messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Solve the given mathematical expression. Compute $(-131+-9) \\bmod 13$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-131+-9) \\bmod 13 $\n\nUse the rule that addition is compatible with reduction mod... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1600
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&-2&-2\\\\\\-3&0&3\\\\\\1&4&5\\end{pmatrix},\\quad b=\\begin{pmatrix}22\\\\\\0\\\\\\-12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1601
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Compute $(-117+-149) \\bmod 24$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-117+-149) \\bmod 24 $\n\nUse the rule that addition is compatible wi... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1602
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Differentiate with respect to $x$: $f(x) = (5x + 8)\\sin(5x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (5x + 8)\\sin(5x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed... | {
"type": "calculus",
"seed": 1337,
"index": 1603
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Compute the indefinite integral: $\\int 3x^3 + -2x^2 + -17x + 16\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3x^3 + -2x^2 + -17x + 16\\,dx $\n\nUse standard antiderivatives (a... | {
"type": "calculus",
"seed": 1337,
"index": 1604
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. -439 - 216 = 69x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -439 - 216 = 69x $\n\nMove all terms to the left (standard form):\n$ -69x + -655 = 0 $\n\nIsolate the $x$ term:\n$ -69x = 655 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 1605
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. -354 + 777 = 42x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -354 + 777 = 42x $\n\nMove all terms to the left (standard form):\n$ -42x + 423 = 0 $\n\nIsolate the $x$ term:\n$ -42x = -423 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 1606
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. 38 + 141x^2 + 15 = 0x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 38 + 141x^2 + 15 = 0x $\n\nMove all terms to the left (standard form):\n$ 141x^2 + 0x + 53 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1607
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Solve for $x$ (in radians): sin(x) = -1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -1 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(-1) = -1.5708 $\n\nT... | {
"type": "trigonometry",
"seed": 1337,
"index": 1608
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Compute the determinant: $A=\\begin{pmatrix}-8&9\\\\-8&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-8&9\\\\\\-8&-4\\end{pmatrix} $\n\nUse $\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1609
} |
[
{
"role": "user",
"content": "solve 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(-\\frac{1}{2}) = -0.463648 $\n\nTh... | {
"type": "trigonometry",
"seed": 1337,
"index": 1610
} |
[
{
"role": "user",
"content": "Solve the following math equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\partial^2 ... | {
"type": "optimization",
"seed": 1337,
"index": 1611
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. -698 - 2x = -421"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -698 - 2x = -421 $\n\nMove all terms to the left (standard form):\n$ -2x + -277 = 0 $\n\nIsolate the $x$ term:\n$ -2x = 277 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1612
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Differentiate with respect to $x$: $f(x) = 6x^3 + 7x^2 + 2x + -2$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 6x^3 + 7x^2 + 2x + -2 $\n\nApply the standard differentiation rules:\n$ f'(x) ... | {
"type": "calculus",
"seed": 1337,
"index": 1613
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-4&3\\\\\\-6&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}8\\\\\\64\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-4&3\\\\\\-6&-2... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1614
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. -122 - 197x = -604"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -122 - 197x = -604 $\n\nMove all terms to the left (standard form):\n$ -197x + 482 = 0 $\n\nIsolate the $x$ term:\n$ -197x = -482 $\n\nDivid... | {
"type": "linear_equation",
"seed": 1337,
"index": 1615
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute $(-117+58) \\bmod 25$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-117+58) \\bmod 25 $\n\nUse the rule that addition is compatible with reduction modulo $n$:\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1616
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. 811x - 799 = -910"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 811x - 799 = -910 $\n\nMove all terms to the left (standard form):\n$ 811x + 111 = 0 $\n\nIsolate the $x$ term:\n$ 811x = -111 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1617
} |
[
{
"role": "user",
"content": "Compute the correct solution for 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": 1618
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 1619
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Evaluate: ((-45 + 234/6) * 3) + 10^5 - log_7(7) + (-63 mod 4) + ceil(7/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-45 + 234/6) * 3) + 10^5 - log_7(7) + (-63 mod 4) + ceil(7/2) $\n\nCompute each ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1620
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Evaluate: ((123 + 120/8) * 7) + 7^2 - log_7(7) + (-92 mod 16) + floor(-186/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((123 + 120/8) * 7) + 7^2 - log_7(7) + (-92 mod 16) + floor(-186/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 1621
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 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": 1622
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Prove that $(\\mathbb{Z}_23, +)$ is a group under addition modulo 23."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_23=\\{0,1,\\dots,22\\}$ with operation $+$ modulo $23$.\n\n**Closure:** If $a,b\\in\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1623
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Evaluate: ((-119 + -196/7) * 13) + 9^2 - log_3(9) + (-456 mod 9) + ceil(-103/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-119 + -196/7) * 13) + 9^2 - log_3(9) + (-456 mod 9) + ceil(-103/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 1624
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Prove that $f(x)=7x^2+-8x+1$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=7x^2+-8x+1$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n... | {
"type": "optimization",
"seed": 1337,
"index": 1625
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 37 - 169x^2 + 132 = 56x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 37 - 169x^2 + 132 = 56x $\n\nMove all terms to the left (standard form):\n$ -169x^2 + -56x + 169 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1626
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Compute the indefinite integral: $\\int \\ln(5x + -8)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(5x + -8)\\,dx $\n\nUse standard antiderivatives (and integration by parts if n... | {
"type": "calculus",
"seed": 1337,
"index": 1627
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? 372x - 619 = -208"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 372x - 619 = -208 $\n\nMove all terms to the left (standard form):\n$ 372x + -411 = 0 $\n\nIsolate the $x$ term:\n$ 372x = 411 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 1628
} |
[
{
"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": 1629
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Evaluate: ((15 + -663/17) * 2) + 8^3 - log_6(46656) + (77 mod 28) + ceil(42/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((15 + -663/17) * 2) + 8^3 - log_6(46656) + (77 mod 28) + ceil(42/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 1630
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Evaluate: ((68 + -16/16) * 4) + 11^5 - log_4(4) + (-323 mod 20) + round(102/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((68 + -16/16) * 4) + 11^5 - log_4(4) + (-323 mod 20) + round(102/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 1631
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Differentiate with respect to $x$: $f(x) = \\ln(7x + -3)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(7x + -3) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\fr... | {
"type": "calculus",
"seed": 1337,
"index": 1632
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. 35 - 116 + 56x^2 = -168x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 35 - 116 + 56x^2 = -168x $\n\nMove all terms to the left (standard form):\n$ 56x^2 + 168x + -81 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1633
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. 29x - 191 + 197 = -155x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 29x - 191 + 197 = -155x^2 $\n\nMove all terms to the left (standard form):\n$ 155x^2 + 29x + 6 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1634
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Evaluate: ((36 + -51/17) * 2) + 7^3 - log_7(2401) + (111 mod 19) + ceil(163/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((36 + -51/17) * 2) + 7^3 - log_7(2401) + (111 mod 19) + ceil(163/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 1635
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. 59x + 198 = 350"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 59x + 198 = 350 $\n\nMove all terms to the left (standard form):\n$ 59x + -152 = 0 $\n\nIsolate the $x$ term:\n$ 59x = 152 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 1636
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Compute $(-154+78) \\bmod 18$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-154+78) \\bmod 18 $\n\nUse the rule that addition is compatible with reduction modu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1637
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&-2&5\\\\\\2&1&3\\\\\\2&-3&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-26\\\\\\1\\\\\\-1\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1638
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}2&4&1\\\\\\5&-4&2\\\\\\0&-3&-5\\end{pmatrix},\\quad b=\\begin{pmatrix}9\\\\\\-33\\\\\\-7\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1639
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. -271 + 102 = -350x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -271 + 102 = -350x $\n\nMove all terms to the left (standard form):\n$ 350x + -169 = 0 $\n\nIsolate the $x$ term:\n$ 350x = 169 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1640
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Evaluate: ((-99 + 520/13) * 20) + 11^2 - log_4(256) + (-93 mod 3) + round(-101/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-99 + 520/13) * 20) + 11^2 - log_4(256) + (-93 mod 3) + round(-101/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 1641
} |
[
{
"role": "user",
"content": "solve Compute the indefinite integral: $\\int \\ln(1x + -6)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(1x + -6)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int \\ln(1x + -6)\\,d... | {
"type": "calculus",
"seed": 1337,
"index": 1642
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Compute the indefinite integral: $\\int (-1x + 7)e^{3x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-1x + 7)e^{3x}\\,dx $\n\nUse standard antiderivatives (and integration by ... | {
"type": "calculus",
"seed": 1337,
"index": 1643
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. 626 + 53x = 618"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 626 + 53x = 618 $\n\nMove all terms to the left (standard form):\n$ 53x + 8 = 0 $\n\nIsolate the $x$ term:\n$ 53x = -8 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 1644
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 5x^2 - 41 - 123x = 8"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 5x^2 - 41 - 123x = 8 $\n\nMove all terms to the left (standard form):\n$ 5x^2 + -123x + -49 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1645
} |
[
{
"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": 1646
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Prove that $f(x,y)=\\frac12(3x^2+6y^2)+1x+6y+-10$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(3x^2+6y^2)+1x+6y+-10 $\n\n$ \\frac{\\partial^2 ... | {
"type": "optimization",
"seed": 1337,
"index": 1647
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. -17x - 70x^2 + 63 = -133"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -17x - 70x^2 + 63 = -133 $\n\nMove all terms to the left (standard form):\n$ -70x^2 + -17x + 196 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1648
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Compute the indefinite integral: $\\int (1x + -4)\\sin(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (1x + -4)\\sin(6x)\\,dx $\n\nUse standard antiderivatives (and in... | {
"type": "calculus",
"seed": 1337,
"index": 1649
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. -19 + 198x^2 - 120x = 144"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -19 + 198x^2 - 120x = 144 $\n\nMove all terms to the left (standard form):\n$ 198x^2 + -120x + -163 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1650
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Differentiate with respect to $x$: $f(x) = 9\\sin(4x) + 6\\cos(2x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 9\\sin(4x) + 6\\cos(2x) $\n\nApply the standard differentiation rules:\n$ f'(x)... | {
"type": "calculus",
"seed": 1337,
"index": 1651
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Solve for $x$ (in radians): cos(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal val... | {
"type": "trigonometry",
"seed": 1337,
"index": 1652
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&-1&-5\\\\\\5&4&1\\\\\\-3&-3&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-10\\\\\\12\\\\\\-11\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $A... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1653
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Evaluate: ((-10 + -660/20) * 12) + 9^3 - log_8(262144) + (312 mod 23) + round(22/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-10 + -660/20) * 12) + 9^3 - log_8(262144) + (312 mod 23) + round(22/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1654
} |
[
{
"role": "user",
"content": "solve 24 + 18x - 52x^2 = 87"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 24 + 18x - 52x^2 = 87 $\n\nMove all terms to the left (standard form):\n$ -52x^2 + 18x + -63 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1655
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Evaluate: ((100 + 16/8) * 2) + 7^4 - log_10(100) + (141 mod 25) + round(154/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((100 + 16/8) * 2) + 7^4 - log_10(100) + (141 mod 25) + round(154/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 1656
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. -37 - 131x - 36x^2 = 197"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -37 - 131x - 36x^2 = 197 $\n\nMove all terms to the left (standard form):\n$ -36x^2 + -131x + -234 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1657
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. -14 - 30 + 62x^2 = 6x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -14 - 30 + 62x^2 = 6x $\n\nMove all terms to the left (standard form):\n$ 62x^2 + -6x + -44 = 0 $\n\nApply the quadratic formula:\n$ x = \\fr... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1658
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-4&-1\\\\\\5&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}23\\\\\\-76\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-4&-1\\\\\\5... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1659
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Differentiate with respect to $x$: $f(x) = 7e^{3x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 7e^{3x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{21e^{3x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 1660
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. 20x - 132x^2 + 3 = 41"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 20x - 132x^2 + 3 = 41 $\n\nMove all terms to the left (standard form):\n$ -132x^2 + 20x + -38 = 0 $\n\nApply the quadratic formula:\n$ x = \\fra... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1661
} |
[
{
"role": "user",
"content": "solve: \n\n Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}7&-8\\\\\\-3&0\\end{pmatrix},\\quad b=\\begin{pmatrix}-32\\\\\\24\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}7&-8\\\\\\-3&0\\end{pmatrix} ,\\quad b=\\begin... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1662
} |
[
{
"role": "user",
"content": "solve: \n\n Compute the indefinite integral: $\\int \\ln(4x + 3)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(4x + 3)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):\n$ \\int \\ln(4x + 3)\\... | {
"type": "calculus",
"seed": 1337,
"index": 1663
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Differentiate with respect to $x$: $f(x) = 3x^3 + 7x^2 + 5x + -9$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3x^3 + 7x^2 + 5x + -9 $\n\nApply the standard differentiation rules:\n$ f'(x) ... | {
"type": "calculus",
"seed": 1337,
"index": 1664
} |
[
{
"role": "user",
"content": "Solve the equation shown below. -802 - 771 = 699x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -802 - 771 = 699x $\n\nMove all terms to the left (standard form):\n$ -699x + -1573 = 0 $\n\nIsolate the $x$ term:\n$ -699x = 1573 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1665
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Differentiate with respect to $x$: $f(x) = (-4x + -7)\\sin(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-4x + -7)\\sin(1x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\... | {
"type": "calculus",
"seed": 1337,
"index": 1666
} |
[
{
"role": "user",
"content": "Find the solution to this math 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{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 1667
} |
[
{
"role": "user",
"content": "solve: \n\n Evaluate: ((-174 + -612/17) * 6) + 5^2 - log_9(531441) + (-440 mod 26) + floor(-57/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-174 + -612/17) * 6) + 5^2 - log_9(531441) + (-440 mod 26) + floor(-57/2) $\n\nCompute each compone... | {
"type": "arithmetic",
"seed": 1337,
"index": 1668
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 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": 1669
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Evaluate: ((-68 + -170/10) * 8) + 4^2 - log_10(100) + (236 mod 29) + floor(-69/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-68 + -170/10) * 8) + 4^2 - log_10(100) + (236 mod 29) + floor(-69/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 1670
} |
[
{
"role": "user",
"content": "Solve the following math equation. Evaluate: ((-146 + -28/14) * 10) + 3^5 - log_7(343) + (-280 mod 8) + floor(-180/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-146 + -28/14) * 10) + 3^5 - log_7(343) + (-280 mod 8) + floor(-180/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 1671
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Evaluate: ((-170 + 60/15) * 12) + 11^4 - log_8(4096) + (-42 mod 11) + round(66/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-170 + 60/15) * 12) + 11^4 - log_8(4096) + (-42 mod 11) + round(66/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 1672
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. 454x - 393 = 340"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 454x - 393 = 340 $\n\nMove all terms to the left (standard form):\n$ 454x + -733 = 0 $\n\nIsolate the $x$ term:\n$ 454x = 733 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1673
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. 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$ \\al... | {
"type": "trigonometry",
"seed": 1337,
"index": 1674
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. - - 150x + 169x^2 = 71"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ - - 150x + 169x^2 = 71 $\n\nMove all terms to the left (standard form):\n$ 169x^2 + -150x + -71 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1675
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}5&8\\\\\\-1&0\\end{pmatrix},\\quad b=\\begin{pmatrix}-83\\\\\\7\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}5&8\\\\\\-1&... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1676
} |
[
{
"role": "user",
"content": "Please solve this math problem. Evaluate: ((138 + -110/11) * 10) + 2^2 - log_10(1000) + (136 mod 20) + floor(-154/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((138 + -110/11) * 10) + 2^2 - log_10(1000) + (136 mod 20) + floor(-154/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 1677
} |
[
{
"role": "user",
"content": "Work out the result of this equation. -49x^2 - 91x + 174 = 112"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -49x^2 - 91x + 174 = 112 $\n\nMove all terms to the left (standard form):\n$ -49x^2 + -91x + 62 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1678
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Find $A^{-1}$ for $A=\\begin{pmatrix}-6&6\\\\4&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -6 & 6 \\\\ 4 & 4 \\end{pmatrix} $\n\nCompute th... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1679
} |
[
{
"role": "user",
"content": "Determine the solution to the math 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)... | {
"type": "optimization",
"seed": 1337,
"index": 1680
} |
[
{
"role": "user",
"content": "Solve the following math equation. Find the modular inverse of 5 modulo 18, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{18}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees intege... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1681
} |
[
{
"role": "user",
"content": "Work through and solve this equation. -126 + 760x = -307"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -126 + 760x = -307 $\n\nMove all terms to the left (standard form):\n$ 760x + 181 = 0 $\n\nIsolate the $x$ term:\n$ 760x = -181 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 1682
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. -3 - 144 + 23x = -64x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -3 - 144 + 23x = -64x^2 $\n\nMove all terms to the left (standard form):\n$ 64x^2 + 23x + -147 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1683
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. -27x + 12 = -341"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -27x + 12 = -341 $\n\nMove all terms to the left (standard form):\n$ -27x + 353 = 0 $\n\nIsolate the $x$ term:\n$ -27x = -353 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 1684
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 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": 1685
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \... | {
"type": "trigonometry",
"seed": 1337,
"index": 1686
} |
[
{
"role": "user",
"content": "Calculate the result 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 $f'(x)=0$, hence... | {
"type": "optimization",
"seed": 1337,
"index": 1687
} |
[
{
"role": "user",
"content": "solve: \n\n Find $A^{-1}$ for $A=\\begin{pmatrix}6&4\\\\-1&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 6 & 4 \\\\ -1 & 2 \\end{pmatrix} $\n\nCompute the determinant: $\\det(A)=ad-bc$.\n$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1688
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Evaluate: ((147 + -92/4) * 16) + 11^4 - log_10(1000) + (-76 mod 11) + round(-42/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((147 + -92/4) * 16) + 11^4 - log_10(1000) + (-76 mod 11) + round(-42... | {
"type": "arithmetic",
"seed": 1337,
"index": 1689
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. 893 - 979x = 676"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 893 - 979x = 676 $\n\nMove all terms to the left (standard form):\n$ -979x + 217 = 0 $\n\nIsolate the $x$ term:\n$ -979x = -217 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 1690
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. Find the modular inverse of 5 modulo 14, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{14}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantee... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1691
} |
[
{
"role": "user",
"content": "Resolve the equation provided. 999 + 309 = -504x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 999 + 309 = -504x $\n\nMove all terms to the left (standard form):\n$ 504x + 1308 = 0 $\n\nIsolate the $x$ term:\n$ 504x = -1308 $\n\nDivide both sides by ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1692
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. -49x^2 - 183x - 60 = 19"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -49x^2 - 183x - 60 = 19 $\n\nMove all terms to the left (standard form):\n$ -49x^2 + -183x + -79 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1693
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-3&-4&5\\\\\\2&-3&0\\\\\\3&5&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}23\\\\\\-11\\\\\\-16\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1694
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 36x^2 + 77x - 66 = -174"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 36x^2 + 77x - 66 = -174 $\n\nMove all terms to the left (standard form):\n$ 36x^2 + 77x + 108 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1695
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. 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 $a,b\\in\\m... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1696
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: -441 + 653 = -331x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -441 + 653 = -331x $\n\nMove all terms to the left (standard form):\n$ 331x + 212 = 0 $\n\nIsolate the $x$ term:\n$ 331x = -212 $\n\nDivide both sides by the coefficient... | {
"type": "linear_equation",
"seed": 1337,
"index": 1697
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Evaluate: ((-103 + 80/8) * 1) + 8^4 - log_8(512) + (115 mod 29) + floor(2/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-103 + 80/8) * 1) + 8^4 - log_8(512) + (115 mod 29) + floor(2/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 1698
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Find $A^{-1}$ for $A=\\begin{pmatrix}-2&5\\\\9&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -2 & 5 \\\\ 9 & 1 \\end{pmatrix} $\n\nCompute the det... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1699
} |
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