messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Find the modular inverse of 13 modulo 14, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $13\\cdot a^{-1} \\equiv 1 \\pmod{14}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarant... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5900
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Differentiate with respect to $x$: $f(x) = -7\\sin(2x) + -6\\cos(8x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -7\\sin(2x) + -6\\cos(8x) $\n\nApply the standard differentiation rules:\... | {
"type": "calculus",
"seed": 1337,
"index": 5901
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. -12x + 87 + 67 = -109x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -12x + 87 + 67 = -109x^2 $\n\nMove all terms to the left (standard form):\n$ 109x^2 + -12x + 154 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5902
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}7&6\\\\3&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 7 & 6 \\\\ 3 & -7 \\end{pmatrix} $\n\nCompute the d... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5903
} |
[
{
"role": "user",
"content": "Resolve the equation provided. -770 - 751 = -87x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -770 - 751 = -87x $\n\nMove all terms to the left (standard form):\n$ 87x + -1521 = 0 $\n\nIsolate the $x$ term:\n$ 87x = 1521 $\n\nDivide both sides by th... | {
"type": "linear_equation",
"seed": 1337,
"index": 5904
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Evaluate: ((30 + 294/21) * 17) + 5^3 - log_9(6561) + (-433 mod 3) + ceil(68/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((30 + 294/21) * 17) + 5^3 - log_9(6561) + (-433 mod 3) + ceil(68/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 5905
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Prove that $f(x,y)=\\frac12(9x^2+4y^2)+-2x+0y+6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+4y^2)+-2x+0y+6 $\n\n$ \\frac{\\partial^2 f}{\\p... | {
"type": "optimization",
"seed": 1337,
"index": 5906
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: 358 - 105 = 348x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 358 - 105 = 348x $\n\nMove all terms to the left (standard form):\n$ -348x + 253 = 0 $\n\nIsolate the $x$ term:\n$ -348x = -253 $\n\nDivide both sides by the coefficient o... | {
"type": "linear_equation",
"seed": 1337,
"index": 5907
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal ... | {
"type": "trigonometry",
"seed": 1337,
"index": 5908
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. 559x + 218 = 522"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 559x + 218 = 522 $\n\nMove all terms to the left (standard form):\n$ 559x + -304 = 0 $\n\nIsolate the $x$ term:\n$ 559x = 304 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 5909
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Find the modular inverse of 5 modulo 22, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{22}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5910
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Prove that $(\\mathbb{Z}_26, +)$ is a group under addition modulo 26."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_26=\\{0,1,\\dots,25\\}$ with operation $+$ modulo $26$.\n\n**Closure:** If $a,b\\in\\mathb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5911
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. 582 - 616x = -329"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 582 - 616x = -329 $\n\nMove all terms to the left (standard form):\n$ -616x + 911 = 0 $\n\nIsolate the $x$ term:\n$ -616x = -911 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 5912
} |
[
{
"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": 5913
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. -29 + 91x^2 - 27 = -45x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -29 + 91x^2 - 27 = -45x $\n\nMove all terms to the left (standard form):\n$ 91x^2 + 45x + -56 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5914
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Prove that $(\\mathbb{Z}_9, +)$ is a group under addition modulo 9."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_9=\\{0,1,\\dots,8\\}$ with operation $+$ modulo $9$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, then $(a+b)\\bmod n\\in\\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5915
} |
[
{
"role": "user",
"content": "Please calculate this equation. Compute $(145+162) \\bmod 16$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (145+162) \\bmod 16 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5916
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Compute the determinant: $A=\\begin{pmatrix}2&-1\\\\2&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}2&-1\\\\\\2&2\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5917
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. -598 + 261x = 724"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -598 + 261x = 724 $\n\nMove all terms to the left (standard form):\n$ 261x + -1322 = 0 $\n\nIsolate the $x$ term:\n$ 261x = 1322 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 5918
} |
[
{
"role": "user",
"content": "Can you compute this equation? Compute the determinant: $A=\\begin{pmatrix}3&-5\\\\7&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&-5\\\\\\7&1\\end{pmatrix} $\n\nUse $\\det(A)=ad-b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5919
} |
[
{
"role": "user",
"content": "Work out the result of this equation. 6x + 144x^2 + 184 = 185"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 6x + 144x^2 + 184 = 185 $\n\nMove all terms to the left (standard form):\n$ 144x^2 + 6x + -1 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5920
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? 44 + 534x = 444"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 44 + 534x = 444 $\n\nMove all terms to the left (standard form):\n$ 534x + -400 = 0 $\n\nIsolate the $x$ term:\n$ 534x = 400 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 5921
} |
[
{
"role": "user",
"content": "Find the value that satisfies 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": 5922
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. -249 + 761 = 959x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -249 + 761 = 959x $\n\nMove all terms to the left (standard form):\n$ -959x + 512 = 0 $\n\nIsolate the $x$ term:\n$ -959x = -512 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 5923
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Evaluate: ((-108 + 120/12) * 12) + 10^2 - log_4(4096) + (-190 mod 23) + ceil(102/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-108 + 120/12) * 12) + 10^2 - log_4(4096) + (-190 mod 23) + ceil(... | {
"type": "arithmetic",
"seed": 1337,
"index": 5924
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 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 ge... | {
"type": "trigonometry",
"seed": 1337,
"index": 5925
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Prove that $f(x)=8x^2+7x+-6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=8x^2+7x+-6$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\... | {
"type": "optimization",
"seed": 1337,
"index": 5926
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Solve for $x$ (in radians): sin(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -1 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(-1) = -1.5708 $\n\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 5927
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 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.... | {
"type": "trigonometry",
"seed": 1337,
"index": 5928
} |
[
{
"role": "user",
"content": "Can you compute this equation? -48 - 191x - 154x^2 = -99"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -48 - 191x - 154x^2 = -99 $\n\nMove all terms to the left (standard form):\n$ -154x^2 + -191x + 51 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5929
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Differentiate with respect to $x$: $f(x) = -6x^3 + 9x^2 + -14x + -5$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6x^3 + 9x^2 + -14x + -5 $\n\nApply the standard differentiation rules:\n$ f'(x)... | {
"type": "calculus",
"seed": 1337,
"index": 5930
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Compute the indefinite integral: $\\int 4e^{1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 4e^{1x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n... | {
"type": "calculus",
"seed": 1337,
"index": 5931
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Evaluate: ((141 + 69/3) * 6) + 3^4 - log_9(59049) + (307 mod 6) + round(-77/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((141 + 69/3) * 6) + 3^4 - log_9(59049) + (307 mod 6) + round(-77/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 5932
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. 28x^2 - 49x + 163 = 50"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 28x^2 - 49x + 163 = 50 $\n\nMove all terms to the left (standard form):\n$ 28x^2 + -49x + 113 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5933
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Prove that $f(x)=6x^2+7x+-1$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=6x^2+7x+-1$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 12x + 7 $... | {
"type": "optimization",
"seed": 1337,
"index": 5934
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Find $A^{-1}$ for $A=\\begin{pmatrix}-3&0\\\\4&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -3 & 0 \\\\ 4 & -7 \\end{pmatrix} $\n\nCompute the de... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5935
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((48 + 496/16) * 20) + 3^5 - log_5(25) + (231 mod 29) + round(89/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((48 + 496/16) * 20) + 3^5 - log_5(25) + (231 mod 29) + round(89/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 5936
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Prove that $f(x,y)=\\frac12(9x^2+10y^2)+-5x+0y+-1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+10y^2)+-5x+0y+-1 $\n\n$ \\frac{\\partial^2 f}... | {
"type": "optimization",
"seed": 1337,
"index": 5937
} |
[
{
"role": "user",
"content": "Please solve this math problem. 543 - 827x = -74"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 543 - 827x = -74 $\n\nMove all terms to the left (standard form):\n$ -827x + 617 = 0 $\n\nIsolate the $x$ term:\n$ -827x = -617 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 5938
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Compute the determinant: $A=\\begin{pmatrix}-7&-7\\\\-6&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-7&-7\\\\\\-6&8\\end{pmatrix} $\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5939
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 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{\\par... | {
"type": "optimization",
"seed": 1337,
"index": 5940
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -37x^2 - 78x - 136 = -149"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -37x^2 - 78x - 136 = -149 $\n\nMove all terms to the left (standard form):\n$ -37x^2 + -78x + 13 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5941
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}7&9\\\\\\-3&-6\\end{pmatrix},\\quad b=\\begin{pmatrix}-6\\\\\\9\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}7&9\\\\\\-3&-6\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5942
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Compute $(-100+-13) \\bmod 14$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-100+-13) \\bmod 14 $\n\nUse the rule that addition is compatible with reduction mod... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5943
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. 960 - 702 = 748x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 960 - 702 = 748x $\n\nMove all terms to the left (standard form):\n$ -748x + 258 = 0 $\n\nIsolate the $x$ term:\n$ -748x = -258 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 5944
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Evaluate: ((-57 + 95/19) * 13) + 2^2 - log_6(1296) + (-368 mod 7) + round(86/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-57 + 95/19) * 13) + 2^2 - log_6(1296) + (-368 mod 7) + round(86/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 5945
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Evaluate: ((-133 + 846/18) * 17) + 5^3 - log_6(6) + (424 mod 19) + round(-164/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-133 + 846/18) * 17) + 5^3 - log_6(6) + (424 mod 19) + round(-164/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 5946
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 5947
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(-\\frac{\... | {
"type": "trigonometry",
"seed": 1337,
"index": 5948
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Compute the indefinite integral: $\\int \\ln(8x + 7)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(8x + 7)\\,dx $\n\nUse standard antiderivatives (and integration by parts if... | {
"type": "calculus",
"seed": 1337,
"index": 5949
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Compute $(140+86) \\bmod 7$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (140+86) \\bmod 7 $\n\nUse the rule that addition is compatible with reduction modu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5950
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((-50 + 1029/21) * 15) + 9^5 - log_9(59049) + (-297 mod 26) + floor(66/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-50 + 1029/21) * 15) + 9^5 - log_9(59049) + (-297 mod 26) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 5951
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha... | {
"type": "trigonometry",
"seed": 1337,
"index": 5952
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. -292 + 47 = -265x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -292 + 47 = -265x $\n\nMove all terms to the left (standard form):\n$ 265x + -245 = 0 $\n\nIsolate the $x$ term:\n$ 265x = 245 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 5953
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Evaluate: ((-7 + -58/2) * 18) + 5^2 - log_4(4096) + (159 mod 7) + ceil(-10/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-7 + -58/2) * 18) + 5^2 - log_4(4096) + (159 mod 7) + ceil(-10/2) $\n\nCompute each comp... | {
"type": "arithmetic",
"seed": 1337,
"index": 5954
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 5955
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}3&-3&-2\\\\\\3&-3&4\\\\\\-4&2&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-12\\\\\\-30\\\\\\27\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5956
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}4&2&5\\\\\\0&-1&1\\\\\\4&5&1\\end{pmatrix},\\quad b=\\begin{pmatrix}-34\\\\\\2\\\\\\-38\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g.,... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5957
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Prove that $f(x,y)=\\frac12(5x^2+7y^2)+-5x+2y+-9$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(5x^2+7y^2)+-5x+2y+-9 $\n\n$ \\frac{\\partial^2 f}{... | {
"type": "optimization",
"seed": 1337,
"index": 5958
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Solve for $x$ (in radians): tan(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(1) = 0.785398... | {
"type": "trigonometry",
"seed": 1337,
"index": 5959
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. -452 + 702 = -861x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -452 + 702 = -861x $\n\nMove all terms to the left (standard form):\n$ 861x + 250 = 0 $\n\nIsolate the $x$ term:\n$ 861x = -250 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 5960
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-5&-1\\\\-6&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -5 & -1 \\\\ -6 & 1 \\end{pmatrix} $\n\nCompute th... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5961
} |
[
{
"role": "user",
"content": "Can you evaluate this math 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": 5962
} |
[
{
"role": "user",
"content": "Solve the following math 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": 5963
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. 20x - 68x^2 - 123 = -38"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 20x - 68x^2 - 123 = -38 $\n\nMove all terms to the left (standard form):\n$ -68x^2 + 20x + -85 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5964
} |
[
{
"role": "user",
"content": "Evaluate the following equation. 11 - 90x + 169 = -113x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 11 - 90x + 169 = -113x^2 $\n\nMove all terms to the left (standard form):\n$ 113x^2 + -90x + 180 = 0 $\n\nApply the quadratic formula:\n$ x = \... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5965
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Evaluate: ((57 + -204/17) * 19) + 5^5 - log_5(5) + (327 mod 28) + ceil(-153/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((57 + -204/17) * 19) + 5^5 - log_5(5) + (327 mod 28) + ceil(-153/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 5966
} |
[
{
"role": "user",
"content": "Please solve this math problem. -x + 84x^2 + 35 = -78"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -x + 84x^2 + 35 = -78 $\n\nMove all terms to the left (standard form):\n$ 84x^2 + -1x + 113 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5967
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? 950 + 618 = -170x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 950 + 618 = -170x $\n\nMove all terms to the left (standard form):\n$ 170x + 1568 = 0 $\n\nIsolate the $x$ term:\n$ 170x = -1568 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 5968
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? -50 - 182x - 116x^2 = -28"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -50 - 182x - 116x^2 = -28 $\n\nMove all terms to the left (standard form):\n$ -116x^2 + -182x + -22 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5969
} |
[
{
"role": "user",
"content": "Please compute the solution to this 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 $\n\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 5970
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. -429x = -80"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -429x = -80 $\n\nMove all terms to the left (standard form):\n$ -429x + 80 = 0 $\n\nIsolate the $x$ term:\n$ -429x = -80 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 5971
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Prove that $(\\mathbb{Z}_21, +)$ is a group under addition modulo 21."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_21=\\{0,1,\\dots,20\\}$ with operation $+$ modulo $21$.\n\n**Closure:** If $a,b\\in\\mathb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5972
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. 3x - 121 + 115x^2 = 95"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 3x - 121 + 115x^2 = 95 $\n\nMove all terms to the left (standard form):\n$ 115x^2 + 3x + -216 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5973
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Differentiate with respect to $x$: $f(x) = -4\\sin(3x) + 2\\cos(2x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -4\\sin(3x) + 2\\cos(2x) $\n\nApply the standard differentiation rules:\n$ f'(x... | {
"type": "calculus",
"seed": 1337,
"index": 5974
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Evaluate: ((118 + 444/12) * 10) + 12^5 - log_2(4) + (437 mod 29) + ceil(-127/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((118 + 444/12) * 10) + 12^5 - log_2(4) + (437 mod 29) + ceil(-127/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 5975
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Prove that $f(x,y)=\\frac12(3x^2+2y^2)+1x+2y+0$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+2y^2)+1x+2y+0 $\n\n$ \\frac{\\partia... | {
"type": "optimization",
"seed": 1337,
"index": 5976
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. -10 - 54x + 2 = 182x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -10 - 54x + 2 = 182x^2 $\n\nMove all terms to the left (standard form):\n$ -182x^2 + -54x + -8 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5977
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Evaluate: ((-192 + -72/9) * 4) + 10^3 - log_4(4) + (313 mod 21) + round(-173/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-192 + -72/9) * 4) + 10^3 - log_4(4) + (313 mod 21) + round(-173/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 5978
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Compute the indefinite integral: $\\int \\ln(5x + 1)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(5x + 1)\\,dx $\n\nUse standard antiderivatives (and integration by parts if neede... | {
"type": "calculus",
"seed": 1337,
"index": 5979
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. 17x - 564 = 857"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 17x - 564 = 857 $\n\nMove all terms to the left (standard form):\n$ 17x + -1421 = 0 $\n\nIsolate the $x$ term:\n$ 17x = 1421 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 5980
} |
[
{
"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": 5981
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Prove that $(\\mathbb{Z}_17, +)$ is a group under addition modulo 17."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_17=\\{0,1,\\dots,16\\}$ with operation $+$ modulo $17$.\n\n**Closure:** If $a,b\\in\\mat... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5982
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&5&-5\\\\\\2&4&2\\\\\\-4&-3&1\\end{pmatrix},\\quad b=\\begin{pmatrix}-4\\\\\\-16\\\\\\12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "So... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5983
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Differentiate with respect to $x$: $f(x) = -5\\sin(6x) + 7\\cos(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -5\\sin(6x) + 7\\cos(4x) $\n\nApply the standard differentiation rules:\n$... | {
"type": "calculus",
"seed": 1337,
"index": 5984
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$... | {
"type": "trigonometry",
"seed": 1337,
"index": 5985
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Find the modular inverse of 4 modulo 31, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $4\\cdot a^{-1} \\equiv 1 \\pmod{31}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5986
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. 30x - 145x^2 + 128 = -47"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 30x - 145x^2 + 128 = -47 $\n\nMove all terms to the left (standard form):\n$ -145x^2 + 30x + 175 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5987
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&1&-5\\\\\\3&4&-3\\\\\\-5&5&0\\end{pmatrix},\\quad b=\\begin{pmatrix}6\\\\\\6\\\\\\-5\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5988
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{... | {
"type": "optimization",
"seed": 1337,
"index": 5989
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Compute the indefinite integral: $\\int \\ln(7x + -2)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(7x + -2)\\,dx $\n\nUse standard antiderivatives (and integration by parts if neede... | {
"type": "calculus",
"seed": 1337,
"index": 5990
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. 4 - 54x + 93 = -139x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 4 - 54x + 93 = -139x^2 $\n\nMove all terms to the left (standard form):\n$ 139x^2 + -54x + 97 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5991
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Prove that $f(x)=3x^2+-8x+-5$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=3x^2+-8x+-5$.\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": 5992
} |
[
{
"role": "user",
"content": "solve: -689x - 411 = -121"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -689x - 411 = -121 $\n\nMove all terms to the left (standard form):\n$ -689x + -290 = 0 $\n\nIsolate the $x$ term:\n$ -689x = 290 $\n\nDivide both sides by the coefficient of $x... | {
"type": "linear_equation",
"seed": 1337,
"index": 5993
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ ... | {
"type": "trigonometry",
"seed": 1337,
"index": 5994
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}2&9\\\\\\-5&0\\end{pmatrix},\\quad b=\\begin{pmatrix}-9\\\\\\0\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}2&9\\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5995
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&-5&1\\\\\\1&3&-1\\\\\\4&5&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}7\\\\\\-6\\\\\\-10\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5996
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. -192x - 701 = 846"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -192x - 701 = 846 $\n\nMove all terms to the left (standard form):\n$ -192x + -1547 = 0 $\n\nIsolate the $x$ term:\n$ -192x = 1547 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 5997
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Find the modular inverse of 5 modulo 6, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{6}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarante... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5998
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((-197 + 480/15) * 19) + 2^3 - log_2(32) + (94 mod 30) + round(125/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-197 + 480/15) * 19) + 2^3 - log_2(32) + (94 mod 30) + round(125/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 5999
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.