messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 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$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 3700
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 580 - 49 = -912x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 580 - 49 = -912x $\n\nMove all terms to the left (standard form):\n$ 912x + 531 = 0 $\n\nIsolate the $x$ term:\n$ 912x = -531 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 3701
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Differentiate with respect to $x$: $f(x) = 6x^3 + 1x^2 + 14x + 1$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 6x^3 + 1x^2 + 14x + 1 $\n\nApply the standard differentiation rules:\n$ f'(x... | {
"type": "calculus",
"seed": 1337,
"index": 3702
} |
[
{
"role": "user",
"content": "Please solve this math problem. -742 + 774 = -785x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -742 + 774 = -785x $\n\nMove all terms to the left (standard form):\n$ 785x + 32 = 0 $\n\nIsolate the $x$ term:\n$ 785x = -32 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 3703
} |
[
{
"role": "user",
"content": "solve: Differentiate with respect to $x$: $f(x) = \\ln(6x + -9)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(6x + -9) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{6}{6x + -9}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 3704
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hen... | {
"type": "optimization",
"seed": 1337,
"index": 3705
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 24 + 160x + 124 = 103x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 24 + 160x + 124 = 103x^2 $\n\nMove all terms to the left (standard form):\n$ -103x^2 + 160x + 148 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3706
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. -7 - 187 - 190x = -106x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -7 - 187 - 190x = -106x^2 $\n\nMove all terms to the left (standard form):\n$ 106x^2 + -190x + -194 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3707
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Find $A^{-1}$ for $A=\\begin{pmatrix}1&-6\\\\0&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 1 & -6 \\\\ 0 & -2 \\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3708
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 3x^2 + 2 + 160x = 164"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 3x^2 + 2 + 160x = 164 $\n\nMove all terms to the left (standard form):\n$ 3x^2 + 160x + -162 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3709
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Prove that $(\\mathbb{Z}_16, +)$ is a group under addition modulo 16."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_16=\\{0,1,\\dots,15\\}$ with operation $+$ modulo $16$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, th... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3710
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Solve for $x$ (in radians): sin(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsi... | {
"type": "trigonometry",
"seed": 1337,
"index": 3711
} |
[
{
"role": "user",
"content": "Please solve this math problem. Differentiate with respect to $x$: $f(x) = 2x^3 + -1x^2 + 12x + 10$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2x^3 + -1x^2 + 12x + 10 $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxe... | {
"type": "calculus",
"seed": 1337,
"index": 3712
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Evaluate: ((89 + 425/25) * 11) + 12^5 - log_6(6) + (258 mod 3) + round(-126/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((89 + 425/25) * 11) + 12^5 - log_6(6) + (258 mod 3) + round(-126/... | {
"type": "arithmetic",
"seed": 1337,
"index": 3713
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x... | {
"type": "optimization",
"seed": 1337,
"index": 3714
} |
[
{
"role": "user",
"content": "solve: Solve for $x$ (in radians): sin(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(\\frac{1}{2}) = 0.523599 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 3715
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Compute $(-197+-169) \\bmod 6$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-197+-169) \\bmod 6 $\n\nUse the rule that addition is compatible with redu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3716
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Evaluate: ((133 + 44/22) * 6) + 10^4 - log_6(1296) + (-16 mod 18) + round(54/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((133 + 44/22) * 6) + 10^4 - log_6(1296) + (-16 mod 18) + round(54/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 3717
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&5&-5\\\\\\-5&3&1\\\\\\-4&4&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}13\\\\\\31\\\\\\33\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3718
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&1&-4\\\\\\0&-3&2\\\\\\-4&-2&5\\end{pmatrix},\\quad b=\\begin{pmatrix}7\\\\\\1\\\\\\-19\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by Gau... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3719
} |
[
{
"role": "user",
"content": "Please find and report the solution to 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\... | {
"type": "trigonometry",
"seed": 1337,
"index": 3720
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Prove that $(\\mathbb{Z}_3, +)$ is a group under addition modulo 3."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_3=\\{0,1,\\dots,2\\}$ with operation $+$ modulo $3$.\n\n**Closure:** If $a,b\\in\\mathbb{Z... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3721
} |
[
{
"role": "user",
"content": "Solve the following math equation. -29 - 26x^2 + 139x = 50"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -29 - 26x^2 + 139x = 50 $\n\nMove all terms to the left (standard form):\n$ -26x^2 + 139x + -79 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3722
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: 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 = \\arcsin(\\frac{\\sq... | {
"type": "trigonometry",
"seed": 1337,
"index": 3723
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Evaluate: ((80 + -564/12) * 19) + 10^4 - log_2(32) + (-125 mod 15) + round(-162/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((80 + -564/12) * 19) + 10^4 - log_2(32) + (-125 mod 15) + round(-16... | {
"type": "arithmetic",
"seed": 1337,
"index": 3724
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute the indefinite integral: $\\int \\ln(3x + 7)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(3x + 7)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 3725
} |
[
{
"role": "user",
"content": "Please evaluate and solve 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": 3726
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Differentiate with respect to $x$: $f(x) = -9\\sin(9x) + 5\\cos(3x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -9\\sin(9x) + 5\\cos(3x) $\n\nApply the standard differentiation rules:\n$ f'(x) ... | {
"type": "calculus",
"seed": 1337,
"index": 3727
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Compute the indefinite integral: $\\int \\ln(2x + -2)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(2x + -2)\\,dx $\n\nUse standard antiderivatives (and integration by part... | {
"type": "calculus",
"seed": 1337,
"index": 3728
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Compute the indefinite integral: $\\int (3x + 5)\\sin(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (3x + 5)\\sin(2x)\\,dx $\n\nUse standard antiderivatives (and integration by ... | {
"type": "calculus",
"seed": 1337,
"index": 3729
} |
[
{
"role": "user",
"content": "Find 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 $f'(x)=0$, henc... | {
"type": "optimization",
"seed": 1337,
"index": 3730
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. 197 - 524 = 881x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 197 - 524 = 881x $\n\nMove all terms to the left (standard form):\n$ -881x + -327 = 0 $\n\nIsolate the $x$ term:\n$ -881x = 327 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 3731
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Compute the indefinite integral: $\\int -3x^3 + -4x^2 + 4x + 19\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3x^3 + -4x^2 + 4x + 19\\,dx $\n\nUse standard antiderivatives (and integra... | {
"type": "calculus",
"seed": 1337,
"index": 3732
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hen... | {
"type": "optimization",
"seed": 1337,
"index": 3733
} |
[
{
"role": "user",
"content": "Compute the final answer to 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": 3734
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Find the modular inverse of 25 modulo 38, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $25\\cdot a^{-1} \\equiv 1 \\pmod{38}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integers $x,y$ with:\n$... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3735
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. 174x + 405 = 681"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 174x + 405 = 681 $\n\nMove all terms to the left (standard form):\n$ 174x + -276 = 0 $\n\nIsolate the $x$ term:\n$ 174x = 276 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 3736
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Prove that $f(x)=5x^2+-2x+-4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+-2x+-4$.\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": 3737
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Compute the indefinite integral: $\\int (-6x + 6)\\sin(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-6x + 6)\\sin(2x)\\,dx $\n\nUse standard antiderivatives (and integrat... | {
"type": "calculus",
"seed": 1337,
"index": 3738
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Evaluate: ((170 + 875/25) * 9) + 8^4 - log_7(343) + (-293 mod 12) + floor(127/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((170 + 875/25) * 9) + 8^4 - log_7(343) + (-293 mod 12) + floor(127/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 3739
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Differentiate with respect to $x$: $f(x) = -4e^{-5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -4e^{-5x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{20e^{-5x}} $"
... | {
"type": "calculus",
"seed": 1337,
"index": 3740
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. 20x^2 - 65 - 84 = 39x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 20x^2 - 65 - 84 = 39x $\n\nMove all terms to the left (standard form):\n$ 20x^2 + -39x + -149 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3741
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&0&-2\\\\\\-3&-5&3\\\\\\-5&5&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}4\\\\\\14\\\\\\-12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3742
} |
[
{
"role": "user",
"content": "Please solve this math problem. Differentiate with respect to $x$: $f(x) = \\ln(7x + 5)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(7x + 5) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{7}{7x + 5}} $... | {
"type": "calculus",
"seed": 1337,
"index": 3743
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Prove that $f(x,y)=\\frac12(5x^2+7y^2)+-6x+4y+8$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(5x^2+7y^2)+-6x+4y+8 $\n\n$ \\frac{\\partial... | {
"type": "optimization",
"seed": 1337,
"index": 3744
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-4&6\\\\\\2&7\\end{pmatrix},\\quad b=\\begin{pmatrix}-30\\\\\\-35\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-4&6\\\\\\2&7\\end... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3745
} |
[
{
"role": "user",
"content": "Determine the solution of the given 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 $f'(x)=0$, hen... | {
"type": "optimization",
"seed": 1337,
"index": 3746
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-3&5&0\\\\\\1&5&2\\\\\\-4&1&2\\end{pmatrix},\\quad b=\\begin{pmatrix}-11\\\\\\-9\\\\\\-15\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by Ga... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3747
} |
[
{
"role": "user",
"content": "Please work out this equation. 210x - 90 = -246"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 210x - 90 = -246 $\n\nMove all terms to the left (standard form):\n$ 210x + 156 = 0 $\n\nIsolate the $x$ term:\n$ 210x = -156 $\n\nDivide both sides by the ... | {
"type": "linear_equation",
"seed": 1337,
"index": 3748
} |
[
{
"role": "user",
"content": "Please calculate this equation. Differentiate with respect to $x$: $f(x) = (-4x + -3)e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-4x + -3)e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-4e^{1x} + (... | {
"type": "calculus",
"seed": 1337,
"index": 3749
} |
[
{
"role": "user",
"content": "Calculate the answer 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 $f'(x)=0$, hence:\n$... | {
"type": "optimization",
"seed": 1337,
"index": 3750
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Evaluate: ((189 + 720/15) * 18) + 8^5 - log_2(8) + (-413 mod 7) + ceil(2/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((189 + 720/15) * 18) + 8^5 - log_2(8) + (-413 mod 7) + ceil(2/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 3751
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 21 + 180 - 95x = -142x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 21 + 180 - 95x = -142x^2 $\n\nMove all terms to the left (standard form):\n$ 142x^2 + -95x + 201 = 0 $\n\nApply the quadratic... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3752
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. 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$ \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 3753
} |
[
{
"role": "user",
"content": "Can you compute this equation? -130x + 953 = -660"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -130x + 953 = -660 $\n\nMove all terms to the left (standard form):\n$ -130x + 1613 = 0 $\n\nIsolate the $x$ term:\n$ -130x = -1613 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 3754
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Prove that $f(x)=4x^2+-8x+-4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+-8x+-4$.\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": 3755
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Find the modular inverse of 19 modulo 24, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $19\\cdot a^{-1} \\equiv 1 \\pmod{24}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3756
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 748x + 468 = 634"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 748x + 468 = 634 $\n\nMove all terms to the left (standard form):\n$ 748x + -166 = 0 $\n\nIsolate the $x$ term:\n$ 748x = 166 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 3757
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. -44 + 164x^2 - 17 = -72x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -44 + 164x^2 - 17 = -72x $\n\nMove all terms to the left (standard form):\n$ 164x^2 + 72x + -61 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3758
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 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": 3759
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Find the modular inverse of 7 modulo 31, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{31}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3760
} |
[
{
"role": "user",
"content": "solve - 127x - 21x^2 = -80"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ - 127x - 21x^2 = -80 $\n\nMove all terms to the left (standard form):\n$ -21x^2 + -127x + 80 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3761
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Differentiate with respect to $x$: $f(x) = 9\\sin(9x) + -3\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 9\\sin(9x) + -3\\cos(7x) $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 3762
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Find $A^{-1}$ for $A=\\begin{pmatrix}-3&-2\\\\-3&0\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -3 & -2 \\\\ -3 & 0 \\end{pmatrix} $\n\nCompute the determina... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3763
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}2&-6\\\\\\3&9\\end{pmatrix},\\quad b=\\begin{pmatrix}24\\\\\\-72\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}2&-6\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3764
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. -29 + 12x^2 + 67 = 97x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -29 + 12x^2 + 67 = 97x $\n\nMove all terms to the left (standard form):\n$ 12x^2 + -97x + 38 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3765
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 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 gen... | {
"type": "trigonometry",
"seed": 1337,
"index": 3766
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$... | {
"type": "optimization",
"seed": 1337,
"index": 3767
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 3768
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. -388x - 856 = -342"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -388x - 856 = -342 $\n\nMove all terms to the left (standard form):\n$ -388x + -514 = 0 $\n\nIsolate the $x$ term:\n$ -388x = 514 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 3769
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Compute the determinant: $A=\\begin{pmatrix}-1&2\\\\4&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-1&2\\\\\\4&4\\end{pmatrix} $\n\nUse $\\det(A)=ad-b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3770
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Compute $(-60+38) \\bmod 23$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-60+38) \\bmod 23 $\n\nUse the rule that addition is compatible with re... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3771
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. 14 + 114x^2 + 51x = -59"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 14 + 114x^2 + 51x = -59 $\n\nMove all terms to the left (standard form):\n$ 114x^2 + 51x + 73 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3772
} |
[
{
"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": 3773
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Evaluate: ((-143 + -675/15) * 11) + 9^2 - log_5(15625) + (198 mod 2) + ceil(90/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-143 + -675/15) * 11) + 9^2 - log_5(15625) + (198 mod 2) + ceil(90/... | {
"type": "arithmetic",
"seed": 1337,
"index": 3774
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. -659 - 346x = -410"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -659 - 346x = -410 $\n\nMove all terms to the left (standard form):\n$ -346x + -249 = 0 $\n\nIsolate the $x$ term:\n$ -346x = 249 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 3775
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. -20 + 63 + 30x = -174x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -20 + 63 + 30x = -174x^2 $\n\nMove all terms to the left (standard form):\n$ 174x^2 + 30x + 43 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3776
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Compute the determinant: $A=\\begin{pmatrix}-4&1\\\\1&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&1\\\\\\1&-4\\end{pmatrix} $\n\nUse... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3777
} |
[
{
"role": "user",
"content": "Work out the result of this equation. 6x^2 + 96 - 101 = -179x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 6x^2 + 96 - 101 = -179x $\n\nMove all terms to the left (standard form):\n$ 6x^2 + 179x + -5 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3778
} |
[
{
"role": "user",
"content": "Please calculate 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 f}{... | {
"type": "optimization",
"seed": 1337,
"index": 3779
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Compute the determinant: $A=\\begin{pmatrix}5&-1\\\\-7&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}5&-1\\\\\\-7&9\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3780
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Evaluate: ((-141 + 232/8) * 1) + 8^5 - log_10(10) + (458 mod 29) + floor(-139/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-141 + 232/8) * 1) + 8^5 - log_10(10) + (458 mod 29) + floor(-139/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 3781
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 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$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 3782
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Compute the indefinite integral: $\\int 5\\sin(5x) + 0\\cos(7x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 5\\sin(5x) + 0\\cos(7x)\\,dx $\n\nUse standard antiderivatives (and i... | {
"type": "calculus",
"seed": 1337,
"index": 3783
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Compute $(9+-90) \\bmod 17$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (9+-90) \\bmod 17 $\n\nUse the rule that addition is compatible with reduction modulo $... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3784
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Evaluate: ((-68 + 36/6) * 2) + 11^3 - log_2(4) + (9 mod 8) + floor(-91/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-68 + 36/6) * 2) + 11^3 - log_2(4) + (9 mod 8) + floor(-91/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 3785
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Compute the indefinite integral: $\\int \\ln(3x + -1)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(3x + -1)\\,dx $\n\nUse standard antiderivatives (and integration by par... | {
"type": "calculus",
"seed": 1337,
"index": 3786
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Evaluate: ((134 + -174/6) * 6) + 2^4 - log_7(2401) + (-308 mod 26) + floor(-3/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((134 + -174/6) * 6) + 2^4 - log_7(2401) + (-308 mod 26) + floor(-3/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 3787
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Prove that $f(x)=5x^2+3x+6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+3x+6$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$... | {
"type": "optimization",
"seed": 1337,
"index": 3788
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((-76 + 286/22) * 15) + 3^4 - log_10(1000000) + (422 mod 8) + round(-162/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-76 + 286/22) * 15) + 3^4 - log_10(1000000) + (422 mod 8) + round(-162/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 3789
} |
[
{
"role": "user",
"content": "Find the solution to the following 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": 3790
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}5&1\\\\\\3&0\\end{pmatrix},\\quad b=\\begin{pmatrix}12\\\\\\3\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}5&1\\\\\\3&0\\end... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3791
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-9&1\\\\\\3&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}-53\\\\\\55\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-9&1\\\\\\3&-5\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 3792
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Differentiate with respect to $x$: $f(x) = \\ln(9x + -8)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(9x + -8) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\b... | {
"type": "calculus",
"seed": 1337,
"index": 3793
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Compute $(132+-115) \\bmod 6$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (132+-115) \\bmod 6 $\n\nUse the rule that addition is compatible with reducti... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3794
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Compute $(-148+-38) \\bmod 6$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-148+-38) \\bmod 6 $\n\nUse the rule that addition is compatible with... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 3795
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. -95 - 356x = 359"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -95 - 356x = 359 $\n\nMove all terms to the left (standard form):\n$ -356x + -454 = 0 $\n\nIsolate the $x$ term:\n$ -356x = 454 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 3796
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. 37x^2 - 28 + 14 = 109x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 37x^2 - 28 + 14 = 109x $\n\nMove all terms to the left (standard form):\n$ 37x^2 + -109x + -14 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 3797
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n -13 - 350x = -27"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -13 - 350x = -27 $\n\nMove all terms to the left (standard form):\n$ -350x + 14 = 0 $\n\nIsolate the $x$ term:\n$ -350x = -14 $\n\nD... | {
"type": "linear_equation",
"seed": 1337,
"index": 3798
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Evaluate: ((-169 + -176/22) * 13) + 4^4 - log_2(16) + (-183 mod 27) + ceil(110/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-169 + -176/22) * 13) + 4^4 - log_2(16) + (-183 mod 27) + ceil(110/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 3799
} |
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