messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Please calculate and resolve 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": 5600
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Evaluate: ((158 + 225/25) * 8) + 7^3 - log_8(4096) + (-432 mod 6) + ceil(-115/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((158 + 225/25) * 8) + 7^3 - log_8(4096) + (-432 mod 6) + ceil(-115/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 5601
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. -939 - 887 = 413x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -939 - 887 = 413x $\n\nMove all terms to the left (standard form):\n$ -413x + -1826 = 0 $\n\nIsolate the $x$ term:\n$ -413x = 1826 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 5602
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? 846 - 141x = -632"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 846 - 141x = -632 $\n\nMove all terms to the left (standard form):\n$ -141x + 1478 = 0 $\n\nIsolate the $x$ term:\n$ -141x = -1478 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 5603
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Compute the indefinite integral: $\\int \\ln(9x + 1)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(9x + 1)\\,dx $\n\nUse standard antiderivatives (and integration by parts if... | {
"type": "calculus",
"seed": 1337,
"index": 5604
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}1&-1\\\\\\-4&9\\end{pmatrix},\\quad b=\\begin{pmatrix}-5\\\\\\30\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}1&-1\\\\\\-4&9\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5605
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. 712x - 676 = 974"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 712x - 676 = 974 $\n\nMove all terms to the left (standard form):\n$ 712x + -1650 = 0 $\n\nIsolate the $x$ term:\n$ 712x = 1650 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 5606
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. -34 + 197x - 99 = -27x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -34 + 197x - 99 = -27x^2 $\n\nMove all terms to the left (standard form):\n$ 27x^2 + 197x + -133 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5607
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Find the modular inverse of 33 modulo 34, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $33\\cdot a^{-1} \\equiv 1 \\pmod{34}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5608
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Find the modular inverse of 7 modulo 34, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{34}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guaran... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5609
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Compute $(-12+106) \\bmod 8$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-12+106) \\bmod 8 $\n\nUse the rule that addition is compatible with reduction... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5610
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. -27x^2 + 105x + 11 = 102"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -27x^2 + 105x + 11 = 102 $\n\nMove all terms to the left (standard form):\n$ -27x^2 + 105x + -91 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5611
} |
[
{
"role": "user",
"content": "Solve this equation step by step. -5 + 123x - 94 = -30x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -5 + 123x - 94 = -30x^2 $\n\nMove all terms to the left (standard form):\n$ 30x^2 + 123x + -99 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5612
} |
[
{
"role": "user",
"content": "solve: Differentiate with respect to $x$: $f(x) = \\ln(3x + -1)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(3x + -1) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{3}{3x + -1}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 5613
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Differentiate with respect to $x$: $f(x) = \\ln(1x + -5)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(1x + -5) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\bo... | {
"type": "calculus",
"seed": 1337,
"index": 5614
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Compute the indefinite integral: $\\int -5x^3 + -3x^2 + 2x + 8\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -5x^3 + -3x^2 + 2x + 8\\,dx $\n\nUse standard antiderivatives (and integrati... | {
"type": "calculus",
"seed": 1337,
"index": 5615
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Evaluate: ((-87 + 462/11) * 9) + 9^2 - log_8(64) + (204 mod 16) + round(116/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-87 + 462/11) * 9) + 9^2 - log_8(64) + (204 mod 16) + round(116/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 5616
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Find $A^{-1}$ for $A=\\begin{pmatrix}1&-4\\\\-2&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 1 & -4 \\\\ -2 & 9 \\end{pmatrix} $\n\nCompute the de... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5617
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. 859 + 702x = 862"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 859 + 702x = 862 $\n\nMove all terms to the left (standard form):\n$ 702x + -3 = 0 $\n\nIsolate the $x$ term:\n$ 702x = 3 $\n\nDivide both sides b... | {
"type": "linear_equation",
"seed": 1337,
"index": 5618
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Evaluate: ((9 + 138/3) * 10) + 4^5 - log_7(49) + (-154 mod 6) + floor(137/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((9 + 138/3) * 10) + 4^5 - log_7(49) + (-154 mod 6) + floor(137/2) $\n\nCompute each compo... | {
"type": "arithmetic",
"seed": 1337,
"index": 5619
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Compute $(40+-111) \\bmod 23$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (40+-111) \\bmod 23 $\n\nUse the rule that addition is compatible with reduction... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5620
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. 205 + 703 = 197x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 205 + 703 = 197x $\n\nMove all terms to the left (standard form):\n$ -197x + 908 = 0 $\n\nIsolate the $x$ term:\n$ -197x = -908 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 5621
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x... | {
"type": "optimization",
"seed": 1337,
"index": 5622
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. 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\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 5623
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Differentiate with respect to $x$: $f(x) = 7e^{4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 7e^{4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{28e^{4x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 5624
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&-3&-2\\\\\\5&1&3\\\\\\0&-1&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}-7\\\\\\17\\\\\\2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5625
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. -6 - 162 - 155x = -51x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -6 - 162 - 155x = -51x^2 $\n\nMove all terms to the left (standard form):\n$ 51x^2 + -155x + -168 = 0 $\n\nApply the quadr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5626
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Differentiate with respect to $x$: $f(x) = -1x^3 + 3x^2 + -7x + 16$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1x^3 + 3x^2 + -7x + 16 $\n\nApply the standard differentiation rules:\n$ f'(x) = \\bo... | {
"type": "calculus",
"seed": 1337,
"index": 5627
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Compute the indefinite integral: $\\int \\ln(1x + -3)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(1x + -3)\\,dx $\n\nUse standard antiderivatives (and integration by parts ... | {
"type": "calculus",
"seed": 1337,
"index": 5628
} |
[
{
"role": "user",
"content": "Please solve this math problem. Compute the indefinite integral: $\\int 2e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 2e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int 2e^{... | {
"type": "calculus",
"seed": 1337,
"index": 5629
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 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": 5630
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}4&-5&-3\\\\\\5&-4&0\\\\\\-2&1&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}-45\\\\\\-36\\\\\\0\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5631
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. 258 - 422x = -183"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 258 - 422x = -183 $\n\nMove all terms to the left (standard form):\n$ -422x + 441 = 0 $\n\nIsolate the $x$ term:\n$ -422x = -441 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 5632
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? -603 + 995x = -895"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -603 + 995x = -895 $\n\nMove all terms to the left (standard form):\n$ 995x + 292 = 0 $\n\nIsolate the $x$ term:\n$ 995x = -292 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 5633
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}4&-9\\\\\\-6&2\\end{pmatrix},\\quad b=\\begin{pmatrix}9\\\\\\44\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}4&-9\\\\\\-6&2\\end{pm... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5634
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Compute the indefinite integral: $\\int -4x^3 + 0x^2 + -10x + -16\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4x^3 + 0x^2 + -10x + -16\\,dx $\n\nUse standard antiderivatives (an... | {
"type": "calculus",
"seed": 1337,
"index": 5635
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Compute the determinant: $A=\\begin{pmatrix}6&6\\\\-7&-1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}6&6\\\\\\-7&-1\\end{pmatrix} $\n\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5636
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Prove that $(\\mathbb{Z}_29, +)$ is a group under addition modulo 29."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_29=\\{0,1,\\dots,28\\}$ with operation $+$ modulo $29$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, then $(a+b)\\bmod n\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5637
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Compute the indefinite integral: $\\int 8\\sin(8x) + 5\\cos(4x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 8\\sin(8x) + 5\\cos(4x)\\,dx $\n\nUse standard antiderivatives (and... | {
"type": "calculus",
"seed": 1337,
"index": 5638
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. 438 + 147x = -599"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 438 + 147x = -599 $\n\nMove all terms to the left (standard form):\n$ 147x + 1037 = 0 $\n\nIsolate the $x$ term:\n$ 147x = -1037 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 5639
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Evaluate: ((19 + 112/8) * 14) + 12^2 - log_8(64) + (223 mod 2) + ceil(125/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((19 + 112/8) * 14) + 12^2 - log_8(64) + (223 mod 2) + ceil(125/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 5640
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. -404 + 805x = -613"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -404 + 805x = -613 $\n\nMove all terms to the left (standard form):\n$ 805x + 209 = 0 $\n\nIsolate the $x$ term:\n$ 805x = -209 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 5641
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\fra... | {
"type": "optimization",
"seed": 1337,
"index": 5642
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Evaluate: ((105 + 105/7) * 20) + 9^5 - log_9(59049) + (-318 mod 4) + floor(142/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((105 + 105/7) * 20) + 9^5 - log_9(59049) + (-318 mod 4) + floor(142/2)... | {
"type": "arithmetic",
"seed": 1337,
"index": 5643
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Prove that $f(x,y)=\\frac12(3x^2+2y^2)+3x+5y+-2$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+2y^2)+3x+5y+-2 $\n\n$ \\frac{\\partial^2 f}{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 5644
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Evaluate: ((-112 + -48/12) * 14) + 4^4 - log_7(7) + (-353 mod 20) + ceil(4/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-112 + -48/12) * 14) + 4^4 - log_7(7) + (-353 mod 20) + ceil(4/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 5645
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Evaluate: ((162 + -481/13) * 9) + 10^3 - log_4(16) + (401 mod 4) + floor(48/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((162 + -481/13) * 9) + 10^3 - log_4(16) + (401 mod 4) + floor(48/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 5646
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. -323 + 469x = 908"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -323 + 469x = 908 $\n\nMove all terms to the left (standard form):\n$ 469x + -1231 = 0 $\n\nIsolate the $x$ term:\n$ 469x = 1231 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 5647
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Compute the determinant: $A=\\begin{pmatrix}7&3\\\\-6&-2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}7&3\\\\\\-6&-2\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5648
} |
[
{
"role": "user",
"content": "solve: \n\n 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 = \\arccos(-\\frac{\\sqr... | {
"type": "trigonometry",
"seed": 1337,
"index": 5649
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: 771 - 997 = 946x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 771 - 997 = 946x $\n\nMove all terms to the left (standard form):\n$ -946x + -226 = 0 $\n\nIsolate the $x$ term:\n$ -946x = 226 $\n\nDivide both sides by the coefficient o... | {
"type": "linear_equation",
"seed": 1337,
"index": 5650
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Differentiate with respect to $x$: $f(x) = -1e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-1e^{1x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 5651
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. -857x - 114 = -12"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -857x - 114 = -12 $\n\nMove all terms to the left (standard form):\n$ -857x + -102 = 0 $\n\nIsolate the $x$ term:\n$ -857x = 102 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 5652
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. -664 + 721 = 587x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -664 + 721 = 587x $\n\nMove all terms to the left (standard form):\n$ -587x + 57 = 0 $\n\nIsolate the $x$ term:\n$ -587x = -57 $\n\nD... | {
"type": "linear_equation",
"seed": 1337,
"index": 5653
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. 37 - 197x^2 - 171x = -127"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 37 - 197x^2 - 171x = -127 $\n\nMove all terms to the left (standard form):\n$ -197x^2 + -171x + 164 = 0 $\n\nApply the quad... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5654
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Evaluate: ((108 + 24/2) * 20) + 11^3 - log_6(1296) + (203 mod 22) + ceil(-110/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((108 + 24/2) * 20) + 11^3 - log_6(1296) + (203 mod 22) + ceil(-110/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 5655
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Solve for $x$ (in radians): sin(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(-\... | {
"type": "trigonometry",
"seed": 1337,
"index": 5656
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Evaluate: ((3 + -336/21) * 11) + 6^3 - log_9(6561) + (-279 mod 5) + ceil(190/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((3 + -336/21) * 11) + 6^3 - log_9(6561) + (-279 mod 5) + ceil(190/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 5657
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. - + 174x^2 + 42 = 188x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ - + 174x^2 + 42 = 188x $\n\nMove all terms to the left (standard form):\n$ 174x^2 + -188x + 42 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5658
} |
[
{
"role": "user",
"content": "Solve this equation accurately. -40x - 84 - 45x^2 = -6"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -40x - 84 - 45x^2 = -6 $\n\nMove all terms to the left (standard form):\n$ -45x^2 + -40x + -78 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5659
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Compute the indefinite integral: $\\int (1x + -8)\\sin(1x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (1x + -8)\\sin(1x)\\,dx $\n\nUse standard antiderivatives (and integration... | {
"type": "calculus",
"seed": 1337,
"index": 5660
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. 2 + 170x^2 + 164 = 159x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 2 + 170x^2 + 164 = 159x $\n\nMove all terms to the left (standard form):\n$ 170x^2 + -159x + 166 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5661
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. 9x^2 - 82x + 61 = 49"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 9x^2 - 82x + 61 = 49 $\n\nMove all terms to the left (standard form):\n$ 9x^2 + -82x + 12 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5662
} |
[
{
"role": "user",
"content": "solve: \n\n 8x - 170x^2 - 29 = -192"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 8x - 170x^2 - 29 = -192 $\n\nMove all terms to the left (standard form):\n$ -170x^2 + 8x + 163 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5663
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-5&-4\\\\-6&-7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -5 & -4 \\\\ -6 & -7 \\end{pmatrix} $\n\nCompute the dete... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5664
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 2x^2 + 36 + 177x = 103"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 2x^2 + 36 + 177x = 103 $\n\nMove all terms to the left (standard form):\n$ 2x^2 + 177x + -67 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5665
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. 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 = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 5666
} |
[
{
"role": "user",
"content": "Can you compute this equation? Evaluate: ((133 + 144/12) * 4) + 5^5 - log_4(4) + (265 mod 12) + ceil(-192/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((133 + 144/12) * 4) + 5^5 - log_4(4) + (265 mod 12) + ceil(-192/2) $\n\nCompute each comp... | {
"type": "arithmetic",
"seed": 1337,
"index": 5667
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? 501 + 69x = 765"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 501 + 69x = 765 $\n\nMove all terms to the left (standard form):\n$ 69x + -264 = 0 $\n\nIsolate the $x$ term:\n$ 69x = 264 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 5668
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Differentiate with respect to $x$: $f(x) = (6x + 7)e^{5x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (6x + 7)e^{5x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{6e^... | {
"type": "calculus",
"seed": 1337,
"index": 5669
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Prove that $(\\mathbb{Z}_10, +)$ is a group under addition modulo 10."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_10=\\{0,1,\\dots,9\\}$ with operation $+$ modulo $10$.\n\n**Closure:** If $a,b\\in\\mathb... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5670
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Compute $(-184+-166) \\bmod 17$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-184+-166) \\bmod 17 $\n\nUse the rule that addition is compatible with reductio... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5671
} |
[
{
"role": "user",
"content": "Work through and solve this equation. -872x - 419 = 554"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -872x - 419 = 554 $\n\nMove all terms to the left (standard form):\n$ -872x + -973 = 0 $\n\nIsolate the $x$ term:\n$ -872x = 973 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 5672
} |
[
{
"role": "user",
"content": "Determine the solution of 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 gen... | {
"type": "trigonometry",
"seed": 1337,
"index": 5673
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Compute $(-145+192) \\bmod 8$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-145+192) \\bmod 8 $\n\nUse the rule that addition is compatible with ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5674
} |
[
{
"role": "user",
"content": "solve: Prove that $(\\mathbb{Z}_12, +)$ is a group under addition modulo 12."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_12=\\{0,1,\\dots,11\\}$ with operation $+$ modulo $12$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, then $(a+b)\\bmod n\\in\\{0,... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5675
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 46x + 30 - 178x^2 = -194"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 46x + 30 - 178x^2 = -194 $\n\nMove all terms to the left (standard form):\n$ -178x^2 + 46x + 224 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5676
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Solve for $x$ (in radians): cos(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 1 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(1) = 0 $\n\nThe gene... | {
"type": "trigonometry",
"seed": 1337,
"index": 5677
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Prove that $f(x)=10x^2+-10x+10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+-10x+10$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n... | {
"type": "optimization",
"seed": 1337,
"index": 5678
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Prove that $f(x)=4x^2+-5x+-6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+-5x+-6$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 8x ... | {
"type": "optimization",
"seed": 1337,
"index": 5679
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. 938x + 125 = -869"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 938x + 125 = -869 $\n\nMove all terms to the left (standard form):\n$ 938x + 994 = 0 $\n\nIsolate the $x$ term:\n$ 938x = -994 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 5680
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-2&-8\\\\\\4&3\\end{pmatrix},\\quad b=\\begin{pmatrix}82\\\\\\-47\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-2&-8\\\\\\4&3\\en... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5681
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Compute $(-191+175) \\bmod 8$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-191+175) \\bmod 8 $\n\nUse the rule that addition is compatible with reduction... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5682
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Evaluate: ((-191 + 50/2) * 16) + 11^2 - log_10(1000) + (369 mod 12) + ceil(-16/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-191 + 50/2) * 16) + 11^2 - log_10(1000) + (369 mod 12) + ceil(-16/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 5683
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. 186 + 768x = 562"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 186 + 768x = 562 $\n\nMove all terms to the left (standard form):\n$ 768x + -376 = 0 $\n\nIsolate the $x$ term:\n$ 768x = 376 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 5684
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Compute $(41+56) \\bmod 12$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (41+56) \\bmod 12 $\n\nUse the rule that addition is compatible with reduction modul... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5685
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-9&1\\\\\\-3&9\\end{pmatrix},\\quad b=\\begin{pmatrix}16\\\\\\-12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-9&1\\\\\\-3&9\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5686
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -32 + 176x - 7 = 95x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -32 + 176x - 7 = 95x^2 $\n\nMove all terms to the left (standard form):\n$ -95x^2 + 176x + -39 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5687
} |
[
{
"role": "user",
"content": "Can you compute this equation? Differentiate with respect to $x$: $f(x) = 4e^{-4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4e^{-4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-16e^{-4x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 5688
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Evaluate: ((96 + 153/17) * 16) + 2^3 - log_3(729) + (-184 mod 30) + ceil(-156/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((96 + 153/17) * 16) + 2^3 - log_3(729) + (-184 mod 30) + ceil(-156/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 5689
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. -239 + 353 = -472x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -239 + 353 = -472x $\n\nMove all terms to the left (standard form):\n$ 472x + 114 = 0 $\n\nIsolate the $x$ term:\n$ 472x = -114 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 5690
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. Evaluate: ((-45 + 78/13) * 18) + 7^2 - log_8(4096) + (297 mod 15) + floor(128/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-45 + 78/13) * 18) + 7^2 - log_8(4096) + (297 mod 15) + floor(128/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 5691
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-4&6\\\\\\0&-7\\end{pmatrix},\\quad b=\\begin{pmatrix}-26\\\\\\63\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-4&6\\\\\\0&-7\\end... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5692
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\partial^2 f}... | {
"type": "optimization",
"seed": 1337,
"index": 5693
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Differentiate with respect to $x$: $f(x) = 2e^{-4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2e^{-4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-8e^{-4x}} $"
... | {
"type": "calculus",
"seed": 1337,
"index": 5694
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((-180 + -264/11) * 5) + 12^2 - log_4(1024) + (-79 mod 30) + ceil(50/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-180 + -264/11) * 5) + 12^2 - log_4(1024) + (-79 mod 30) + ceil(50/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 5695
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Evaluate: ((46 + 114/19) * 11) + 12^4 - log_5(15625) + (-432 mod 24) + ceil(50/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((46 + 114/19) * 11) + 12^4 - log_5(15625) + (-432 mod 24) + ceil(50/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 5696
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. 30 - 24x - 8 = -142x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 30 - 24x - 8 = -142x^2 $\n\nMove all terms to the left (standard form):\n$ 142x^2 + -24x + 22 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5697
} |
[
{
"role": "user",
"content": "solve Compute the indefinite integral: $\\int 7e^{4x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 7e^{4x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int 7e^{4x}\\,dx = \\boxed{\\frac... | {
"type": "calculus",
"seed": 1337,
"index": 5698
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Evaluate: ((26 + -24/8) * 11) + 4^5 - log_5(625) + (82 mod 23) + ceil(91/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((26 + -24/8) * 11) + 4^5 - log_5(625) + (82 mod 23) + ceil(91/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 5699
} |
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