messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "solve Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x^2-1)=0 \\Rightarrow x\\in\\... | {
"type": "optimization",
"seed": 1337,
"index": 1900
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Compute the indefinite integral: $\\int 5x^3 + -1x^2 + 12x + 3\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 5x^3 + -1x^2 + 12x + 3\\,dx $\n\nUse standard antiderivatives (and integ... | {
"type": "calculus",
"seed": 1337,
"index": 1901
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Evaluate: ((3 + -966/21) * 13) + 12^2 - log_5(5) + (-24 mod 4) + round(158/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((3 + -966/21) * 13) + 12^2 - log_5(5) + (-24 mod 4) + round(158/2) $\n\nCompute each component:\n$ -966/... | {
"type": "arithmetic",
"seed": 1337,
"index": 1902
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Prove that $f(x,y)=\\frac12(6x^2+5y^2)+0x+-5y+4$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(6x^2+5y^2)+0x+-5y+4 $\n\n$ \\frac{\\partial^2 f}{\... | {
"type": "optimization",
"seed": 1337,
"index": 1903
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. 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": 1904
} |
[
{
"role": "user",
"content": "Please work out this equation. Prove that $f(x,y)=\\frac12(9x^2+1y^2)+4x+4y+1$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+1y^2)+4x+4y+1 $\n\n$ \\frac{\\partial^2 f}{\\partial x^2} = ... | {
"type": "optimization",
"seed": 1337,
"index": 1905
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. -26 + 137x^2 + 28 = -26x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -26 + 137x^2 + 28 = -26x $\n\nMove all terms to the left (standard form):\n$ 137x^2 + 26x + 2 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1906
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. -123 + 633x = 758"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -123 + 633x = 758 $\n\nMove all terms to the left (standard form):\n$ 633x + -881 = 0 $\n\nIsolate the $x$ term:\n$ 633x = 881 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1907
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Evaluate: ((9 + 280/14) * 13) + 12^4 - log_4(4096) + (-460 mod 19) + round(-70/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((9 + 280/14) * 13) + 12^4 - log_4(4096) + (-460 mod 19) + round(-70/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1908
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}0&3&-5\\\\\\4&-1&5\\\\\\1&1&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}18\\\\\\-8\\\\\\9\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1909
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. Evaluate: ((-34 + -357/21) * 10) + 11^2 - log_2(8) + (215 mod 20) + round(-148/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-34 + -357/21) * 10) + 11^2 - log_2(8) + (215 mod 20) + round(-148/... | {
"type": "arithmetic",
"seed": 1337,
"index": 1910
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Differentiate with respect to $x$: $f(x) = (1x + 9)e^{6x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (1x + 9)e^{6x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{1e^{6x} ... | {
"type": "calculus",
"seed": 1337,
"index": 1911
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. 34x + 948 = -220"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 34x + 948 = -220 $\n\nMove all terms to the left (standard form):\n$ 34x + 1168 = 0 $\n\nIsolate the $x$ term:\n$ 34x = -1168 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 1912
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Solve for $x$ (in radians): cos(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(\\frac{1}{2... | {
"type": "trigonometry",
"seed": 1337,
"index": 1913
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. -16x + 26x^2 - 56 = -66"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -16x + 26x^2 - 56 = -66 $\n\nMove all terms to the left (standard form):\n$ 26x^2 + -16x + 10 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1914
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. -29 - 15 - 197x^2 = -183x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -29 - 15 - 197x^2 = -183x $\n\nMove all terms to the left (standard form):\n$ -197x^2 + 183x + -44 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1915
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Compute the indefinite integral: $\\int \\ln(9x + 1)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(9x + 1)\\,dx $\n\nUse standard antiderivatives (and integration by p... | {
"type": "calculus",
"seed": 1337,
"index": 1916
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. -156 + 503x = 238"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -156 + 503x = 238 $\n\nMove all terms to the left (standard form):\n$ 503x + -394 = 0 $\n\nIsolate the $x$ term:\n$ 503x = 394 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1917
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-6&3\\\\\\7&4\\end{pmatrix},\\quad b=\\begin{pmatrix}36\\\\\\-12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-6&3\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1918
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. 367x - 856 = 279"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 367x - 856 = 279 $\n\nMove all terms to the left (standard form):\n$ 367x + -1135 = 0 $\n\nIsolate the $x$ term:\n$ 367x = 1135 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 1919
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. -15 - 138x + 181 = 9x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -15 - 138x + 181 = 9x^2 $\n\nMove all terms to the left (standard form):\n$ -9x^2 + -138x + 166 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1920
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? -963x + 666 = 975"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -963x + 666 = 975 $\n\nMove all terms to the left (standard form):\n$ -963x + -309 = 0 $\n\nIsolate the $x$ term:\n$ -963x = 309 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 1921
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Evaluate: ((141 + 833/17) * 10) + 11^4 - log_9(6561) + (-496 mod 22) + ceil(-10/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((141 + 833/17) * 10) + 11^4 - log_9(6561) + (-496 mod 22) + ceil(-10/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 1922
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. Compute the indefinite integral: $\\int -6\\sin(6x) + 4\\cos(7x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -6\\sin(6x) + 4\\cos(7x)\\,dx $\n\nUse standard antiderivatives (and ... | {
"type": "calculus",
"seed": 1337,
"index": 1923
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Prove that $f(x)=2x^2+-6x+9$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+-6x+9$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 4x ... | {
"type": "optimization",
"seed": 1337,
"index": 1924
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Prove that $f(x,y)=\\frac12(4x^2+10y^2)+2x+2y+-6$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+10y^2)+2x+2y+-6 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 1925
} |
[
{
"role": "user",
"content": "Compute the solution for 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 = \\arcsin(\\f... | {
"type": "trigonometry",
"seed": 1337,
"index": 1926
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. 381 + 220x = -63"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 381 + 220x = -63 $\n\nMove all terms to the left (standard form):\n$ 220x + 444 = 0 $\n\nIsolate the $x$ term:\n$ 220x = -444 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1927
} |
[
{
"role": "user",
"content": "Find the correct solution for 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": 1928
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. Differentiate with respect to $x$: $f(x) = -3x^3 + 3x^2 + 10x + 10$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3x^3 + 3x^2 + 10x + 10 $\n\nApply the standard differentiation rules:\n$ f'(x... | {
"type": "calculus",
"seed": 1337,
"index": 1929
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Compute the determinant: $A=\\begin{pmatrix}4&9\\\\-5&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}4&9\\\\\\-5&4\\end{pmatrix} $\n\nUse $\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1930
} |
[
{
"role": "user",
"content": "Calculate the solution of the equation below. Compute $(143+-11) \\bmod 3$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (143+-11) \\bmod 3 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1931
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Compute the indefinite integral: $\\int -4\\sin(1x) + 5\\cos(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4\\sin(1x) + 5\\cos(2x)\\,dx $\n\nUse standard antiderivatives (an... | {
"type": "calculus",
"seed": 1337,
"index": 1932
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. 21x^2 + 156x + 34 = 135"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 21x^2 + 156x + 34 = 135 $\n\nMove all terms to the left (standard form):\n$ 21x^2 + 156x + -101 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1933
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}3&-7\\\\\\-9&3\\end{pmatrix},\\quad b=\\begin{pmatrix}32\\\\\\-6\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}3&-7\\\\\\-9&... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1934
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. 47x - 100 - 73 = -81x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 47x - 100 - 73 = -81x^2 $\n\nMove all terms to the left (standard form):\n$ 81x^2 + 47x + -173 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1935
} |
[
{
"role": "user",
"content": "Solve this equation accurately. -377 - 466 = 875x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -377 - 466 = 875x $\n\nMove all terms to the left (standard form):\n$ -875x + -843 = 0 $\n\nIsolate the $x$ term:\n$ -875x = 843 $\n\nDivide both sides by... | {
"type": "linear_equation",
"seed": 1337,
"index": 1936
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Evaluate: ((-166 + 660/20) * 6) + 12^3 - log_6(216) + (-19 mod 20) + floor(0/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-166 + 660/20) * 6) + 12^3 - log_6(216) + (-19 mod 20) + floor(0/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 1937
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. 3 - 87 + 177x = -198x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 3 - 87 + 177x = -198x^2 $\n\nMove all terms to the left (standard form):\n$ 198x^2 + 177x + -84 = 0 $\n\nApply the quadratic formula:\n$ x... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1938
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Differentiate with respect to $x$: $f(x) = -1x^3 + 8x^2 + -10x + -10$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1x^3 + 8x^2 + -10x + -10 $\n\nApply the standard differentiation rules:\n$ f... | {
"type": "calculus",
"seed": 1337,
"index": 1939
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. 565 + 782 = 891x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 565 + 782 = 891x $\n\nMove all terms to the left (standard form):\n$ -891x + 1347 = 0 $\n\nIsolate the $x$ term:\n$ -891x = -1347 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1940
} |
[
{
"role": "user",
"content": "Please work out this equation. 33x^2 - 44 + 18x = 107"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 33x^2 - 44 + 18x = 107 $\n\nMove all terms to the left (standard form):\n$ 33x^2 + 18x + -151 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1941
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Evaluate: ((56 + -561/17) * 6) + 2^4 - log_8(262144) + (29 mod 18) + ceil(0/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((56 + -561/17) * 6) + 2^4 - log_8(262144) + (29 mod 18) + ceil(0/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 1942
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Compute the indefinite integral: $\\int 3x^3 + -9x^2 + 4x + -10\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 3x^3 + -9x^2 + 4x + -10\\,dx $\n\nUse standard antiderivatives... | {
"type": "calculus",
"seed": 1337,
"index": 1943
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. -161x - 229 = 243"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -161x - 229 = 243 $\n\nMove all terms to the left (standard form):\n$ -161x + -472 = 0 $\n\nIsolate the $x$ term:\n$ -161x = 472 $\n\... | {
"type": "linear_equation",
"seed": 1337,
"index": 1944
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \... | {
"type": "trigonometry",
"seed": 1337,
"index": 1945
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 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 $f'(x)=0$, he... | {
"type": "optimization",
"seed": 1337,
"index": 1946
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. 178 - 298 = 693x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 178 - 298 = 693x $\n\nMove all terms to the left (standard form):\n$ -693x + -120 = 0 $\n\nIsolate the $x$ term:\n$ -693x = 120 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1947
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Prove that $f(x)=5x^2+9x+-9$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+9x+-9$.\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": 1948
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Compute the determinant: $A=\\begin{pmatrix}-5&-8\\\\-8&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-5&-8\\\\\\-8&8\\end{pmatrix} $\n\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1949
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, h... | {
"type": "optimization",
"seed": 1337,
"index": 1950
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. 37 + 162 - 41x = 155x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 37 + 162 - 41x = 155x^2 $\n\nMove all terms to the left (standard form):\n$ -155x^2 + -41x + 199 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1951
} |
[
{
"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": 1952
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-1&2&-1\\\\\\-3&-1&0\\\\\\1&-4&2\\end{pmatrix},\\quad b=\\begin{pmatrix}-6\\\\\\-9\\\\\\8\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1953
} |
[
{
"role": "user",
"content": "Please calculate this 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 $a,b\\in\\mathbb{Z}_n$, then ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1954
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. -32x - 142 + 102 = 85x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -32x - 142 + 102 = 85x^2 $\n\nMove all terms to the left (standard form):\n$ -85x^2 + -32x + -40 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1955
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Compute $(47+183) \\bmod 2$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (47+183) \\bmod 2 $\n\nUse the rule that addition is compatible with reduction mod... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1956
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Evaluate: ((156 + -893/19) * 16) + 7^5 - log_8(32768) + (-488 mod 4) + ceil(5/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((156 + -893/19) * 16) + 7^5 - log_8(32768) + (-488 mod 4) + ceil(5/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 1957
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 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).... | {
"type": "trigonometry",
"seed": 1337,
"index": 1958
} |
[
{
"role": "user",
"content": "solve: \n\n 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}{\\partial x\\partial... | {
"type": "optimization",
"seed": 1337,
"index": 1959
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Compute the determinant: $A=\\begin{pmatrix}-3&5\\\\-5&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-3&5\\\\\\-5&-9\\end{pmatri... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1960
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Evaluate: ((-105 + 322/7) * 8) + 8^2 - log_4(256) + (-83 mod 2) + ceil(-112/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-105 + 322/7) * 8) + 8^2 - log_4(256) + (-83 mod 2) + ceil(-112/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 1961
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. -36x + 176 + 136x^2 = -68"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -36x + 176 + 136x^2 = -68 $\n\nMove all terms to the left (standard form):\n$ 136x^2 + -36x + 244 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1962
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-4&-9\\\\\\-8&5\\end{pmatrix},\\quad b=\\begin{pmatrix}36\\\\\\72\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-4&-9\\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1963
} |
[
{
"role": "user",
"content": "Solve the equation and provide the answer. 21x^2 - 21 - 164 = 5x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 21x^2 - 21 - 164 = 5x $\n\nMove all terms to the left (standard form):\n$ 21x^2 + -5x + -185 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1964
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Differentiate with respect to $x$: $f(x) = -1e^{4x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -1e^{4x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-4e^{4x}} ... | {
"type": "calculus",
"seed": 1337,
"index": 1965
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Evaluate: ((-3 + -375/15) * 13) + 7^5 - log_3(729) + (-302 mod 19) + ceil(121/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-3 + -375/15) * 13) + 7^5 - log_3(729) + (-302 mod 19) + ceil(121/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1966
} |
[
{
"role": "user",
"content": "Please solve this math problem. 692x - 714 = -205"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 692x - 714 = -205 $\n\nMove all terms to the left (standard form):\n$ 692x + -509 = 0 $\n\nIsolate the $x$ term:\n$ 692x = 509 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 1967
} |
[
{
"role": "user",
"content": "solve: Evaluate: ((-136 + 989/23) * 5) + 10^4 - log_10(1000000) + (289 mod 3) + ceil(-192/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-136 + 989/23) * 5) + 10^4 - log_10(1000000) + (289 mod 3) + ceil(-192/2) $\n\nCompute each component:\... | {
"type": "arithmetic",
"seed": 1337,
"index": 1968
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. 478 + 679 = -366x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 478 + 679 = -366x $\n\nMove all terms to the left (standard form):\n$ 366x + 1157 = 0 $\n\nIsolate the $x$ term:\n$ 366x = -1157 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 1969
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. 211x - 88 = -437"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 211x - 88 = -437 $\n\nMove all terms to the left (standard form):\n$ 211x + 349 = 0 $\n\nIsolate the $x$ term:\n$ 211x = -349 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 1970
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Prove that $f(x,y)=\\frac12(2x^2+1y^2)+-5x+-1y+-5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(2x^2+1y^2)+-5x+-1y+-5 $\n\n$ \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 1971
} |
[
{
"role": "user",
"content": "solve: Evaluate: ((90 + -299/13) * 13) + 9^3 - log_7(16807) + (-409 mod 10) + ceil(62/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((90 + -299/13) * 13) + 9^3 - log_7(16807) + (-409 mod 10) + ceil(62/2) $\n\nCompute each component:\n$ -299/... | {
"type": "arithmetic",
"seed": 1337,
"index": 1972
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Evaluate: ((126 + 400/16) * 20) + 10^2 - log_9(531441) + (418 mod 17) + round(26/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((126 + 400/16) * 20) + 10^2 - log_9(531441) + (418 mod 17) + round(... | {
"type": "arithmetic",
"seed": 1337,
"index": 1973
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Differentiate with respect to $x$: $f(x) = 9\\sin(8x) + 8\\cos(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 9\\sin(8x) + 8\\cos(4x) $\n\nApply the standard differentiation rul... | {
"type": "calculus",
"seed": 1337,
"index": 1974
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Compute the indefinite integral: $\\int 4\\sin(3x) + 0\\cos(3x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int 4\\sin(3x) + 0\\cos(3x)\\,dx $\n\nUse standard antiderivatives (and inte... | {
"type": "calculus",
"seed": 1337,
"index": 1975
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Compute the determinant: $A=\\begin{pmatrix}-4&5\\\\-2&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&5\\\\\\-2&-8\\end{pmatrix} $\n\nUse $\\det(A)... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1976
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((74 + -225/25) * 7) + 12^5 - log_5(125) + (-14 mod 30) + floor(-188/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((74 + -225/25) * 7) + 12^5 - log_5(125) + (-14 mod 30) + floor(-188/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 1977
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. 338x - 363 = 466"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 338x - 363 = 466 $\n\nMove all terms to the left (standard form):\n$ 338x + -829 = 0 $\n\nIsolate the $x$ term:\n$ 338x = 829 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1978
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Compute $(-21+-13) \\bmod 12$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-21+-13) \\bmod 12 $\n\nUse the rule that addition is compatible with reduction mod... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 1979
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n 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": 1980
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Compute the determinant: $A=\\begin{pmatrix}4&2\\\\-2&-5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}4&2\\\\\\-2&-5\\end{pmatri... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1981
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. -8x^2 - 2 - 29 = 22x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -8x^2 - 2 - 29 = 22x $\n\nMove all terms to the left (standard form):\n$ -8x^2 + -22x + -31 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1982
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Compute the indefinite integral: $\\int -9\\sin(9x) + -5\\cos(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -9\\sin(9x) + -5\\cos(2x)\\,dx $\n\nUse standard antiderivatives (and int... | {
"type": "calculus",
"seed": 1337,
"index": 1983
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}7&5\\\\\\-2&6\\end{pmatrix},\\quad b=\\begin{pmatrix}-1\\\\\\30\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}7&5\\\\\\-2&6\\e... | {
"type": "linear_algebra",
"seed": 1337,
"index": 1984
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Differentiate with respect to $x$: $f(x) = \\ln(6x + 9)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(6x + 9) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed... | {
"type": "calculus",
"seed": 1337,
"index": 1985
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. 523 - 127 = -333x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 523 - 127 = -333x $\n\nMove all terms to the left (standard form):\n$ 333x + 396 = 0 $\n\nIsolate the $x$ term:\n$ 333x = -396 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 1986
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Differentiate with respect to $x$: $f(x) = (-4x + -9)\\sin(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-4x + -9)\\sin(1x) $\n\nApply the standard differentiation rules:\n$ f'(x) ... | {
"type": "calculus",
"seed": 1337,
"index": 1987
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. -6x^2 - 94 + 78 = 165x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -6x^2 - 94 + 78 = 165x $\n\nMove all terms to the left (standard form):\n$ -6x^2 + -165x + -16 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1988
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Prove that $f(x,y)=\\frac12(1x^2+1y^2)+-4x+-5y+10$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+1y^2)+-4x+-5y+10 $\n\n$ \\frac{\\partial... | {
"type": "optimization",
"seed": 1337,
"index": 1989
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Evaluate: ((-114 + -148/4) * 8) + 6^3 - log_9(9) + (35 mod 10) + ceil(-55/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-114 + -148/4) * 8) + 6^3 - log_9(9) + (35 mod 10) + ceil(-55/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 1990
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Prove that $f(x,y)=\\frac12(1x^2+7y^2)+3x+3y+-5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+7y^2)+3x+3y+-5 $\n\n$ \\frac{\\partial^2 f}{\\partia... | {
"type": "optimization",
"seed": 1337,
"index": 1991
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Differentiate with respect to $x$: $f(x) = \\ln(1x + -2)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(1x + -2) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\f... | {
"type": "calculus",
"seed": 1337,
"index": 1992
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. 15x^2 - 92 - 38 = 138x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 15x^2 - 92 - 38 = 138x $\n\nMove all terms to the left (standard form):\n$ 15x^2 + -138x + -130 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 1993
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Compute the indefinite integral: $\\int (-1x + 1)\\sin(3x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-1x + 1)\\sin(3x)\\,dx $\n\nUse standard antiderivatives (and integratio... | {
"type": "calculus",
"seed": 1337,
"index": 1994
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Evaluate: ((81 + -200/8) * 5) + 7^2 - log_3(729) + (37 mod 12) + ceil(-117/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((81 + -200/8) * 5) + 7^2 - log_3(729) + (37 mod 12) + ceil(-117/2) $\n\... | {
"type": "arithmetic",
"seed": 1337,
"index": 1995
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. 535x - 45 = -974"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 535x - 45 = -974 $\n\nMove all terms to the left (standard form):\n$ 535x + 929 = 0 $\n\nIsolate the $x$ term:\n$ 535x = -929 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 1996
} |
[
{
"role": "user",
"content": "Work through and solve this equation. -977 - 722x = -124"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -977 - 722x = -124 $\n\nMove all terms to the left (standard form):\n$ -722x + -853 = 0 $\n\nIsolate the $x$ term:\n$ -722x = 853 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 1997
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n 512 - 221x = -240"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 512 - 221x = -240 $\n\nMove all terms to the left (standard form):\n$ -221x + 752 = 0 $\n\nIsolate the $x$ term:\n$ -221x = -752 $\... | {
"type": "linear_equation",
"seed": 1337,
"index": 1998
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((-110 + -506/11) * 14) + 11^4 - log_4(256) + (194 mod 3) + floor(-170/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-110 + -506/11) * 14) + 11^4 - log_4(256) + (194 mod 3) + ... | {
"type": "arithmetic",
"seed": 1337,
"index": 1999
} |
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