messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Solve the following mathematical problem. -16x - 27 - 130x^2 = -142"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -16x - 27 - 130x^2 = -142 $\n\nMove all terms to the left (standard form):\n$ -130x^2 + -16x + 115 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6800
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 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 $\n\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 6801
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. 13 + 164x^2 - 107 = 47x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 13 + 164x^2 - 107 = 47x $\n\nMove all terms to the left (standard form):\n$ 164x^2 + -47x + -94 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6802
} |
[
{
"role": "user",
"content": "Can you solve the equation below? -37 + 89x^2 - 179 = 136x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -37 + 89x^2 - 179 = 136x $\n\nMove all terms to the left (standard form):\n$ 89x^2 + -136x + -216 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6803
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. -42 + 129x - 194 = 32x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -42 + 129x - 194 = 32x^2 $\n\nMove all terms to the left (standard form):\n$ -32x^2 + 129x + -236 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6804
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 6805
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Compute the determinant: $A=\\begin{pmatrix}9&1\\\\-5&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}9&1\\\\\\-5&-6\\end{pmatrix} $\n\nUse... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6806
} |
[
{
"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\nTh... | {
"type": "trigonometry",
"seed": 1337,
"index": 6807
} |
[
{
"role": "user",
"content": "Please work out this equation. Prove that $f(x)=3x^2+6x+6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=3x^2+6x+6$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 6x + 6 $\n$ ... | {
"type": "optimization",
"seed": 1337,
"index": 6808
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Evaluate: ((-26 + -154/14) * 19) + 5^4 - log_5(15625) + (95 mod 25) + round(72/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-26 + -154/14) * 19) + 5^4 - log_5(15625) + (95 mod 25) + round(72/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 6809
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Compute $(-148+160) \\bmod 25$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-148+160) \\bmod 25 $\n\nUse the rule that addition is compatible with reduct... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6810
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((6 + 527/17) * 13) + 8^3 - log_2(8) + (-335 mod 30) + ceil(20/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((6 + 527/17) * 13) + 8^3 - log_2(8) + (-335 mod 30) + ceil(20/2) $\n\nCompute each componen... | {
"type": "arithmetic",
"seed": 1337,
"index": 6811
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Differentiate with respect to $x$: $f(x) = -6x^3 + -5x^2 + 14x + 0$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6x^3 + -5x^2 + 14x + 0 $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 6812
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Evaluate: ((-1 + 539/11) * 12) + 12^4 - log_6(1296) + (399 mod 22) + round(-163/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-1 + 539/11) * 12) + 12^4 - log_6(1296) + (399 mod 22) + round(-163/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 6813
} |
[
{
"role": "user",
"content": "Work out the result of this equation. -460 + 222x = 887"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -460 + 222x = 887 $\n\nMove all terms to the left (standard form):\n$ 222x + -1347 = 0 $\n\nIsolate the $x$ term:\n$ 222x = 1347 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 6814
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}8&-2\\\\7&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 8 & -2 \\\\ 7 & -3 \\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6815
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Differentiate with respect to $x$: $f(x) = 8e^{-2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 8e^{-2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-16e^{-2x}} ... | {
"type": "calculus",
"seed": 1337,
"index": 6816
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. -225x - 552 = 741"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -225x - 552 = 741 $\n\nMove all terms to the left (standard form):\n$ -225x + -1293 = 0 $\n\nIsolate the $x$ term:\n$ -225x = 1293 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 6817
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Prove that $f(x,y)=\\frac12(1x^2+5y^2)+-3x+-2y+-5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+5y^2)+-3x+-2y+-5 $\n\n$ \\frac{\\partial^2 ... | {
"type": "optimization",
"seed": 1337,
"index": 6818
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Evaluate: ((-81 + 420/10) * 3) + 9^4 - log_3(729) + (444 mod 20) + round(-168/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-81 + 420/10) * 3) + 9^4 - log_3(729) + (444 mod 20) + round(-168/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6819
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? 20x^2 - 61 + 24x = 76"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 20x^2 - 61 + 24x = 76 $\n\nMove all terms to the left (standard form):\n$ 20x^2 + 24x + -137 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6820
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? 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\nThe general solu... | {
"type": "trigonometry",
"seed": 1337,
"index": 6821
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Solve for $x$ (in radians): cos(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(... | {
"type": "trigonometry",
"seed": 1337,
"index": 6822
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. 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(\\f... | {
"type": "trigonometry",
"seed": 1337,
"index": 6823
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\... | {
"type": "optimization",
"seed": 1337,
"index": 6824
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. 36 - 59 - 42x = 163x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 36 - 59 - 42x = 163x^2 $\n\nMove all terms to the left (standard form):\n$ -163x^2 + -42x + -23 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6825
} |
[
{
"role": "user",
"content": "Please solve this math problem. Evaluate: ((20 + -240/5) * 12) + 12^3 - log_5(15625) + (50 mod 3) + round(-42/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((20 + -240/5) * 12) + 12^3 - log_5(15625) + (50 mod 3) + round(-42/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 6826
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-4&9\\\\\\8&-6\\end{pmatrix},\\quad b=\\begin{pmatrix}75\\\\\\-66\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-4&9\\\\\\8&-6... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6827
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Evaluate: ((-188 + -120/15) * 6) + 7^4 - log_7(117649) + (-213 mod 24) + ceil(51/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-188 + -120/15) * 6) + 7^4 - log_7(117649) + (-213 mod 24) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 6828
} |
[
{
"role": "user",
"content": "Can you solve the equation below? -15x^2 - 133x - 132 = -115"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -15x^2 - 133x - 132 = -115 $\n\nMove all terms to the left (standard form):\n$ -15x^2 + -133x + -17 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6829
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Find the modular inverse of 33 modulo 34, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $33\\cdot a^{-1} \\equiv 1 \\pmod{34}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6830
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Compute the indefinite integral: $\\int 3e^{-2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3e^{-2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed... | {
"type": "calculus",
"seed": 1337,
"index": 6831
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Differentiate with respect to $x$: $f(x) = 1x^3 + 7x^2 + -10x + 20$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 1x^3 + 7x^2 + -10x + 20 $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 6832
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n -573x + 740 = -790"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -573x + 740 = -790 $\n\nMove all terms to the left (standard form):\n$ -573x + 1530 = 0 $\n\nIsolate the $x$ term:\n$ -573x = -153... | {
"type": "linear_equation",
"seed": 1337,
"index": 6833
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Solve for $x$ (in radians): cos(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -1 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(-1) = 3.14159 $\n\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 6834
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. -3x + 100x^2 - 145 = 83"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -3x + 100x^2 - 145 = 83 $\n\nMove all terms to the left (standard form):\n$ 100x^2 + -3x + -228 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6835
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Solve for $x$ (in radians): cos(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 1 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(1) = 0 $\n\nThe general s... | {
"type": "trigonometry",
"seed": 1337,
"index": 6836
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&3&-3\\\\\\0&-4&1\\\\\\4&5&5\\end{pmatrix},\\quad b=\\begin{pmatrix}-14\\\\\\11\\\\\\9\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6837
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. 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(\\f... | {
"type": "trigonometry",
"seed": 1337,
"index": 6838
} |
[
{
"role": "user",
"content": "Can you compute this equation? -390 + 772 = -164x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -390 + 772 = -164x $\n\nMove all terms to the left (standard form):\n$ 164x + 382 = 0 $\n\nIsolate the $x$ term:\n$ 164x = -382 $\n\nDivide both sides by ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6839
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Prove that $f(x,y)=\\frac12(8x^2+6y^2)+-2x+2y+-5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(8x^2+6y^2)+-2x+2y+-5 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 6840
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. 45x - 18 - 117 = 98x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 45x - 18 - 117 = 98x^2 $\n\nMove all terms to the left (standard form):\n$ -98x^2 + 45x + -135 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6841
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Evaluate: ((-87 + -533/13) * 18) + 5^4 - log_4(4096) + (343 mod 4) + floor(191/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-87 + -533/13) * 18) + 5^4 - log_4(4096) + (343 mod 4) + floor(191/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 6842
} |
[
{
"role": "user",
"content": "solve: Compute the determinant: $A=\\begin{pmatrix}9&-7\\\\1&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}9&-7\\\\\\1&-3\\end{pmatrix} $\n\nUse $\\det(A)=ad-bc$: \n$ \\det(A) = (9... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6843
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. -32x^2 + 193 - 181 = 68x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -32x^2 + 193 - 181 = 68x $\n\nMove all terms to the left (standard form):\n$ -32x^2 + -68x + 12 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6844
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? 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(-\\f... | {
"type": "trigonometry",
"seed": 1337,
"index": 6845
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n -48 + 123 - 21x^2 = 193x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -48 + 123 - 21x^2 = 193x $\n\nMove all terms to the left (standard form):\n$ -21x^2 + -193x + 75 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6846
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Evaluate: ((-126 + 26/13) * 5) + 9^3 - log_2(4) + (59 mod 25) + ceil(126/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-126 + 26/13) * 5) + 9^3 - log_2(4) + (59 mod 25) + ceil(126/2) $\n\nCompute eac... | {
"type": "arithmetic",
"seed": 1337,
"index": 6847
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 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\nThe general solutio... | {
"type": "trigonometry",
"seed": 1337,
"index": 6848
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Differentiate with respect to $x$: $f(x) = \\ln(2x + -5)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(2x + -5) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\... | {
"type": "calculus",
"seed": 1337,
"index": 6849
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Find the modular inverse of 11 modulo 14, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{14}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarant... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6850
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Prove that $(\\mathbb{Z}_12, +)$ is a group under addition modulo 12."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_12=\\{0,1,\\dots,11\\}$ with operation $+$ modulo $12$.\n\n**Closure:** If $a,b\\in\\mathbb{... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6851
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Prove that $(\\mathbb{Z}_11, +)$ is a group under addition modulo 11."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_11=\\{0,1,\\dots,10\\}$ with operation $+$ modulo $11$.\n\n**Closure:** If $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6852
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Prove that $(\\mathbb{Z}_11, +)$ is a group under addition modulo 11."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_11=\\{0,1,\\dots,10\\}$ with operation $+$ modulo $11$.\n\n**Closure:** If $a,b\\in\\mathb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6853
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Compute the indefinite integral: $\\int 7e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 7e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\... | {
"type": "calculus",
"seed": 1337,
"index": 6854
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Evaluate: ((13 + -135/15) * 16) + 7^3 - log_7(343) + (450 mod 4) + floor(181/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((13 + -135/15) * 16) + 7^3 - log_7(343) + (450 mod 4) + floor(181/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 6855
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Compute the determinant: $A=\\begin{pmatrix}3&-1\\\\5&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&-1\\\\\\5&2\\end{pmatrix} $\n\nUse $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6856
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Evaluate: ((-130 + 24/2) * 4) + 10^5 - log_7(16807) + (270 mod 11) + ceil(10/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-130 + 24/2) * 4) + 10^5 - log_7(16807) + (270 mod 11) + ceil(10/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6857
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. 193 + 859 = 627x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 193 + 859 = 627x $\n\nMove all terms to the left (standard form):\n$ -627x + 1052 = 0 $\n\nIsolate the $x$ term:\n$ -627x = -1052 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 6858
} |
[
{
"role": "user",
"content": "solve: \n\n Evaluate: ((138 + -279/9) * 13) + 9^5 - log_5(625) + (-271 mod 22) + round(168/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((138 + -279/9) * 13) + 9^5 - log_5(625) + (-271 mod 22) + round(168/2) $\n\nCompute each component:\n$ -... | {
"type": "arithmetic",
"seed": 1337,
"index": 6859
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. -624x - 254 = 964"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -624x - 254 = 964 $\n\nMove all terms to the left (standard form):\n$ -624x + -1218 = 0 $\n\nIsolate the $x$ term:\n$ -624x = 1218 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 6860
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Compute the indefinite integral: $\\int \\ln(5x + 5)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(5x + 5)\\,dx $\n\nUse standard antiderivatives (and integration by parts if... | {
"type": "calculus",
"seed": 1337,
"index": 6861
} |
[
{
"role": "user",
"content": "Please work out this equation. Prove that $(\\mathbb{Z}_19, +)$ is a group under addition modulo 19."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_19=\\{0,1,\\dots,18\\}$ with operation $+$ modulo $19$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, then ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6862
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. 27 + 62x + 25x^2 = 91"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 27 + 62x + 25x^2 = 91 $\n\nMove all terms to the left (standard form):\n$ 25x^2 + 62x + -64 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6863
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Prove that $f(x,y)=\\frac12(5x^2+8y^2)+-6x+2y+-6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(5x^2+8y^2)+-6x+2y+-6 $\n\n$ \\frac{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 6864
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Find $A^{-1}$ for $A=\\begin{pmatrix}9&-7\\\\-6&0\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 9 & -7 \\\\ -6 & 0 \\end{pmatrix} $\n\nCompute ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6865
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Compute the indefinite integral: $\\int 5\\sin(2x) + 7\\cos(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 5\\sin(2x) + 7\\cos(6x)\\,dx $\n\nUse standard antiderivatives (and i... | {
"type": "calculus",
"seed": 1337,
"index": 6866
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 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": 6867
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}8&3\\\\\\-6&1\\end{pmatrix},\\quad b=\\begin{pmatrix}96\\\\\\-46\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}8&3\\\\\\-6&1\\end{p... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6868
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 3x - 167 - 179x^2 = -194"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 3x - 167 - 179x^2 = -194 $\n\nMove all terms to the left (standard form):\n$ -179x^2 + 3x + 27 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6869
} |
[
{
"role": "user",
"content": "Solve the equation shown below. 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 parts if needed):\n... | {
"type": "calculus",
"seed": 1337,
"index": 6870
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Prove that $f(x)=7x^2+-10x+4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+-10x+4$.\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": 6871
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Find the modular inverse of 7 modulo 9, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{9}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6872
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. 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$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 6873
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. 818x - 222 = -311"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 818x - 222 = -311 $\n\nMove all terms to the left (standard form):\n$ 818x + 89 = 0 $\n\nIsolate the $x$ term:\n$ 818x = -89 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6874
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Compute the indefinite integral: $\\int (1x + 1)e^{2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (1x + 1)e^{2x}\\,dx $\n\nUse standard antiderivatives (and integration by part... | {
"type": "calculus",
"seed": 1337,
"index": 6875
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Differentiate with respect to $x$: $f(x) = (1x + 1)\\sin(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (1x + 1)\\sin(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) ... | {
"type": "calculus",
"seed": 1337,
"index": 6876
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 540x + 343 = -623"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 540x + 343 = -623 $\n\nMove all terms to the left (standard form):\n$ 540x + 966 = 0 $\n\nIsolate the $x$ term:\n$ 540x = -966 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 6877
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Prove that $f(x)=9x^2+-9x+-9$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+-9x+-9$.\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": 6878
} |
[
{
"role": "user",
"content": "Please calculate this equation. Evaluate: ((181 + -384/24) * 19) + 10^3 - log_4(16) + (-117 mod 14) + round(-90/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((181 + -384/24) * 19) + 10^3 - log_4(16) + (-117 mod 14) + round(-90/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 6879
} |
[
{
"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": 6880
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. 11x^2 - 163 - 65 = -193x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 11x^2 - 163 - 65 = -193x $\n\nMove all terms to the left (standard form):\n$ 11x^2 + 193x + -228 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 6881
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}9&2\\\\\\4&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}90\\\\\\-13\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}9&2\\\\\\4&-5\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6882
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-2&-4\\\\\\-9&-9\\end{pmatrix},\\quad b=\\begin{pmatrix}-22\\\\\\-63\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-2&-4\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6883
} |
[
{
"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$ \\alpha... | {
"type": "trigonometry",
"seed": 1337,
"index": 6884
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Evaluate: ((-111 + -111/3) * 5) + 7^5 - log_5(3125) + (454 mod 29) + ceil(-45/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-111 + -111/3) * 5) + 7^5 - log_5(3125) + (454 mod 29) + ceil(-45/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 6885
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-1&-4\\\\\\7&-6\\end{pmatrix},\\quad b=\\begin{pmatrix}-26\\\\\\-90\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-1&-4\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6886
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Evaluate: ((-191 + 48/16) * 4) + 2^3 - log_8(512) + (-287 mod 24) + ceil(104/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-191 + 48/16) * 4) + 2^3 - log_8(512) + (-287 mod 24) + ceil(104/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 6887
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Evaluate: ((-60 + -320/16) * 18) + 5^2 - log_8(64) + (-222 mod 30) + floor(-4/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-60 + -320/16) * 18) + 5^2 - log_8(64) + (-222 mod 30) + floor(-4/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 6888
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Find the modular inverse of 36 modulo 37, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $36\\cdot a^{-1} \\equiv 1 \\pmod{37}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 6889
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. -553x + 243 = -238"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -553x + 243 = -238 $\n\nMove all terms to the left (standard form):\n$ -553x + 481 = 0 $\n\nIsolate the $x$ term:\n$ -553x = -481 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 6890
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Differentiate with respect to $x$: $f(x) = -7\\sin(6x) + 7\\cos(3x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -7\\sin(6x) + 7\\cos(3x) $\n\nApply the standard differentiation ru... | {
"type": "calculus",
"seed": 1337,
"index": 6891
} |
[
{
"role": "user",
"content": "Solve this equation accurately. 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 = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 6892
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Find $A^{-1}$ for $A=\\begin{pmatrix}-1&1\\\\6&0\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -1 & 1 \\\\ 6 & 0 \\end{pmatrix} $\n\nCompute the determ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6893
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-2&-4&-1\\\\\\-3&1&4\\\\\\-5&0&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-7\\\\\\-20\\\\\\-9\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $A... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6894
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 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 ... | {
"type": "trigonometry",
"seed": 1337,
"index": 6895
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 653 + 256 = -274x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 653 + 256 = -274x $\n\nMove all terms to the left (standard form):\n$ 274x + 909 = 0 $\n\nIsolate the $x$ term:\n$ 274x = -909 $\n\nDivide both sides by... | {
"type": "linear_equation",
"seed": 1337,
"index": 6896
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-5&7\\\\\\0&-8\\end{pmatrix},\\quad b=\\begin{pmatrix}50\\\\\\-40\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-5&7\\\\\\0&-... | {
"type": "linear_algebra",
"seed": 1337,
"index": 6897
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Evaluate: ((150 + 140/4) * 4) + 11^5 - log_10(1000000) + (46 mod 7) + ceil(96/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((150 + 140/4) * 4) + 11^5 - log_10(1000000) + (46 mod 7) + ceil(96/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 6898
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. 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": 6899
} |
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