messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Determine the value produced by this equation. -29x^2 - 19 + 42 = 150x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -29x^2 - 19 + 42 = 150x $\n\nMove all terms to the left (standard form):\n$ -29x^2 + -150x + 23 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4700
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. -22 - 234 = 741x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -22 - 234 = 741x $\n\nMove all terms to the left (standard form):\n$ -741x + -256 = 0 $\n\nIsolate the $x$ term:\n$ -741x = 256 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4701
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: -554x - 107 = -402"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -554x - 107 = -402 $\n\nMove all terms to the left (standard form):\n$ -554x + 295 = 0 $\n\nIsolate the $x$ term:\n$ -554x = -295 $\n\nDivide both sides by the coefficie... | {
"type": "linear_equation",
"seed": 1337,
"index": 4702
} |
[
{
"role": "user",
"content": "Can you compute this equation? Differentiate with respect to $x$: $f(x) = -1\\sin(1x) + -4\\cos(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1\\sin(1x) + -4\\cos(4x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\b... | {
"type": "calculus",
"seed": 1337,
"index": 4703
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&-1&0\\\\\\0&2&-3\\\\\\0&-1&0\\end{pmatrix},\\quad b=\\begin{pmatrix}-17\\\\\\3\\\\\\3\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4704
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Compute $(-174+166) \\bmod 15$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-174+166) \\bmod 15 $\n\nUse the rule that addition is compatible with reducti... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4705
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. + 149x^2 - 148 = -179x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ + 149x^2 - 148 = -179x $\n\nMove all terms to the left (standard form):\n$ 149x^2 + 179x + -148 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4706
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-4&1&-1\\\\\\-2&2&-5\\\\\\5&-5&4\\end{pmatrix},\\quad b=\\begin{pmatrix}-7\\\\\\-5\\\\\\21\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4707
} |
[
{
"role": "user",
"content": "Compute the result for the following 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": 4708
} |
[
{
"role": "user",
"content": "Please work out 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^2-1... | {
"type": "optimization",
"seed": 1337,
"index": 4709
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. 918 - 119x = -601"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 918 - 119x = -601 $\n\nMove all terms to the left (standard form):\n$ -119x + 1519 = 0 $\n\nIsolate the $x$ term:\n$ -119x = -1519 ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4710
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. 626 - 183 = -184x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 626 - 183 = -184x $\n\nMove all terms to the left (standard form):\n$ 184x + 443 = 0 $\n\nIsolate the $x$ term:\n$ 184x = -443 $\n\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 4711
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, henc... | {
"type": "optimization",
"seed": 1337,
"index": 4712
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Differentiate with respect to $x$: $f(x) = (3x + 5)\\sin(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (3x + 5)\\sin(1x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{3\\s... | {
"type": "calculus",
"seed": 1337,
"index": 4713
} |
[
{
"role": "user",
"content": "Please calculate this equation. Prove that $f(x,y)=\\frac12(4x^2+2y^2)+1x+-6y+-4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+2y^2)+1x+-6y+-4 $\n\n$ \\frac{\\partial^2 f}{\\partial x^... | {
"type": "optimization",
"seed": 1337,
"index": 4714
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Evaluate: ((-198 + -437/19) * 13) + 8^5 - log_6(1296) + (-23 mod 26) + floor(173/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-198 + -437/19) * 13) + 8^5 - log_6(1296) + (-23 mod 26) + fl... | {
"type": "arithmetic",
"seed": 1337,
"index": 4715
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Prove that $f(x)=9x^2+10x+7$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+10x+7$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x)... | {
"type": "optimization",
"seed": 1337,
"index": 4716
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((47 + -115/23) * 14) + 9^2 - log_8(512) + (-212 mod 10) + floor(-184/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((47 + -115/23) * 14) + 9^2 - log_8(512) + (-212 mod 10) + floor(-184/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 4717
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 6x - 142 + 55x^2 = 70"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 6x - 142 + 55x^2 = 70 $\n\nMove all terms to the left (standard form):\n$ 55x^2 + 6x + -212 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4718
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Differentiate with respect to $x$: $f(x) = 7\\sin(5x) + -2\\cos(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 7\\sin(5x) + -2\\cos(5x) $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 4719
} |
[
{
"role": "user",
"content": "Solve the following math equation. Solve for $x$ (in radians): cos(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(\\frac{1... | {
"type": "trigonometry",
"seed": 1337,
"index": 4720
} |
[
{
"role": "user",
"content": "Can you solve the equation below? -361x - 836 = 979"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -361x - 836 = 979 $\n\nMove all terms to the left (standard form):\n$ -361x + -1815 = 0 $\n\nIsolate the $x$ term:\n$ -361x = 1815 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 4721
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Differentiate with respect to $x$: $f(x) = \\ln(3x + -9)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(3x + -9) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\... | {
"type": "calculus",
"seed": 1337,
"index": 4722
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. -20 - 188x + 144 = -42x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -20 - 188x + 144 = -42x^2 $\n\nMove all terms to the left (standard form):\n$ 42x^2 + -188x + 124 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4723
} |
[
{
"role": "user",
"content": "Determine the value produced by this 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... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4724
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. 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$ \\alpha = ... | {
"type": "trigonometry",
"seed": 1337,
"index": 4725
} |
[
{
"role": "user",
"content": "Solve this equation accurately. -250x + 473 = 641"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -250x + 473 = 641 $\n\nMove all terms to the left (standard form):\n$ -250x + -168 = 0 $\n\nIsolate the $x$ term:\n$ -250x = 168 $\n\nDivide both sides by... | {
"type": "linear_equation",
"seed": 1337,
"index": 4726
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Differentiate with respect to $x$: $f(x) = (-5x + -5)e^{2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-5x + -5)e^{2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-5... | {
"type": "calculus",
"seed": 1337,
"index": 4727
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 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... | {
"type": "optimization",
"seed": 1337,
"index": 4728
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((30 + -96/24) * 7) + 6^3 - log_4(64) + (-78 mod 22) + floor(-79/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((30 + -96/24) * 7) + 6^3 - log_4(64) + (-78 mod 22) + floor(-79/2) $\n\nCompute each comp... | {
"type": "arithmetic",
"seed": 1337,
"index": 4729
} |
[
{
"role": "user",
"content": "Find the final answer to the given 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 = \\arc... | {
"type": "trigonometry",
"seed": 1337,
"index": 4730
} |
[
{
"role": "user",
"content": "Can you evaluate 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$ \\alpha =... | {
"type": "trigonometry",
"seed": 1337,
"index": 4731
} |
[
{
"role": "user",
"content": "Can you compute this equation? Differentiate with respect to $x$: $f(x) = -8\\sin(8x) + 5\\cos(3x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -8\\sin(8x) + 5\\cos(3x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\box... | {
"type": "calculus",
"seed": 1337,
"index": 4732
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Evaluate: ((-131 + 500/10) * 3) + 6^5 - log_6(6) + (-400 mod 30) + round(162/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-131 + 500/10) * 3) + 6^5 - log_6(6) + (-400 mod 30) + round(162/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 4733
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Evaluate: ((-187 + -286/11) * 5) + 7^3 - log_4(1024) + (-100 mod 4) + round(169/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-187 + -286/11) * 5) + 7^3 - log_4(1024) + (-100 mod 4) + round(169... | {
"type": "arithmetic",
"seed": 1337,
"index": 4734
} |
[
{
"role": "user",
"content": "Work out the result of this equation. 5x + 41 - 69 = -89x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 5x + 41 - 69 = -89x^2 $\n\nMove all terms to the left (standard form):\n$ 89x^2 + 5x + -28 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4735
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Compute the indefinite integral: $\\int (4x + 7)e^{1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (4x + 7)e^{1x}\\,dx $\n\nUse standard antiderivatives (and integration by par... | {
"type": "calculus",
"seed": 1337,
"index": 4736
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Prove that $f(x,y)=\\frac12(3x^2+5y^2)+1x+0y+-6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+5y^2)+1x+0y+-6 $\n\n$ \\frac{\\partial^2 f}{\... | {
"type": "optimization",
"seed": 1337,
"index": 4737
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Evaluate: ((-135 + -924/22) * 19) + 10^3 - log_7(343) + (172 mod 12) + round(-14/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-135 + -924/22) * 19) + 10^3 - log_7(343) + (172 mod 12) + round(-14/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 4738
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. 44x - 5 + 144x^2 = -89"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 44x - 5 + 144x^2 = -89 $\n\nMove all terms to the left (standard form):\n$ 144x^2 + 44x + 84 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4739
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. -344 + 220 = -573x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -344 + 220 = -573x $\n\nMove all terms to the left (standard form):\n$ 573x + -124 = 0 $\n\nIsolate the $x$ term:\n$ 573x = 124 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 4740
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. -28 - 19 - 20x^2 = 105x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -28 - 19 - 20x^2 = 105x $\n\nMove all terms to the left (standard form):\n$ -20x^2 + -105x + -47 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4741
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. -221x + 420 = -146"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -221x + 420 = -146 $\n\nMove all terms to the left (standard form):\n$ -221x + 566 = 0 $\n\nIsolate the $x$ term:\n$ -221x = -566 $... | {
"type": "linear_equation",
"seed": 1337,
"index": 4742
} |
[
{
"role": "user",
"content": "Please solve this mathematical 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{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 4743
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 867 + 378x = 211"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 867 + 378x = 211 $\n\nMove all terms to the left (standard form):\n$ 378x + 656 = 0 $\n\nIsolate the $x$ term:\n$ 378x = -656 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 4744
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Compute $(-115+-175) \\bmod 10$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-115+-175) \\bmod 10 $\n\nUse the rule that addition is compatible with reducti... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4745
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Evaluate: ((11 + -105/15) * 5) + 11^4 - log_7(117649) + (-374 mod 16) + floor(82/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((11 + -105/15) * 5) + 11^4 - log_7(117649) + (-374 mod 16) + floor(82... | {
"type": "arithmetic",
"seed": 1337,
"index": 4746
} |
[
{
"role": "user",
"content": "Calculate the answer for 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(\\f... | {
"type": "trigonometry",
"seed": 1337,
"index": 4747
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 887 - 345x = 663"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 887 - 345x = 663 $\n\nMove all terms to the left (standard form):\n$ -345x + 224 = 0 $\n\nIsolate the $x$ term:\n$ -345x = -224 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 4748
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Compute the indefinite integral: $\\int \\ln(7x + 7)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(7x + 7)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int \\ln(7x + ... | {
"type": "calculus",
"seed": 1337,
"index": 4749
} |
[
{
"role": "user",
"content": "Solve the equation shown below. -41 + 127x + 156x^2 = 154"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -41 + 127x + 156x^2 = 154 $\n\nMove all terms to the left (standard form):\n$ 156x^2 + 127x + -195 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4750
} |
[
{
"role": "user",
"content": "Please compute the solution to this 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{\\... | {
"type": "optimization",
"seed": 1337,
"index": 4751
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. 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": 4752
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Evaluate: ((-162 + -132/11) * 9) + 9^2 - log_5(625) + (191 mod 26) + floor(48/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-162 + -132/11) * 9) + 9^2 - log_5(625) + (191 mod 26) + floor(48/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 4753
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical 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 value... | {
"type": "trigonometry",
"seed": 1337,
"index": 4754
} |
[
{
"role": "user",
"content": "Compute the solution for 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": 4755
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Prove that $f(x)=8x^2+-4x+-3$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=8x^2+-4x+-3$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) =... | {
"type": "optimization",
"seed": 1337,
"index": 4756
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Differentiate with respect to $x$: $f(x) = -1\\sin(1x) + 3\\cos(9x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1\\sin(1x) + 3\\cos(9x) $\n\nApply the standard differentiation rules:... | {
"type": "calculus",
"seed": 1337,
"index": 4757
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. -110x - 10 = -949"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -110x - 10 = -949 $\n\nMove all terms to the left (standard form):\n$ -110x + 939 = 0 $\n\nIsolate the $x$ term:\n$ -110x = -939 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 4758
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Compute the determinant: $A=\\begin{pmatrix}-2&2\\\\5&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-2&2\\\\\\5&-4\\end{pmatrix} $\n\nUse $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4759
} |
[
{
"role": "user",
"content": "Please calculate this equation. Evaluate: ((-107 + 18/2) * 20) + 3^4 - log_10(100) + (-425 mod 15) + floor(-77/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-107 + 18/2) * 20) + 3^4 - log_10(100) + (-425 mod 15) + floor(-77/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 4760
} |
[
{
"role": "user",
"content": "Find the value that satisfies this 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 $a,b\\in\\mathb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4761
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Evaluate: ((109 + 893/19) * 19) + 5^5 - log_3(81) + (97 mod 6) + ceil(143/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((109 + 893/19) * 19) + 5^5 - log_3(81) + (97 mod 6) + ceil(143/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 4762
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. 11 + 196 - 155x = -136x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 11 + 196 - 155x = -136x^2 $\n\nMove all terms to the left (standard form):\n$ 136x^2 + -155x + 207 = 0 $\n\nApply the quadr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4763
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Differentiate with respect to $x$: $f(x) = -2e^{5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -2e^{5x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-10e^{5x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 4764
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Find $A^{-1}$ for $A=\\begin{pmatrix}-6&-9\\\\-4&-5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -6 & -9 \\\\ -4 & -5 \\end{pmatrix} $\n\nCompute the de... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4765
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Evaluate: ((111 + -88/8) * 17) + 3^4 - log_3(243) + (390 mod 8) + round(-182/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((111 + -88/8) * 17) + 3^4 - log_3(243) + (390 mod 8) + round(-182/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 4766
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. 32 - 178x - 83 = 86x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 32 - 178x - 83 = 86x^2 $\n\nMove all terms to the left (standard form):\n$ -86x^2 + -178x + -51 = 0 $\n\nApply the quadratic ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4767
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Solve for $x$ (in radians): sin(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 0 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(0) = 0 $\n\nThe gen... | {
"type": "trigonometry",
"seed": 1337,
"index": 4768
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. 42x + 45 - 98x^2 = 177"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 42x + 45 - 98x^2 = 177 $\n\nMove all terms to the left (standard form):\n$ -98x^2 + 42x + -132 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4769
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 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": 4770
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. 683x - 456 = 671"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 683x - 456 = 671 $\n\nMove all terms to the left (standard form):\n$ 683x + -1127 = 0 $\n\nIsolate the $x$ term:\n$ 683x = 1127 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 4771
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Prove that $(\\mathbb{Z}_19, +)$ is a group under addition modulo 19."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_19=\\{0,1,\\dots,18\\}$ with operation $+$ modulo $19$.\n\n**Closure:** If $a,b\\in\\ma... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4772
} |
[
{
"role": "user",
"content": "Please evaluate and compute 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{\\pa... | {
"type": "optimization",
"seed": 1337,
"index": 4773
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Find the modular inverse of 17 modulo 23, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $17\\cdot a^{-1} \\equiv 1 \\pmod{23}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantee... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4774
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Solve for $x$ (in radians): tan(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 0 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(0) = 0 $\n\nThe general so... | {
"type": "trigonometry",
"seed": 1337,
"index": 4775
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Compute the determinant: $A=\\begin{pmatrix}-7&-3\\\\6&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-7&-3\\\\\\6&8\\end{pmatrix} $\n\nUse... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4776
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Evaluate: ((-186 + 1056/22) * 15) + 12^2 - log_3(9) + (-377 mod 4) + floor(141/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-186 + 1056/22) * 15) + 12^2 - log_3(9) + (-377 mod 4) + floor(141/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 4777
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Evaluate: ((-5 + 141/3) * 12) + 8^4 - log_6(6) + (-287 mod 20) + round(99/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-5 + 141/3) * 12) + 8^4 - log_6(6) + (-287 mod 20) + round(99/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4778
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Evaluate: ((-117 + 72/9) * 13) + 4^5 - log_5(5) + (312 mod 22) + floor(179/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-117 + 72/9) * 13) + 4^5 - log_5(5) + (312 mod 22) + floor(179/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4779
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. 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": 4780
} |
[
{
"role": "user",
"content": "Find the answer to the following 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$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 4781
} |
[
{
"role": "user",
"content": "solve: \n\n 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 $(a+b)\\bmod n\\in\\{0,1... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4782
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. -49 + 167x^2 - 139 = 195x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -49 + 167x^2 - 139 = 195x $\n\nMove all terms to the left (standard form):\n$ 167x^2 + -195x + -188 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4783
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Compute the indefinite integral: $\\int (-3x + 0)e^{6x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-3x + 0)e^{6x}\\,dx $\n\nUse standard antiderivatives (and integration by par... | {
"type": "calculus",
"seed": 1337,
"index": 4784
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Compute $(-122+-36) \\bmod 9$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-122+-36) \\bmod 9 $\n\nUse the rule that addition is compatible with reductio... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4785
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. -274 - 823 = -258x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -274 - 823 = -258x $\n\nMove all terms to the left (standard form):\n$ 258x + -1097 = 0 $\n\nIsolate the $x$ term:\n$ 258x = 1097 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 4786
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Evaluate: ((-34 + -270/6) * 12) + 6^3 - log_7(16807) + (173 mod 26) + ceil(-71/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-34 + -270/6) * 12) + 6^3 - log_7(16807) + (173 mod 26) + ceil(-71/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 4787
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Evaluate: ((138 + 675/15) * 2) + 4^3 - log_3(729) + (97 mod 2) + floor(-74/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((138 + 675/15) * 2) + 4^3 - log_3(729) + (97 mod 2) + floor(-74/2) $\n\nCompute... | {
"type": "arithmetic",
"seed": 1337,
"index": 4788
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. -4 + 127 - 27x = -64x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -4 + 127 - 27x = -64x^2 $\n\nMove all terms to the left (standard form):\n$ 64x^2 + -27x + 123 = 0 $\n\nApply the quadratic... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4789
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Compute the indefinite integral: $\\int \\ln(5x + 4)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(5x + 4)\\,dx $\n\nUse standard antiderivatives (and integration by parts i... | {
"type": "calculus",
"seed": 1337,
"index": 4790
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. 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": 4791
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. -784 - 976 = -346x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -784 - 976 = -346x $\n\nMove all terms to the left (standard form):\n$ 346x + -1760 = 0 $\n\nIsolate the $x$ term:\n$ 346x = 1760 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 4792
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. -913 + 373 = -256x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -913 + 373 = -256x $\n\nMove all terms to the left (standard form):\n$ 256x + -540 = 0 $\n\nIsolate the $x$ term:\n$ 256x = 540 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 4793
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Compute the indefinite integral: $\\int \\ln(2x + -2)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(2x + -2)\\,dx $\n\nUse standard antiderivatives (and integration by parts if... | {
"type": "calculus",
"seed": 1337,
"index": 4794
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. 520 - 646x = 408"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 520 - 646x = 408 $\n\nMove all terms to the left (standard form):\n$ -646x + 112 = 0 $\n\nIsolate the $x$ term:\n$ -646x = -112 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 4795
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Solve for $x$ (in radians): tan(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha ... | {
"type": "trigonometry",
"seed": 1337,
"index": 4796
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. 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": 4797
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Solve for $x$ (in radians): cos(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\ar... | {
"type": "trigonometry",
"seed": 1337,
"index": 4798
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Evaluate: ((119 + 575/25) * 19) + 5^2 - log_2(16) + (-298 mod 24) + floor(54/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((119 + 575/25) * 19) + 5^2 - log_2(16) + (-298 mod 24) + floor(54/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 4799
} |
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