messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Please evaluate and solve this equation. 803x + 538 = 401"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 803x + 538 = 401 $\n\nMove all terms to the left (standard form):\n$ 803x + 137 = 0 $\n\nIsolate the $x$ term:\n$ 803x = -137 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 300
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. -63 + 867 = -175x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -63 + 867 = -175x $\n\nMove all terms to the left (standard form):\n$ 175x + 804 = 0 $\n\nIsolate the $x$ term:\n$ 175x = -804 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 301
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. 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": 302
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Find the modular inverse of 21 modulo 25, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $21\\cdot a^{-1} \\equiv 1 \\pmod{25}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 303
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Find the modular inverse of 20 modulo 39, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $20\\cdot a^{-1} \\equiv 1 \\pmod{39}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 304
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Prove that $(\\mathbb{Z}_20, +)$ is a group under addition modulo 20."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_20=\\{0,1,\\dots,19\\}$ with operation $+$ modulo $20$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 305
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Compute the indefinite integral: $\\int -2x^3 + -4x^2 + 18x + 1\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -2x^3 + -4x^2 + 18x + 1\\,dx $\n\nUse standard antiderivatives (and integrat... | {
"type": "calculus",
"seed": 1337,
"index": 306
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Evaluate: ((-156 + -90/5) * 14) + 5^3 - log_8(8) + (378 mod 14) + floor(162/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-156 + -90/5) * 14) + 5^3 - log_8(8) + (378 mod 14) + floor(162/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 307
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Solve for $x$ (in radians): cos(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 308
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal va... | {
"type": "trigonometry",
"seed": 1337,
"index": 309
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 40 - 196 + 98x^2 = 58x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 40 - 196 + 98x^2 = 58x $\n\nMove all terms to the left (standard form):\n$ 98x^2 + -58x + -156 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 310
} |
[
{
"role": "user",
"content": "solve: Differentiate with respect to $x$: $f(x) = -4x^3 + 6x^2 + 19x + -19$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -4x^3 + 6x^2 + 19x + -19 $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-12x^2 + 12x + 19} $... | {
"type": "calculus",
"seed": 1337,
"index": 311
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Prove that $f(x)=4x^2+-7x+4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+-7x+4$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 8x + -7 $\n$ f''(x) = 8 $... | {
"type": "optimization",
"seed": 1337,
"index": 312
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Evaluate: ((-107 + -410/10) * 7) + 5^3 - log_9(9) + (-21 mod 26) + ceil(40/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-107 + -410/10) * 7) + 5^3 - log_9(9) + (-21 mod 26) + ceil(40/2) $\n\nCompute each co... | {
"type": "arithmetic",
"seed": 1337,
"index": 313
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. -35 - 33x + 64 = 170x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -35 - 33x + 64 = 170x^2 $\n\nMove all terms to the left (standard form):\n$ -170x^2 + -33x + 29 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 314
} |
[
{
"role": "user",
"content": "solve: Differentiate with respect to $x$: $f(x) = (-2x + -2)e^{6x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-2x + -2)e^{6x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-2e^{6x} + (-2x + -2)\\cdot 6e^{6x}}... | {
"type": "calculus",
"seed": 1337,
"index": 315
} |
[
{
"role": "user",
"content": "Please find the solution of 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 $\n\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 316
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. -546 - 569 = -738x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -546 - 569 = -738x $\n\nMove all terms to the left (standard form):\n$ 738x + -1115 = 0 $\n\nIsolate the $x$ term:\n$ 738x = 1115 $\n\nD... | {
"type": "linear_equation",
"seed": 1337,
"index": 317
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Prove that $(\\mathbb{Z}_7, +)$ is a group under addition modulo 7."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_7=\\{0,1,\\dots,6\\}$ with operation $+$ modulo $7$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 318
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Compute $(10+61) \\bmod 6$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (10+61) \\bmod 6 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\n$ (a+b... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 319
} |
[
{
"role": "user",
"content": "Please solve this math problem. Evaluate: ((-102 + -192/16) * 4) + 4^3 - log_7(2401) + (81 mod 18) + ceil(133/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-102 + -192/16) * 4) + 4^3 - log_7(2401) + (81 mod 18) + ceil(133/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 320
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Evaluate: ((195 + 222/6) * 14) + 9^2 - log_5(625) + (-371 mod 24) + ceil(181/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((195 + 222/6) * 14) + 9^2 - log_5(625) + (-371 mod 24) + ceil(181/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 321
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Evaluate: ((166 + -152/19) * 12) + 9^5 - log_3(27) + (194 mod 5) + ceil(122/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((166 + -152/19) * 12) + 9^5 - log_3(27) + (194 mod 5) + ceil(122/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 322
} |
[
{
"role": "user",
"content": "Work out the result of this equation. -35x^2 + 140 + 81 = -188x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -35x^2 + 140 + 81 = -188x $\n\nMove all terms to the left (standard form):\n$ -35x^2 + 188x + 221 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 323
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-8&0\\\\3&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -8 & 0 \\\\ 3 & 3 \\end{pmatrix} $\n\nCompute the d... | {
"type": "linear_algebra",
"seed": 1337,
"index": 324
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. 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{\\pa... | {
"type": "optimization",
"seed": 1337,
"index": 325
} |
[
{
"role": "user",
"content": "Work through 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": 326
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. 13 + 181x^2 - 122 = 119x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 13 + 181x^2 - 122 = 119x $\n\nMove all terms to the left (standard form):\n$ 181x^2 + -119x + -109 = 0 $\n\nApply the quad... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 327
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Solve for $x$ (in radians): tan(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(-1) = -0.785398 $\n\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 328
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Find $A^{-1}$ for $A=\\begin{pmatrix}3&-2\\\\-1&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 3 & -2 \\\\ -1 & -6 \\end{pmatrix} $\n\nCompute... | {
"type": "linear_algebra",
"seed": 1337,
"index": 329
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Compute the determinant: $A=\\begin{pmatrix}7&6\\\\8&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}7&6\\\\\\8&3\\end{pmatrix} $\n\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 330
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. 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{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 331
} |
[
{
"role": "user",
"content": "solve: \n\n Compute the indefinite integral: $\\int -4e^{2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4e^{2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int -4e^{2x}\\,dx = \\boxe... | {
"type": "calculus",
"seed": 1337,
"index": 332
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Evaluate: ((66 + 828/23) * 8) + 9^4 - log_5(3125) + (-348 mod 16) + ceil(-155/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((66 + 828/23) * 8) + 9^4 - log_5(3125) + (-348 mod 16) + ceil(-155/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 333
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-8&-2\\\\-8&-5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -8 & -2 \\\\ -8 & -5 \\end{pmatrix} $\n\nCompu... | {
"type": "linear_algebra",
"seed": 1337,
"index": 334
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-3&-8\\\\-4&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -3 & -8 \\\\ -4 & -7 \\end{pmatrix} $\n\nCom... | {
"type": "linear_algebra",
"seed": 1337,
"index": 335
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. -67 + 300x = -298"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -67 + 300x = -298 $\n\nMove all terms to the left (standard form):\n$ 300x + 231 = 0 $\n\nIsolate the $x$ term:\n$ 300x = -231 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 336
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((-180 + 234/6) * 13) + 5^5 - log_5(5) + (-49 mod 21) + round(-99/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-180 + 234/6) * 13) + 5^5 - log_5(5) + (-49 mod 21) + round(-99... | {
"type": "arithmetic",
"seed": 1337,
"index": 337
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Compute the indefinite integral: $\\int -5\\sin(8x) + -4\\cos(1x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -5\\sin(8x) + -4\\cos(1x)\\,dx $\n\nUse standard antideri... | {
"type": "calculus",
"seed": 1337,
"index": 338
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Evaluate: ((-177 + -260/13) * 15) + 6^4 - log_2(2) + (-487 mod 27) + ceil(30/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-177 + -260/13) * 15) + 6^4 - log_2(2) + (-487 mod 27) + ceil(30/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 339
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}8&8\\\\\\-9&8\\end{pmatrix},\\quad b=\\begin{pmatrix}48\\\\\\31\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}8&8\\\\\\-9&8\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 340
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Evaluate: ((-81 + 80/10) * 16) + 4^4 - log_9(9) + (-133 mod 29) + round(-146/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-81 + 80/10) * 16) + 4^4 - log_9(9) + (-133 mod 29) + round(-146/2) $\n\nCompute eac... | {
"type": "arithmetic",
"seed": 1337,
"index": 341
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Prove that $(\\mathbb{Z}_23, +)$ is a group under addition modulo 23."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_23=\\{0,1,\\dots,22\\}$ with operation $+$ modulo $23$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 342
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Compute the determinant: $A=\\begin{pmatrix}-9&7\\\\-1&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-9&7\\\\\\-1&4\\end{pmatrix} $\n\nUse $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 343
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Compute the determinant: $A=\\begin{pmatrix}3&2\\\\4&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&2\\\\\\4&4\\end{pmatrix} $\n\nUse $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 344
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 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 = \\arc... | {
"type": "trigonometry",
"seed": 1337,
"index": 345
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. -2x - 165 + 94x^2 = 12"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -2x - 165 + 94x^2 = 12 $\n\nMove all terms to the left (standard form):\n$ 94x^2 + -2x + -177 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 346
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 717 + 998 = -332x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 717 + 998 = -332x $\n\nMove all terms to the left (standard form):\n$ 332x + 1715 = 0 $\n\nIsolate the $x$ term:\n$ 332x = -1715 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 347
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Differentiate with respect to $x$: $f(x) = 3x^3 + 1x^2 + -11x + -6$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3x^3 + 1x^2 + -11x + -6 $\n\nApply the standard differentiation rules:\n$ f'(x)... | {
"type": "calculus",
"seed": 1337,
"index": 348
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((181 + 48/16) * 10) + 5^4 - log_6(6) + (-466 mod 27) + ceil(-198/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((181 + 48/16) * 10) + 5^4 - log_6(6) + (-466 mod 27) + ceil(-198/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 349
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. 952x + 36 = 711"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 952x + 36 = 711 $\n\nMove all terms to the left (standard form):\n$ 952x + -675 = 0 $\n\nIsolate the $x$ term:\n$ 952x = 675 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 350
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Compute $(-34+-53) \\bmod 15$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-34+-53) \\bmod 15 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 351
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. 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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 352
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-3&-3&-4\\\\\\-5&0&0\\\\\\0&-3&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-8\\\\\\-15\\\\\\3\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "So... | {
"type": "linear_algebra",
"seed": 1337,
"index": 353
} |
[
{
"role": "user",
"content": "Solve the following math equation. Find the modular inverse of 5 modulo 24, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{24}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees intege... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 354
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Prove that $(\\mathbb{Z}_27, +)$ is a group under addition modulo 27."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_27=\\{0,1,\\dots,26\\}$ with operation $+$ modulo $27$.\n\n**Closure:** If $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 355
} |
[
{
"role": "user",
"content": "Please determine the solution 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... | {
"type": "optimization",
"seed": 1337,
"index": 356
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Evaluate: ((-70 + -238/14) * 5) + 3^5 - log_6(46656) + (210 mod 12) + ceil(105/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-70 + -238/14) * 5) + 3^5 - log_6(46656) + (210 mod 12) + ceil(105/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 357
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. -29 - 586x = -265"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -29 - 586x = -265 $\n\nMove all terms to the left (standard form):\n$ -586x + 236 = 0 $\n\nIsolate the $x$ term:\n$ -586x = -236 $\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 358
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Find $A^{-1}$ for $A=\\begin{pmatrix}-5&6\\\\0&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -5 & 6 \\\\ 0 & 3 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 359
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Differentiate with respect to $x$: $f(x) = \\ln(8x + 4)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(8x + 4) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac... | {
"type": "calculus",
"seed": 1337,
"index": 360
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n -42 - 13 + 71x^2 = 83x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -42 - 13 + 71x^2 = 83x $\n\nMove all terms to the left (standard form):\n$ 71x^2 + -83x + -55 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 361
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. -49x - 772 = -452"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -49x - 772 = -452 $\n\nMove all terms to the left (standard form):\n$ -49x + -320 = 0 $\n\nIsolate the $x$ term:\n$ -49x = 320 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 362
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. -470 + 580x = 365"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -470 + 580x = 365 $\n\nMove all terms to the left (standard form):\n$ 580x + -835 = 0 $\n\nIsolate the $x$ term:\n$ 580x = 835 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 363
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Evaluate: ((71 + -111/3) * 17) + 10^2 - log_9(6561) + (-244 mod 18) + floor(-126/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((71 + -111/3) * 17) + 10^2 - log_9(6561) + (-244 mod 18) + floor(-126/... | {
"type": "arithmetic",
"seed": 1337,
"index": 364
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Compute the determinant: $A=\\begin{pmatrix}-7&6\\\\2&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-7&6\\\\\\2&2\\end{pmatrix} $\n\nUse $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 365
} |
[
{
"role": "user",
"content": "solve: 245 - 626 = -555x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 245 - 626 = -555x $\n\nMove all terms to the left (standard form):\n$ 555x + -381 = 0 $\n\nIsolate the $x$ term:\n$ 555x = 381 $\n\nDivide both sides by the coefficient of $x$:\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 366
} |
[
{
"role": "user",
"content": "Evaluate the following equation. 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 $a,b\\in\\mathbb{Z}_n$, the... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 367
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. -17 + 3x^2 + 115x = -21"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -17 + 3x^2 + 115x = -21 $\n\nMove all terms to the left (standard form):\n$ 3x^2 + 115x + 4 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 368
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Evaluate: ((148 + 324/9) * 1) + 3^2 - log_3(729) + (-190 mod 29) + ceil(-86/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((148 + 324/9) * 1) + 3^2 - log_3(729) + (-190 mod 29) + ceil(-86/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 369
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((74 + -720/16) * 18) + 4^2 - log_5(15625) + (415 mod 13) + round(131/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((74 + -720/16) * 18) + 4^2 - log_5(15625) + (415 mod 13) + round(131/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 370
} |
[
{
"role": "user",
"content": "Find the solution of the math equation 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{\... | {
"type": "optimization",
"seed": 1337,
"index": 371
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. -17x - 12 = -22"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -17x - 12 = -22 $\n\nMove all terms to the left (standard form):\n$ -17x + 10 = 0 $\n\nIsolate the $x$ term:\n$ -17x = -10 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 372
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. 764 - 686 = 436x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 764 - 686 = 436x $\n\nMove all terms to the left (standard form):\n$ -436x + 78 = 0 $\n\nIsolate the $x$ term:\n$ -436x = -78 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 373
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Find $A^{-1}$ for $A=\\begin{pmatrix}-5&2\\\\7&0\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -5 & 2 \\\\ 7 & 0 \\end{pmatrix} $\n\nCompute the de... | {
"type": "linear_algebra",
"seed": 1337,
"index": 374
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Evaluate: ((-94 + -736/16) * 19) + 8^4 - log_2(2) + (-5 mod 9) + ceil(20/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-94 + -736/16) * 19) + 8^4 - log_2(2) + (-5 mod 9) + ceil(20/2) $\n\nCompute each compo... | {
"type": "arithmetic",
"seed": 1337,
"index": 375
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((-106 + 686/14) * 10) + 10^3 - log_5(625) + (-293 mod 17) + round(-50/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-106 + 686/14) * 10) + 10^3 - log_5(625) + (-293 mod 17) + round(-50/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 376
} |
[
{
"role": "user",
"content": "Calculate the result of the given 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": 377
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Evaluate: ((66 + -1012/23) * 13) + 12^4 - log_10(1000000) + (-100 mod 25) + floor(-62/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((66 + -1012/23) * 13) + 12^4 - log_10(1000000) + (-100 ... | {
"type": "arithmetic",
"seed": 1337,
"index": 378
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&4&2\\\\\\-5&-2&4\\\\\\-2&-4&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-4\\\\\\-8\\\\\\-17\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $A... | {
"type": "linear_algebra",
"seed": 1337,
"index": 379
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Evaluate: ((-118 + 198/18) * 8) + 9^5 - log_5(15625) + (-377 mod 4) + ceil(144/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-118 + 198/18) * 8) + 9^5 - log_5(15625) + (-377 mod 4) + ceil(144/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 380
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. 45 + 42 - 59x^2 = -31x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 45 + 42 - 59x^2 = -31x $\n\nMove all terms to the left (standard form):\n$ -59x^2 + 31x + 87 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 381
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Compute $(31+-7) \\bmod 15$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (31+-7) \\bmod 15 $\n\nUse the rule that addition is compatible with reduction modulo $n$:... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 382
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Compute the indefinite integral: $\\int (-2x + 6)e^{5x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-2x + 6)e^{5x}\\,dx $\n\nUse standard antiderivatives (and integrat... | {
"type": "calculus",
"seed": 1337,
"index": 383
} |
[
{
"role": "user",
"content": "Find the numerical solution 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 = \\ar... | {
"type": "trigonometry",
"seed": 1337,
"index": 384
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. 386 + 845 = 568x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 386 + 845 = 568x $\n\nMove all terms to the left (standard form):\n$ -568x + 1231 = 0 $\n\nIsolate the $x$ term:\n$ -568x = -1231 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 385
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. + 198x^2 - 110 = -185x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ + 198x^2 - 110 = -185x $\n\nMove all terms to the left (standard form):\n$ 198x^2 + 185x + -110 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 386
} |
[
{
"role": "user",
"content": "Please find the value of 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{\\... | {
"type": "optimization",
"seed": 1337,
"index": 387
} |
[
{
"role": "user",
"content": "Please calculate this equation. Evaluate: ((180 + -1250/25) * 1) + 12^2 - log_7(117649) + (468 mod 15) + floor(-88/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((180 + -1250/25) * 1) + 12^2 - log_7(117649) + (468 mod 15) + floor(-88/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 388
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. -44x^2 + 120 - 74x = 84"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -44x^2 + 120 - 74x = 84 $\n\nMove all terms to the left (standard form):\n$ -44x^2 + -74x + 36 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 389
} |
[
{
"role": "user",
"content": "Can you find the solution to 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... | {
"type": "optimization",
"seed": 1337,
"index": 390
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Evaluate: ((-135 + -112/4) * 17) + 2^5 - log_4(64) + (158 mod 26) + floor(-114/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-135 + -112/4) * 17) + 2^5 - log_4(64) + (158 mod 26) + floor(-114/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 391
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 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": 392
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Evaluate: ((35 + 288/9) * 9) + 10^4 - log_4(16) + (178 mod 25) + floor(126/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((35 + 288/9) * 9) + 10^4 - log_4(16) + (178 mod 25) + floor(126/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 393
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Prove that $f(x,y)=\\frac12(6x^2+9y^2)+0x+0y+-1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(6x^2+9y^2)+0x+0y+-1 $\n\n$ \\frac{\\partial^2 f}... | {
"type": "optimization",
"seed": 1337,
"index": 394
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. -46 + 119 - 64x = 182x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -46 + 119 - 64x = 182x^2 $\n\nMove all terms to the left (standard form):\n$ -182x^2 + -64x + 73 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 395
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Evaluate: ((82 + 42/3) * 1) + 6^5 - log_5(5) + (-247 mod 22) + floor(-76/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((82 + 42/3) * 1) + 6^5 - log_5(5) + (-247 mod 22) + floor(-76/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 396
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. -20x - 738 = 480"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -20x - 738 = 480 $\n\nMove all terms to the left (standard form):\n$ -20x + -1218 = 0 $\n\nIsolate the $x$ term:\n$ -20x = 1218 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 397
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Find $A^{-1}$ for $A=\\begin{pmatrix}-6&9\\\\6&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -6 & 9 \\\\ 6 & 2 \\end{pmatrix} $\n\nCompute the determinant: ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 398
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Evaluate: ((115 + -108/6) * 7) + 11^4 - log_6(216) + (-299 mod 25) + floor(-87/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((115 + -108/6) * 7) + 11^4 - log_6(216) + (-299 mod 25) + floor(-87/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 399
} |
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