messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Solve the equation and return the answer. 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$ \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 4300
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n... | {
"type": "optimization",
"seed": 1337,
"index": 4301
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Evaluate: ((95 + 414/9) * 19) + 6^3 - log_9(6561) + (-366 mod 17) + ceil(103/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((95 + 414/9) * 19) + 6^3 - log_9(6561) + (-366 mod 17) + ceil(103/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 4302
} |
[
{
"role": "user",
"content": "Please find the solution of 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 = \\arcta... | {
"type": "trigonometry",
"seed": 1337,
"index": 4303
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. -2 - 159x - 113x^2 = -187"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -2 - 159x - 113x^2 = -187 $\n\nMove all terms to the left (standard form):\n$ -113x^2 + -159x + 185 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4304
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Prove that $f(x,y)=\\frac12(10x^2+9y^2)+2x+4y+1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(10x^2+9y^2)+2x+4y+1 $\n\n$ \\frac{\\partial^2 f}... | {
"type": "optimization",
"seed": 1337,
"index": 4305
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}3&-3\\\\\\-5&-7\\end{pmatrix},\\quad b=\\begin{pmatrix}15\\\\\\35\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}3&-3\\\\\\-5&... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4306
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Evaluate: ((-138 + 264/22) * 13) + 8^2 - log_6(1296) + (340 mod 29) + round(-55/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-138 + 264/22) * 13) + 8^2 - log_6(1296) + (340 mod 29) + round(-55/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 4307
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((133 + -224/16) * 7) + 6^5 - log_5(3125) + (271 mod 10) + round(87/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((133 + -224/16) * 7) + 6^5 - log_5(3125) + (271 mod 10) + round(87/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 4308
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Find $A^{-1}$ for $A=\\begin{pmatrix}6&9\\\\5&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 6 & 9 \\\\ 5 & 9 \\end{pmatrix} $\n\nCompute the determ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4309
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. -266 + 780x = -584"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -266 + 780x = -584 $\n\nMove all terms to the left (standard form):\n$ 780x + 318 = 0 $\n\nIsolate the $x$ term:\n$ 780x = -318 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 4310
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Differentiate with respect to $x$: $f(x) = (-5x + 8)e^{5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-5x + 8)e^{5x} $\n\nApply the standard differentiation rules:\n$ f'(x) =... | {
"type": "calculus",
"seed": 1337,
"index": 4311
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Evaluate: ((66 + 180/20) * 19) + 9^2 - log_10(1000000) + (101 mod 4) + floor(199/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((66 + 180/20) * 19) + 9^2 - log_10(1000000) + (101 mod 4) + floor(1... | {
"type": "arithmetic",
"seed": 1337,
"index": 4312
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Evaluate: ((195 + -385/11) * 6) + 9^5 - log_3(27) + (95 mod 15) + ceil(190/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((195 + -385/11) * 6) + 9^5 - log_3(27) + (95 mod 15) + ceil(190/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4313
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}2&-5\\\\\\6&1\\end{pmatrix},\\quad b=\\begin{pmatrix}29\\\\\\-57\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}2&-5\\\\\\6&1\\end{... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4314
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 365 - 599x = -313"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 365 - 599x = -313 $\n\nMove all terms to the left (standard form):\n$ -599x + 678 = 0 $\n\nIsolate the $x$ term:\n$ -599x = -678 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 4315
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. -6 + 0 + 81x^2 = -41x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -6 + 0 + 81x^2 = -41x $\n\nMove all terms to the left (standard form):\n$ 81x^2 + 41x + -6 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4316
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. 380x - 758 = -983"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 380x - 758 = -983 $\n\nMove all terms to the left (standard form):\n$ 380x + 225 = 0 $\n\nIsolate the $x$ term:\n$ 380x = -225 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 4317
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Prove that $(\\mathbb{Z}_25, +)$ is a group under addition modulo 25."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_25=\\{0,1,\\dots,24\\}$ with operation $+$ modulo $25$.\n\n**Closure:** If $a,b\\in... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4318
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 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}... | {
"type": "trigonometry",
"seed": 1337,
"index": 4319
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Evaluate: ((-17 + -448/16) * 6) + 9^5 - log_5(5) + (-233 mod 24) + round(35/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-17 + -448/16) * 6) + 9^5 - log_5(5) + (-233 mod 24) + round(35/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 4320
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Find the modular inverse of 8 modulo 27, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $8\\cdot a^{-1} \\equiv 1 \\pmod{27}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identit... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4321
} |
[
{
"role": "user",
"content": "Resolve this equation and give 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$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 4322
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute the indefinite integral: $\\int \\ln(6x + -9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(6x + -9)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n... | {
"type": "calculus",
"seed": 1337,
"index": 4323
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}9&-3\\\\\\-5&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}-12\\\\\\16\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}9&-3\\\\\\-5&-3\\end{pm... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4324
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Compute $(-84+119) \\bmod 2$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-84+119) \\bmod 2 $\n\nUse the rule that addition is compatible with reduction modulo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4325
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. -639 + 221 = 312x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -639 + 221 = 312x $\n\nMove all terms to the left (standard form):\n$ -312x + -418 = 0 $\n\nIsolate the $x$ term:\n$ -312x = 418 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 4326
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. 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": 4327
} |
[
{
"role": "user",
"content": "Evaluate the following equation. -383 - 912x = -844"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -383 - 912x = -844 $\n\nMove all terms to the left (standard form):\n$ -912x + 461 = 0 $\n\nIsolate the $x$ term:\n$ -912x = -461 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 4328
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. -322 + 26 = 345x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -322 + 26 = 345x $\n\nMove all terms to the left (standard form):\n$ -345x + -296 = 0 $\n\nIsolate the $x$ term:\n$ -345x = 296 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 4329
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Evaluate: ((111 + -480/10) * 4) + 6^4 - log_5(25) + (-123 mod 20) + round(186/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((111 + -480/10) * 4) + 6^4 - log_5(25) + (-123 mod 20) + round(186/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 4330
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. -36x^2 + 48 - 15x = 198"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -36x^2 + 48 - 15x = 198 $\n\nMove all terms to the left (standard form):\n$ -36x^2 + -15x + -150 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4331
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. 222 - 256 = -288x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 222 - 256 = -288x $\n\nMove all terms to the left (standard form):\n$ 288x + -34 = 0 $\n\nIsolate the $x$ term:\n$ 288x = 34 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 4332
} |
[
{
"role": "user",
"content": "Please calculate this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-2&4\\\\\\5&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}-4\\\\\\-15\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-2&4\\\\\\5&-5\\end{pmatri... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4333
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. 43x^2 - 2x - 184 = -167"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 43x^2 - 2x - 184 = -167 $\n\nMove all terms to the left (standard form):\n$ 43x^2 + -2x + -17 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4334
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Evaluate: ((-132 + 144/16) * 20) + 7^5 - log_10(100) + (471 mod 22) + ceil(82/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-132 + 144/16) * 20) + 7^5 - log_10(100) + (471 mod 22) + cei... | {
"type": "arithmetic",
"seed": 1337,
"index": 4335
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. 25 + 74 + 199x = -93x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 25 + 74 + 199x = -93x^2 $\n\nMove all terms to the left (standard form):\n$ 93x^2 + 199x + 99 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4336
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. -32 + 78x^2 - 164x = 176"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -32 + 78x^2 - 164x = 176 $\n\nMove all terms to the left (standard form):\n$ 78x^2 + -164x + -208 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4337
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 22 + 182 + 65x^2 = -19x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 22 + 182 + 65x^2 = -19x $\n\nMove all terms to the left (standard form):\n$ 65x^2 + 19x + 204 = 0 $\n\nApply the quadratic... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4338
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Evaluate: ((200 + -135/3) * 6) + 12^4 - log_6(7776) + (-107 mod 14) + ceil(124/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((200 + -135/3) * 6) + 12^4 - log_6(7776) + (-107 mod 14) + ceil(124/... | {
"type": "arithmetic",
"seed": 1337,
"index": 4339
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Evaluate: ((177 + 130/5) * 8) + 10^5 - log_2(8) + (-241 mod 2) + round(-140/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((177 + 130/5) * 8) + 10^5 - log_2(8) + (-241 mod 2) + round(-140/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4340
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Differentiate with respect to $x$: $f(x) = -2\\sin(3x) + 9\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -2\\sin(3x) + 9\\cos(7x) $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 4341
} |
[
{
"role": "user",
"content": "Solve this equation accurately. -638 - 71x = -874"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -638 - 71x = -874 $\n\nMove all terms to the left (standard form):\n$ -71x + 236 = 0 $\n\nIsolate the $x$ term:\n$ -71x = -236 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 4342
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. 784 + 714x = -53"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 784 + 714x = -53 $\n\nMove all terms to the left (standard form):\n$ 714x + 837 = 0 $\n\nIsolate the $x$ term:\n$ 714x = -837 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 4343
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-8&9\\\\\\-9&2\\end{pmatrix},\\quad b=\\begin{pmatrix}-24\\\\\\-27\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-8&9\\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4344
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. -50x + 87 + 8x^2 = -82"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -50x + 87 + 8x^2 = -82 $\n\nMove all terms to the left (standard form):\n$ 8x^2 + -50x + 169 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4345
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. -37x + 321 = -323"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -37x + 321 = -323 $\n\nMove all terms to the left (standard form):\n$ -37x + 644 = 0 $\n\nIsolate the $x$ term:\n$ -37x = -644 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 4346
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-8&2\\\\-9&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -8 & 2 \\\\ -9 & 9 \\end{pmatrix} $\n\nCompute the ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4347
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Compute $(-35+90) \\bmod 11$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-35+90) \\bmod 11 $\n\nUse the rule that addition is compatible with reductio... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4348
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Compute the determinant: $A=\\begin{pmatrix}-5&-3\\\\-7&5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-5&-3\\\\\\-7&5\\end{pmatrix} $\n\nUse $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4349
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Evaluate: ((62 + 51/3) * 17) + 7^2 - log_5(125) + (-99 mod 22) + round(121/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((62 + 51/3) * 17) + 7^2 - log_5(125) + (-99 mod 22) + round(121/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 4350
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-2&1\\\\\\-2&5\\end{pmatrix},\\quad b=\\begin{pmatrix}-6\\\\\\-22\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-2&... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4351
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Evaluate: ((129 + -204/6) * 10) + 8^4 - log_10(1000) + (64 mod 19) + round(156/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((129 + -204/6) * 10) + 8^4 - log_10(1000) + (64 mod 19) + round(156/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 4352
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. -21x^2 + 82 + 63 = -41x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -21x^2 + 82 + 63 = -41x $\n\nMove all terms to the left (standard form):\n$ -21x^2 + 41x + 145 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4353
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Differentiate with respect to $x$: $f(x) = 7\\sin(3x) + -9\\cos(9x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 7\\sin(3x) + -9\\cos(9x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\bo... | {
"type": "calculus",
"seed": 1337,
"index": 4354
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. -36x^2 + 39 - 140 = -167x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -36x^2 + 39 - 140 = -167x $\n\nMove all terms to the left (standard form):\n$ -36x^2 + 167x + -101 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4355
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 12 + 92x^2 + 154 = -54x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 12 + 92x^2 + 154 = -54x $\n\nMove all terms to the left (standard form):\n$ 92x^2 + 54x + 166 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4356
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. 31x^2 - 8x + 90 = -58"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 31x^2 - 8x + 90 = -58 $\n\nMove all terms to the left (standard form):\n$ 31x^2 + -8x + 148 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4357
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Evaluate: ((-167 + 902/22) * 9) + 8^4 - log_8(8) + (-180 mod 12) + round(196/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-167 + 902/22) * 9) + 8^4 - log_8(8) + (-180 mod 12) + round(196/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 4358
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: 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^2-1)=0 \\Rightarro... | {
"type": "optimization",
"seed": 1337,
"index": 4359
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&1&3\\\\\\0&-1&5\\\\\\-5&-3&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-3\\\\\\4\\\\\\7\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4360
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Compute the determinant: $A=\\begin{pmatrix}1&-7\\\\7&6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}1&-7\\\\\\7&6\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4361
} |
[
{
"role": "user",
"content": "Compute the value of the following 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) = 0 $\n\nThe gene... | {
"type": "trigonometry",
"seed": 1337,
"index": 4362
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Evaluate: ((-189 + -30/5) * 20) + 12^5 - log_7(2401) + (249 mod 4) + ceil(110/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-189 + -30/5) * 20) + 12^5 - log_7(2401) + (249 mod 4) + ceil(11... | {
"type": "arithmetic",
"seed": 1337,
"index": 4363
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. -55x + 258 = 215"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -55x + 258 = 215 $\n\nMove all terms to the left (standard form):\n$ -55x + 43 = 0 $\n\nIsolate the $x$ term:\n$ -55x = -43 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 4364
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute $(-197+-66) \\bmod 15$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-197+-66) \\bmod 15 $\n\nUse the rule that addition is compatible with reduction modulo $n$... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4365
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Differentiate with respect to $x$: $f(x) = -4\\sin(6x) + -2\\cos(7x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -4\\sin(6x) + -2\\cos(7x) $\n\nApply the standard differentiation rules:\... | {
"type": "calculus",
"seed": 1337,
"index": 4366
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. -678 + 424x = 406"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -678 + 424x = 406 $\n\nMove all terms to the left (standard form):\n$ 424x + -1084 = 0 $\n\nIsolate the $x$ term:\n$ 424x = 1084 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 4367
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. 422 + 110 = 583x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 422 + 110 = 583x $\n\nMove all terms to the left (standard form):\n$ -583x + 532 = 0 $\n\nIsolate the $x$ term:\n$ -583x = -532 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 4368
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((-30 + 855/19) * 4) + 8^4 - log_9(6561) + (449 mod 29) + floor(46/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-30 + 855/19) * 4) + 8^4 - log_9(6561) + (449 mod 29) + floor(... | {
"type": "arithmetic",
"seed": 1337,
"index": 4369
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Differentiate with respect to $x$: $f(x) = -9e^{-5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -9e^{-5x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{45e^{-5x}} $"... | {
"type": "calculus",
"seed": 1337,
"index": 4370
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. 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 val... | {
"type": "trigonometry",
"seed": 1337,
"index": 4371
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Evaluate: ((-48 + 165/5) * 18) + 6^4 - log_6(7776) + (134 mod 7) + ceil(178/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-48 + 165/5) * 18) + 6^4 - log_6(7776) + (134 mod 7) + ceil(178/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4372
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Compute the determinant: $A=\\begin{pmatrix}9&-2\\\\9&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}9&-2\\\\\\9&1\\end{pmatrix} $\n\nUse... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4373
} |
[
{
"role": "user",
"content": "Determine the solution of the given 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 $\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 4374
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. -372x - 717 = 471"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -372x - 717 = 471 $\n\nMove all terms to the left (standard form):\n$ -372x + -1188 = 0 $\n\nIsolate the $x$ term:\n$ -372x = 1188 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 4375
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, henc... | {
"type": "optimization",
"seed": 1337,
"index": 4376
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? -21 + 181x^2 + 107x = -140"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -21 + 181x^2 + 107x = -140 $\n\nMove all terms to the left (standard form):\n$ 181x^2 + 107x + 119 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4377
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Differentiate with respect to $x$: $f(x) = -7e^{-5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -7e^{-5x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{35e^{-5x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 4378
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Compute the indefinite integral: $\\int -2x^3 + 3x^2 + 8x + 13\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -2x^3 + 3x^2 + 8x + 13\\,dx $\n\nUse standard antiderivatives (and ... | {
"type": "calculus",
"seed": 1337,
"index": 4379
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-6&-6\\\\0&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -6 & -6 \\\\ 0 & 8 \\end{pmatrix} $\n\nCompute the dete... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4380
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. 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 $a,b\\in\\mathbb{Z}_n$, ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4381
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Evaluate: ((49 + -473/11) * 10) + 12^3 - log_6(6) + (-148 mod 9) + floor(-91/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((49 + -473/11) * 10) + 12^3 - log_6(6) + (-148 mod 9) + floor(-91/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 4382
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Compute the determinant: $A=\\begin{pmatrix}-4&-6\\\\-9&7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&-6\\\\\\-9&7\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4383
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. -187x - 674 = -61"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -187x - 674 = -61 $\n\nMove all terms to the left (standard form):\n$ -187x + -613 = 0 $\n\nIsolate the $x$ term:\n$ -187x = 613 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 4384
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 20 - 95x + 38x^2 = -199"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 20 - 95x + 38x^2 = -199 $\n\nMove all terms to the left (standard form):\n$ 38x^2 + -95x + 219 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4385
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Find the modular inverse of 17 modulo 18, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $17\\cdot a^{-1} \\equiv 1 \\pmod{18}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4386
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. -753x - 298 = -426"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -753x - 298 = -426 $\n\nMove all terms to the left (standard form):\n$ -753x + 128 = 0 $\n\nIsolate the $x$ term:\n$ -753x = -128 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4387
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Compute $(-165+113) \\bmod 24$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-165+113) \\bmod 24 $\n\nUse the rule that addition is compatible with reducti... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4388
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. -615 + 88 = -275x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -615 + 88 = -275x $\n\nMove all terms to the left (standard form):\n$ 275x + -527 = 0 $\n\nIsolate the $x$ term:\n$ 275x = 527 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 4389
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. -42 + 27x - 160 = 55x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -42 + 27x - 160 = 55x^2 $\n\nMove all terms to the left (standard form):\n$ -55x^2 + 27x + -202 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4390
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. 5 - 70x - 171 = -9x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 5 - 70x - 171 = -9x^2 $\n\nMove all terms to the left (standard form):\n$ 9x^2 + -70x + -166 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4391
} |
[
{
"role": "user",
"content": "Please evaluate and solve this 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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 4392
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. -24x^2 + 57 - 189 = -143x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -24x^2 + 57 - 189 = -143x $\n\nMove all terms to the left (standard form):\n$ -24x^2 + 143x + -132 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4393
} |
[
{
"role": "user",
"content": "Evaluate the following equation. -529 + 416 = 945x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -529 + 416 = 945x $\n\nMove all terms to the left (standard form):\n$ -945x + -113 = 0 $\n\nIsolate the $x$ term:\n$ -945x = 113 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 4394
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Evaluate: ((146 + 352/22) * 9) + 9^3 - log_10(10) + (411 mod 8) + round(72/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((146 + 352/22) * 9) + 9^3 - log_10(10) + (411 mod 8) + round(72/2) $\n\nCompute each component:\n$ 352/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 4395
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? -41x^2 - 92x + 117 = -165"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -41x^2 - 92x + 117 = -165 $\n\nMove all terms to the left (standard form):\n$ -41x^2 + -92x + 282 = 0 $\n\nApply the quadratic... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4396
} |
[
{
"role": "user",
"content": "Please work out this equation. -352x - 266 = -45"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -352x - 266 = -45 $\n\nMove all terms to the left (standard form):\n$ -352x + -221 = 0 $\n\nIsolate the $x$ term:\n$ -352x = 221 $\n\nDivide both sides by ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4397
} |
[
{
"role": "user",
"content": "Calculate the solution to this math 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": 4398
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. -177 - 738 = 470x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -177 - 738 = 470x $\n\nMove all terms to the left (standard form):\n$ -470x + -915 = 0 $\n\nIsolate the $x$ term:\n$ -470x = 915 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 4399
} |
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