messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Solve the equation shown below. Evaluate: ((-58 + 248/8) * 16) + 3^5 - log_9(6561) + (323 mod 11) + ceil(-81/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-58 + 248/8) * 16) + 3^5 - log_9(6561) + (323 mod 11) + ceil(-81/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 2600
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Find $A^{-1}$ for $A=\\begin{pmatrix}0&8\\\\-2&-5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 0 & 8 \\\\ -2 & -5 \\end{pmatrix} $\n\nCompute the de... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2601
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Evaluate: ((49 + 105/5) * 20) + 3^2 - log_2(32) + (304 mod 20) + round(96/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((49 + 105/5) * 20) + 3^2 - log_2(32) + (304 mod 20) + round(96/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 2602
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Find the modular inverse of 23 modulo 25, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $23\\cdot a^{-1} \\equiv 1 \\pmod{25}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2603
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Differentiate with respect to $x$: $f(x) = (-1x + 2)\\sin(2x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-1x + 2)\\sin(2x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\b... | {
"type": "calculus",
"seed": 1337,
"index": 2604
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. 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$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 2605
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((1 + 135/5) * 3) + 3^2 - log_10(1000) + (-318 mod 8) + floor(124/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((1 + 135/5) * 3) + 3^2 - log_10(1000) + (-318 mod 8) + floor(124/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 2606
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical 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\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 2607
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-1&-2&2\\\\\\2&4&-2\\\\\\4&2&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-2\\\\\\6\\\\\\2\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2608
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Prove that $f(x)=8x^2+2x+5$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=8x^2+2x+5$.\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": 2609
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n -15x^2 + 177 + 64 = 112x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -15x^2 + 177 + 64 = 112x $\n\nMove all terms to the left (standard form):\n$ -15x^2 + -112x + 241 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2610
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Compute the determinant: $A=\\begin{pmatrix}1&6\\\\-6&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}1&6\\\\\\-6&1\\end{pmatrix} $\n\nUse $\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2611
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Evaluate: ((-165 + 217/7) * 18) + 8^3 - log_9(59049) + (-167 mod 14) + floor(-130/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-165 + 217/7) * 18) + 8^3 - log_9(59049) + (-167 mod 14) + floor(-130/... | {
"type": "arithmetic",
"seed": 1337,
"index": 2612
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Differentiate with respect to $x$: $f(x) = 2e^{-2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 2e^{-2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-4e^{-2x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 2613
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Compute the indefinite integral: $\\int -1\\sin(9x) + 0\\cos(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -1\\sin(9x) + 0\\cos(6x)\\,dx $\n\nUse standard antiderivatives (and ... | {
"type": "calculus",
"seed": 1337,
"index": 2614
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Compute the indefinite integral: $\\int -6x^3 + 0x^2 + -14x + 5\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -6x^3 + 0x^2 + -14x + 5\\,dx $\n\nUse standard antiderivatives (an... | {
"type": "calculus",
"seed": 1337,
"index": 2615
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 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": 2616
} |
[
{
"role": "user",
"content": "Determine the solution of the given 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 $f'(x)=0$, hen... | {
"type": "optimization",
"seed": 1337,
"index": 2617
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. 946x - 383 = -758"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 946x - 383 = -758 $\n\nMove all terms to the left (standard form):\n$ 946x + 375 = 0 $\n\nIsolate the $x$ term:\n$ 946x = -375 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 2618
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Solve for $x$ (in radians): cos(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 0 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(0) = 1.5708 $\n\nThe gen... | {
"type": "trigonometry",
"seed": 1337,
"index": 2619
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Solve for $x$ (in radians): cos(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 0 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(0) = 1.5708 $\n\nTh... | {
"type": "trigonometry",
"seed": 1337,
"index": 2620
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 2621
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}3&-2\\\\\\-6&1\\end{pmatrix},\\quad b=\\begin{pmatrix}18\\\\\\-27\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}3&-2\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2622
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Prove that $f(x)=8x^2+7x+8$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=8x^2+7x+8$.\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": 2623
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Find the modular inverse of 4 modulo 5, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $4\\cdot a^{-1} \\equiv 1 \\pmod{5}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2624
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. 10 + 157x^2 + 150x = 155"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 10 + 157x^2 + 150x = 155 $\n\nMove all terms to the left (standard form):\n$ 157x^2 + 150x + -145 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2625
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. -545x + 450 = -809"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -545x + 450 = -809 $\n\nMove all terms to the left (standard form):\n$ -545x + 1259 = 0 $\n\nIsolate the $x$ term:\n$ -545x = -1259 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2626
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. -65 + 833 = -756x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -65 + 833 = -756x $\n\nMove all terms to the left (standard form):\n$ 756x + 768 = 0 $\n\nIsolate the $x$ term:\n$ 756x = -768 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2627
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. 23x^2 - 32x + 184 = -182"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 23x^2 - 32x + 184 = -182 $\n\nMove all terms to the left (standard form):\n$ 23x^2 + -32x + 366 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2628
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Evaluate: ((54 + -120/6) * 13) + 7^2 - log_2(32) + (-397 mod 2) + ceil(-121/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((54 + -120/6) * 13) + 7^2 - log_2(32) + (-397 mod 2) + ceil(-121/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 2629
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Evaluate: ((-182 + 476/17) * 16) + 2^3 - log_9(6561) + (226 mod 17) + floor(-89/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-182 + 476/17) * 16) + 2^3 - log_9(6561) + (226 mod 17) + floor(-89/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2630
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-4&-1&3\\\\\\-2&-1&2\\\\\\1&-2&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-1\\\\\\-2\\\\\\-11\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2631
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Compute the indefinite integral: $\\int \\ln(8x + -9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(8x + -9)\\,dx $\n\nUse standard antiderivatives (and integration... | {
"type": "calculus",
"seed": 1337,
"index": 2632
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Evaluate: ((80 + 272/8) * 2) + 6^3 - log_10(10000) + (-383 mod 21) + ceil(-163/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((80 + 272/8) * 2) + 6^3 - log_10(10000) + (-383 mod 21) + ceil(-163/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 2633
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Prove that $f(x,y)=\\frac12(7x^2+7y^2)+6x+-6y+10$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+7y^2)+6x+-6y+10 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 2634
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. -628x - 78 = -853"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -628x - 78 = -853 $\n\nMove all terms to the left (standard form):\n$ -628x + 775 = 0 $\n\nIsolate the $x$ term:\n$ -628x = -775 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 2635
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. 23 - 179x^2 + 100x = 175"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 23 - 179x^2 + 100x = 175 $\n\nMove all terms to the left (standard form):\n$ -179x^2 + 100x + -152 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2636
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. 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... | {
"type": "trigonometry",
"seed": 1337,
"index": 2637
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Differentiate with respect to $x$: $f(x) = -7\\sin(8x) + -5\\cos(3x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -7\\sin(8x) + -5\\cos(3x) $\n\nApply the standard differentiation rules:... | {
"type": "calculus",
"seed": 1337,
"index": 2638
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-4&0&2\\\\\\0&4&-1\\\\\\2&0&2\\end{pmatrix},\\quad b=\\begin{pmatrix}18\\\\\\-9\\\\\\-6\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2639
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Find the modular inverse of 13 modulo 15, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $13\\cdot a^{-1} \\equiv 1 \\pmod{15}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identit... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2640
} |
[
{
"role": "user",
"content": "Please work out this equation. 37 - 74 - 199x = -60x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 37 - 74 - 199x = -60x^2 $\n\nMove all terms to the left (standard form):\n$ 60x^2 + -199x + -37 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2641
} |
[
{
"role": "user",
"content": "Find the answer to the following 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": 2642
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. 389 + 339x = -344"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 389 + 339x = -344 $\n\nMove all terms to the left (standard form):\n$ 339x + 733 = 0 $\n\nIsolate the $x$ term:\n$ 339x = -733 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 2643
} |
[
{
"role": "user",
"content": "Solve the following math equation. Prove that $f(x)=5x^2+-7x+-1$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+-7x+-1$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 10x ... | {
"type": "optimization",
"seed": 1337,
"index": 2644
} |
[
{
"role": "user",
"content": "Please work out this equation. Compute the indefinite integral: $\\int -5e^{-1x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -5e^{-1x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int -... | {
"type": "calculus",
"seed": 1337,
"index": 2645
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Prove that $f(x,y)=\\frac12(5x^2+3y^2)+-5x+-6y+-4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(5x^2+3y^2)+-5x+-6y+-4 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 2646
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Solve for $x$ (in radians): cos(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -1 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(-1) = 3.14159 $\... | {
"type": "trigonometry",
"seed": 1337,
"index": 2647
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Compute the indefinite integral: $\\int -2\\sin(4x) + 8\\cos(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -2\\sin(4x) + 8\\cos(2x)\\,dx $\n\nUse standard antiderivatives (and ... | {
"type": "calculus",
"seed": 1337,
"index": 2648
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. -254x - 703 = -464"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -254x - 703 = -464 $\n\nMove all terms to the left (standard form):\n$ -254x + -239 = 0 $\n\nIsolate the $x$ term:\n$ -254x = 239 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 2649
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Differentiate with respect to $x$: $f(x) = -5x^3 + -7x^2 + 15x + -12$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -5x^3 + -7x^2 + 15x + -12 $\n\nApply the standard differentiation rules:... | {
"type": "calculus",
"seed": 1337,
"index": 2650
} |
[
{
"role": "user",
"content": "Please solve this math problem. -5x^2 - 142 - 126x = 28"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -5x^2 - 142 - 126x = 28 $\n\nMove all terms to the left (standard form):\n$ -5x^2 + -126x + -170 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2651
} |
[
{
"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": 2652
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Evaluate: ((109 + 99/9) * 16) + 11^5 - log_6(7776) + (181 mod 18) + round(-135/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((109 + 99/9) * 16) + 11^5 - log_6(7776) + (181 mod 18) + round(-135/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 2653
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}3&-3\\\\8&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 3 & -3 \\\\ 8 & -9 \\end{pmatrix} $\n\nCompute the ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2654
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. 27 + 157 - 43x = -87x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 27 + 157 - 43x = -87x^2 $\n\nMove all terms to the left (standard form):\n$ 87x^2 + -43x + 184 = 0 $\n\nApply the quadratic formula:\n$ x = \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2655
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Find the modular inverse of 13 modulo 19, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $13\\cdot a^{-1} \\equiv 1 \\pmod{19}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identit... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2656
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Evaluate: ((-85 + 825/25) * 5) + 11^4 - log_5(625) + (-131 mod 20) + round(-156/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-85 + 825/25) * 5) + 11^4 - log_5(625) + (-131 mod 20) + round(-156/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2657
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. -312 + 245 = -63x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -312 + 245 = -63x $\n\nMove all terms to the left (standard form):\n$ 63x + -67 = 0 $\n\nIsolate the $x$ term:\n$ 63x = 67 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 2658
} |
[
{
"role": "user",
"content": "Solve the following math equation. Prove that $f(x)=10x^2+-3x+4$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+-3x+4$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 20x ... | {
"type": "optimization",
"seed": 1337,
"index": 2659
} |
[
{
"role": "user",
"content": "Please calculate this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&-4&2\\\\\\-5&-1&-3\\\\\\2&-3&-1\\end{pmatrix},\\quad b=\\begin{pmatrix}-7\\\\\\28\\\\\\1\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., by ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2660
} |
[
{
"role": "user",
"content": "Please solve this math problem. 15 + 1x + 27x^2 = -143"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 15 + 1x + 27x^2 = -143 $\n\nMove all terms to the left (standard form):\n$ 27x^2 + 1x + 158 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2661
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Evaluate: ((164 + 72/24) * 2) + 6^4 - log_4(256) + (-8 mod 18) + ceil(1/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((164 + 72/24) * 2) + 6^4 - log_4(256) + (-8 mod 18) + ceil(1/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2662
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Differentiate with respect to $x$: $f(x) = 3\\sin(7x) + 1\\cos(8x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3\\sin(7x) + 1\\cos(8x) $\n\nApply the standard differentiation rules:\n... | {
"type": "calculus",
"seed": 1337,
"index": 2663
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Compute the indefinite integral: $\\int -2x^3 + -1x^2 + 18x + 20\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -2x^3 + -1x^2 + 18x + 20\\,dx $\n\nUse standard antiderivatives (and integrati... | {
"type": "calculus",
"seed": 1337,
"index": 2664
} |
[
{
"role": "user",
"content": "Calculate the answer for 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$ \\alph... | {
"type": "trigonometry",
"seed": 1337,
"index": 2665
} |
[
{
"role": "user",
"content": "solve: \n\n Evaluate: ((41 + -855/19) * 2) + 9^2 - log_6(6) + (-410 mod 14) + round(-77/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((41 + -855/19) * 2) + 9^2 - log_6(6) + (-410 mod 14) + round(-77/2) $\n\nCompute each component:\n$ -855/19... | {
"type": "arithmetic",
"seed": 1337,
"index": 2666
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{... | {
"type": "optimization",
"seed": 1337,
"index": 2667
} |
[
{
"role": "user",
"content": "Determine the correct answer to this 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 = \\arc... | {
"type": "trigonometry",
"seed": 1337,
"index": 2668
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Compute the determinant: $A=\\begin{pmatrix}3&-1\\\\8&9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&-1\\\\\\8&9\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2669
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Differentiate with respect to $x$: $f(x) = (1x + -5)e^{2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (1x + -5)e^{2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed... | {
"type": "calculus",
"seed": 1337,
"index": 2670
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. 457 + 827 = -220x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 457 + 827 = -220x $\n\nMove all terms to the left (standard form):\n$ 220x + 1284 = 0 $\n\nIsolate the $x$ term:\n$ 220x = -1284 $\n\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 2671
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\... | {
"type": "optimization",
"seed": 1337,
"index": 2672
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 255 - 422x = -106"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 255 - 422x = -106 $\n\nMove all terms to the left (standard form):\n$ -422x + 361 = 0 $\n\nIsolate the $x$ term:\n$ -422x = -361 $\... | {
"type": "linear_equation",
"seed": 1337,
"index": 2673
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Differentiate with respect to $x$: $f(x) = 4x^3 + 5x^2 + 8x + 9$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4x^3 + 5x^2 + 8x + 9 $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{... | {
"type": "calculus",
"seed": 1337,
"index": 2674
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Find the modular inverse of 3 modulo 25, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $3\\cdot a^{-1} \\equiv 1 \\pmod{25}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2675
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. -22x - 6 - 94x^2 = 150"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -22x - 6 - 94x^2 = 150 $\n\nMove all terms to the left (standard form):\n$ -94x^2 + -22x + -156 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2676
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Compute $(-126+-151) \\bmod 13$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-126+-151) \\bmod 13 $\n\nUse the rule that addition is compatible with redu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2677
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Find $A^{-1}$ for $A=\\begin{pmatrix}5&8\\\\5&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 5 & 8 \\\\ 5 & -9 \\end{pmatrix} $\n\nComput... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2678
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. -25x^2 - 45 - 60 = -104x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -25x^2 - 45 - 60 = -104x $\n\nMove all terms to the left (standard form):\n$ -25x^2 + 104x + -105 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2679
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Differentiate with respect to $x$: $f(x) = \\ln(4x + 9)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(4x + 9) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\box... | {
"type": "calculus",
"seed": 1337,
"index": 2680
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Differentiate with respect to $x$: $f(x) = -9\\sin(7x) + 9\\cos(6x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -9\\sin(7x) + 9\\cos(6x) $\n\nApply the standard differentiation rules:\n$ f'(x)... | {
"type": "calculus",
"seed": 1337,
"index": 2681
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Evaluate: ((-84 + 323/17) * 16) + 8^4 - log_2(2) + (18 mod 16) + round(92/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-84 + 323/17) * 16) + 8^4 - log_2(2) + (18 mod 16) + round(92/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 2682
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. 857 - 803x = 76"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 857 - 803x = 76 $\n\nMove all terms to the left (standard form):\n$ -803x + 781 = 0 $\n\nIsolate the $x$ term:\n$ -803x = -781 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 2683
} |
[
{
"role": "user",
"content": "solve: \n\n Compute $(-107+-107) \\bmod 11$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-107+-107) \\bmod 11 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\n$ (a+b)\\bmod n... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2684
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Find $A^{-1}$ for $A=\\begin{pmatrix}-5&9\\\\7&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -5 & 9 \\\\ 7 & -9 \\end{pmatrix} $\n\nCompute the dete... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2685
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Find the modular inverse of 5 modulo 16, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{16}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integers $x,y$ with:\n$ 5... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2686
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Evaluate: ((-179 + 39/3) * 17) + 6^4 - log_10(1000) + (-204 mod 13) + floor(-69/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-179 + 39/3) * 17) + 6^4 - log_10(1000) + (-204 mod 13) + floor(-69/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 2687
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. 21 + 188x + 167 = 146x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 21 + 188x + 167 = 146x^2 $\n\nMove all terms to the left (standard form):\n$ -146x^2 + 188x + 188 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2688
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. 290 - 916 = 959x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 290 - 916 = 959x $\n\nMove all terms to the left (standard form):\n$ -959x + -626 = 0 $\n\nIsolate the $x$ term:\n$ -959x = 626 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 2689
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Evaluate: ((-5 + -817/19) * 7) + 6^2 - log_9(81) + (191 mod 29) + round(50/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-5 + -817/19) * 7) + 6^2 - log_9(81) + (191 mod 29) + round(50/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 2690
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Find the modular inverse of 5 modulo 22, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{22}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2691
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. 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 = \\arcc... | {
"type": "trigonometry",
"seed": 1337,
"index": 2692
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Compute the indefinite integral: $\\int -1x^3 + 8x^2 + 16x + 3\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -1x^3 + 8x^2 + 16x + 3\\,dx $\n\nUse standard antiderivatives (and integrat... | {
"type": "calculus",
"seed": 1337,
"index": 2693
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. -21x^2 + 48 + 37x = 22"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -21x^2 + 48 + 37x = 22 $\n\nMove all terms to the left (standard form):\n$ -21x^2 + 37x + 26 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2694
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Evaluate: ((137 + 120/4) * 13) + 2^5 - log_4(4) + (350 mod 11) + round(-142/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((137 + 120/4) * 13) + 2^5 - log_4(4) + (350 mod 11) + round(-142/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 2695
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. 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": 2696
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. 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": 2697
} |
[
{
"role": "user",
"content": "Determine the result of 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 $f'(x)=0... | {
"type": "optimization",
"seed": 1337,
"index": 2698
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. 21 + 203 = 695x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 21 + 203 = 695x $\n\nMove all terms to the left (standard form):\n$ -695x + 224 = 0 $\n\nIsolate the $x$ term:\n$ -695x = -224 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 2699
} |
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