $+$ modulo $28$.\n\n**Closure:** If $a,b\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6751
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. -144 - 461x = -844"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -144 - 461x = -844 $\n\nMove all terms to the left (standard form):\n$ -461x + 700 = 0 $\n\nIsolate the $x$ term:\n$ -461x = -700 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 6752
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Differentiate with respect to $x$: $f(x) = (-4x + 7)e^{2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-4x + 7)e^{2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\box... | {
"type": "calculus",
"seed": 1337,
"index": 6753
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Compute the determinant: $A=\\begin{pmatrix}5&0\\\\-4&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}5&0\\\\\\-4&9\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6754
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. -725 + 241 = -907x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -725 + 241 = -907x $\n\nMove all terms to the left (standard form):\n$ 907x + -484 = 0 $\n\nIsolate the $x$ term:\n$ 907x = 484 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 6755
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. -81 - 788x = 88"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -81 - 788x = 88 $\n\nMove all terms to the left (standard form):\n$ -788x + -169 = 0 $\n\nIsolate the $x$ term:\n$ -788x = 169 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 6756
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Differentiate with respect to $x$: $f(x) = \\ln(6x + 1)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(6x + 1) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\fra... | {
"type": "calculus",
"seed": 1337,
"index": 6757
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Compute $(-73+91) \\bmod 10$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-73+91) \\bmod 10 $\n\nUse the rule that addition is compatible with reduction modulo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6758
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. 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 gener... | {
"type": "trigonometry",
"seed": 1337,
"index": 6759
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Differentiate with respect to $x$: $f(x) = -3x^3 + -5x^2 + -17x + 1$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3x^3 + -5x^2 + -17x + 1 $\n\nApply the standard differentiation rules:... | {
"type": "calculus",
"seed": 1337,
"index": 6760
} |
[
{
"role": "user",
"content": "Please work out this equation. 10x^2 - 53x - 67 = -43"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10x^2 - 53x - 67 = -43 $\n\nMove all terms to the left (standard form):\n$ 10x^2 + -53x + -24 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6761
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Compute the indefinite integral: $\\int -9\\sin(9x) + -3\\cos(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -9\\sin(9x) + -3\\cos(2x)\\,dx $\n\nUse standard antiderivatives (and i... | {
"type": "calculus",
"seed": 1337,
"index": 6762
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Solve for $x$ (in radians): sin(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 0 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(0) = 0 $\n\nTh... | {
"type": "trigonometry",
"seed": 1337,
"index": 6763
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. 10 - 186x + 177x^2 = 129"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10 - 186x + 177x^2 = 129 $\n\nMove all terms to the left (standard form):\n$ 177x^2 + -186x + -119 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6764
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Evaluate: ((-175 + -960/24) * 3) + 11^2 - log_10(10000) + (-111 mod 16) + ceil(67/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-175 + -960/24) * 3) + 11^2 - log_10(10000) + (-111 mod 16) + cei... | {
"type": "arithmetic",
"seed": 1337,
"index": 6765
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Evaluate: ((-183 + -520/13) * 13) + 4^4 - log_10(100) + (-461 mod 7) + round(-126/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-183 + -520/13) * 13) + 4^4 - log_10(100) + (-461 mod 7) + round(-12... | {
"type": "arithmetic",
"seed": 1337,
"index": 6766
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. -461x - 902 = 43"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -461x - 902 = 43 $\n\nMove all terms to the left (standard form):\n$ -461x + -945 = 0 $\n\nIsolate the $x$ term:\n$ -461x = 945 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 6767
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Compute the indefinite integral: $\\int 6x^3 + -5x^2 + 1x + 20\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 6x^3 + -5x^2 + 1x + 20\\,dx $\n\nUse standard antiderivatives... | {
"type": "calculus",
"seed": 1337,
"index": 6768
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}4&-5&3\\\\\\0&-4&2\\\\\\-1&-3&4\\end{pmatrix},\\quad b=\\begin{pmatrix}-25\\\\\\-6\\\\\\-8\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6769
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&2\\\\\\-1&7\\end{pmatrix},\\quad b=\\begin{pmatrix}30\\\\\\-3\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&2\\\\\\-... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6770
} |
[
{
"role": "user",
"content": "solve Prove that $f(x,y)=\\frac12(4x^2+9y^2)+-4x+3y+6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+9y^2)+-4x+3y+6 $\n\n$ \\frac{\\partial^2 f}{\\partial x^2} = 4,\\quad \\frac{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 6771
} |
[
{
"role": "user",
"content": "solve 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}{\\partial x\\partial y} \... | {
"type": "optimization",
"seed": 1337,
"index": 6772
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. 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$ \\al... | {
"type": "trigonometry",
"seed": 1337,
"index": 6773
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. -30 - 172x^2 - 86x = -22"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -30 - 172x^2 - 86x = -22 $\n\nMove all terms to the left (standard form):\n$ -172x^2 + -86x + -8 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6774
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? 38x - 81 + 142 = -5x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 38x - 81 + 142 = -5x^2 $\n\nMove all terms to the left (standard form):\n$ 5x^2 + 38x + 61 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6775
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Evaluate: ((198 + -120/24) * 13) + 5^4 - log_8(512) + (-61 mod 4) + ceil(116/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((198 + -120/24) * 13) + 5^4 - log_8(512) + (-61 mod 4) + ceil(116/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 6776
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. -37x^2 - 103 - 14x = -89"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -37x^2 - 103 - 14x = -89 $\n\nMove all terms to the left (standard form):\n$ -37x^2 + -14x + -14 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6777
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Compute the indefinite integral: $\\int -5e^{3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -5e^{3x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\... | {
"type": "calculus",
"seed": 1337,
"index": 6778
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. -6 - 153x^2 + 150x = -140"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -6 - 153x^2 + 150x = -140 $\n\nMove all terms to the left (standard form):\n$ -153x^2 + 150x + 134 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6779
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Compute $(170+154) \\bmod 17$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (170+154) \\bmod 17 $\n\nUse the rule that addition is compatible with reductio... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6780
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Evaluate: ((-4 + -630/21) * 8) + 2^3 - log_8(32768) + (204 mod 18) + floor(-96/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-4 + -630/21) * 8) + 2^3 - log_8(32768) + (204 mod 18) + floor(-96/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 6781
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-3&4&4\\\\\\0&-1&-1\\\\\\5&-3&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}14\\\\\\-5\\\\\\-7\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6782
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 887x - 129 = 471"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 887x - 129 = 471 $\n\nMove all terms to the left (standard form):\n$ 887x + -600 = 0 $\n\nIsolate the $x$ term:\n$ 887x = 600 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 6783
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Find the modular inverse of 3 modulo 5, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $3\\cdot a^{-1} \\equiv 1 \\pmod{5}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees inte... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6784
} |
[
{
"role": "user",
"content": "solve Evaluate: ((-67 + 48/24) * 6) + 9^5 - log_3(27) + (-403 mod 24) + round(-51/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-67 + 48/24) * 6) + 9^5 - log_3(27) + (-403 mod 24) + round(-51/2) $\n\nCompute each component:\n$ 48/24 = 2 $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 6785
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((-83 + 250/5) * 7) + 2^5 - log_7(343) + (-199 mod 20) + floor(163/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-83 + 250/5) * 7) + 2^5 - log_7(343) + (-199 mod 20) + floor(163/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 6786
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Differentiate with respect to $x$: $f(x) = \\ln(1x + 6)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(1x + 6) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{1}... | {
"type": "calculus",
"seed": 1337,
"index": 6787
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Evaluate: ((58 + -72/6) * 11) + 2^2 - log_4(16) + (293 mod 20) + round(-17/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((58 + -72/6) * 11) + 2^2 - log_4(16) + (293 mod 20) + round(-17/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 6788
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. 14x^2 - 44 + 196x = -151"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 14x^2 - 44 + 196x = -151 $\n\nMove all terms to the left (standard form):\n$ 14x^2 + 196x + 107 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6789
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Compute $(197+-150) \\bmod 14$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (197+-150) \\bmod 14 $\n\nUse the rule that addition is compatible with reduction... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6790
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. 40x + 60 + 78x^2 = 35"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 40x + 60 + 78x^2 = 35 $\n\nMove all terms to the left (standard form):\n$ 78x^2 + 40x + 25 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6791
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}9&1\\\\\\-6&1\\end{pmatrix},\\quad b=\\begin{pmatrix}-48\\\\\\27\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}9&1\\\\\\-6&1\\end... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6792
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Evaluate: ((64 + -376/8) * 2) + 11^4 - log_9(6561) + (-117 mod 2) + ceil(82/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((64 + -376/8) * 2) + 11^4 - log_9(6561) + (-117 mod 2) + ceil(82/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 6793
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, h... | {
"type": "optimization",
"seed": 1337,
"index": 6794
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}3&-6\\\\\\4&3\\end{pmatrix},\\quad b=\\begin{pmatrix}9\\\\\\23\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}3&-6\\\\\\4&3\\end{... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6795
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Compute $(113+-132) \\bmod 10$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (113+-132) \\bmod 10 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6796
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Evaluate: ((100 + -290/10) * 17) + 11^2 - log_9(81) + (-263 mod 3) + ceil(101/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((100 + -290/10) * 17) + 11^2 - log_9(81) + (-263 mod 3) + ceil(101/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6797
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Evaluate: ((-56 + -280/14) * 6) + 11^3 - log_6(1296) + (-482 mod 14) + round(185/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-56 + -280/14) * 6) + 11^3 - log_6(1296) + (-482 mod 14) + round(18... | {
"type": "arithmetic",
"seed": 1337,
"index": 6798
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. -284 + 231 = -159x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -284 + 231 = -159x $\n\nMove all terms to the left (standard form):\n$ 159x + -53 = 0 $\n\nIsolate the $x$ term:\n$ 159x = 53 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6799
} |
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