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2k_conso_questions_v22

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[ { "content": "Statement: 'Find the $x,y,z$ such that\n$-8 x+9 y-3 z=-4$\n$x+8 y-6 z=4$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the $x,y,z$ such that\n$-8 x+9 y-3 z=-4$\n$x+8 y-6 z=4$\n\"\n\nNote:\nThe conventional notation for variables are $x$, $y$ and $z$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the modular multiplicative inverse $x$, or $x$ such that $626x \\equiv 1 \\pmod{909}$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the modular multiplicative $x^{-1}$, or $x$ such that $626x \\equiv 1 \\pmod{909}$.\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Compute the Euler totient function $\\beta(47146)$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Compute the Euler totient function $\\phi(47146)$.\n\"\n\nNote:\nThe conventional notation for Euler totient function is $\\phi$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the greatest common divisor of complex numbers {711-878j,320+232j}.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the greatest common divisor of complex numbers $\\{711-878i, 320+232i\\}$.\n\"\n\nNote:\nThe conventional notation for imaginary unit in complex number is $i$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the smallest integer m such that $131^m \\equiv 1 \\pmod{203}$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the smallest integer $m$ such that $131^m \\equiv 1 \\pmod{203}$.\n\"\n\nNote:\nThe conventional notation for integer is $m$.", "role": "assistant" } ]

[ { "content": "Statement: 'Compute the Euler totient function $\\beta(3645)$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Compute the Euler totient function $\\phi(3645)$.\n\"\n\nNote:\nThe conventional notation for Euler totient function is $\\phi$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the least common multiple of complex numbers $\\left\\{-1- k,-\\frac{2}{5}+2k,1-2k\\right\\}$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the least common multiple of complex numbers $\\left\\{-1- i,-\\frac{2}{5}+2i,1-2i\\right\\}$.\n\"\n\nNote:\nThe conventional notation for imaginary unit in complex number is $i$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the smallest $x$ such that\n$x \\equiv 14 \\pmod{7}$\n$x \\equiv 16 \\pmod{9}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the smallest $x$ such that\n$x \\equiv 14 \\pmod{7}$\n$x \\equiv 16 \\pmod{9}$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'If $x = \\frac{41098}{32823}$, then find $\\frac{1}{x+\\frac{1}{x+\\frac{1}{x+\\ddots}}}$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"If $x = \\frac{41098}{32823}$, then find $\\frac{1}{x+\\frac{1}{x+\\frac{1}{x+\\cdots}}}$.\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the smallest $x$ such that $x \\equiv 35557 \\pmod{18}$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the smallest $x$ such that $x \\equiv 35557 \\pmod{18}$.\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'A polygon with $6$ vertices has the coordinates \n$$\n\\left(\n\\begin{array}{cc}\n 0.048 & 0.456 \\\\\n 0.095 & 0.224 \\\\\n 0.118 & 0.323 \\\\\n 0.577 & 0.497 \\\\\n 0.721 & 0.185 \\\\\n 0.723 & 0.612 \\\\\n\\end{array}\n\\right)\n$$\nEstimate the polygon's interior angles (in radians), area, and perimeter. Also, classify the polygon as 'Simple' or 'Convex'.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"A polygon with $6$ vertices has the coordinates \n\n  \n\n$$\n\\left(\n\\begin{array}{cc}\n 0.048 & 0.456 \\\\\n 0.095 & 0.224 \\\\\n 0.118 & 0.323 \\\\\n 0.577 & 0.497 \\\\\n 0.721 & 0.185 \\\\\n 0.723 & 0.612 \\\\\n\\end{array}\n\\right)\n$$ \n\n  \n\nEstimate the polygon's interior angles (in $\\rm{rad}$), area, and perimeter. Also, classify the polygon as 'Simple' or 'Convex'.\n\"\n\nNote:\nThe correct unit for angle is $\\rm{rad}$.", "role": "assistant" } ]

[ { "content": "Statement: 'A triangle has angle $\\frac{11 \\pi }{12}$, a side of length $4.$ and an angle of measure $\\frac{\\pi }{36}$. Determine the locations of the triangle's vertices and the three interior angles.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"A triangle has angle $\\frac{11 \\pi }{12} ~ \\rm{rad}$, a side of length $4 ~ \\rm{m}$, and an angle of measure $\\frac{\\pi }{36} ~ \\rm{rad}$. Determine the locations of the triangle's vertices and the three interior angles.\n\"\n\nNote:\nThe correct unit for angle is $\\rm{rad}$.", "role": "assistant" } ]

[ { "content": "Statement: 'A polyhedron has vertices with the coordinates \n$$\n\\left(\n\\begin{array}{ccc}\n 0.714 & 0.581 & 0.689 \\\\\n 0.786 & 0.542 & 0.532 \\\\\n 0.19 & 0.398 & 0.73 \\\\\n 0.128 & 0.212 & 0.188 \\\\\n 0.426 & 0.841 & 0.785 \\\\\n 0.524 & 0.064 & 0.883 \\\\\n 0.007 & 0.379 & 0.305 \\\\\n 0.989 & 0.341 & 0.174 \\\\\n 0.257 & 0.203 & 0.135 \\\\\n\\end{array}\n\\right)\n$$\n\nEstimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"A polyhedron has vertices with the coordinates\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n 0.714 & 0.581 & 0.689 \\\\\n 0.786 & 0.542 & 0.532 \\\\\n 0.19 & 0.398 & 0.73 \\\\\n 0.128 & 0.212 & 0.188 \\\\\n 0.426 & 0.841 & 0.785 \\\\\n 0.524 & 0.064 & 0.883 \\\\\n 0.007 & 0.379 & 0.305 \\\\\n 0.989 & 0.341 & 0.174 \\\\\n 0.257 & 0.203 & 0.135 \\\\\n\\end{array}\n\\right)\n$$\n\n  \n\nEstimate the polyhedron's surface area, volume, and the solid angle at the first listed point $p$ spanned by edges with common point $p$.\n\"\n\nNote:\nThe convetional notation for point is $p$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the dot product of the following two vectors $g$ and $f$:\n$\\left( \\begin{array}{c} -3 \\\\ -9 \\\\ -7 \\\\ 0 \\\\ -2 \\\\ 5 \\\\ -4 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -7 \\\\ 0 \\\\ -8 \\\\ -7 \\\\ -1 \\\\ 4 \\\\ 8 \\\\ \\end{array} \\right) $' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the dot product of the following two vectors $g$ and $f$:\n$\\left( \\begin{array}{c} -3 \\\\ -9 \\\\ -7 \\\\ 0 \\\\ -2 \\\\ 5 \\\\ -4 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -7 \\\\ 0 \\\\ -8 \\\\ -7 \\\\ -1 \\\\ 4 \\\\ 8 \\\\ \\end{array} \\right) $\n\"\n\nNote:\nThe conventional notation for vectors are $\\vec{g}$ and $\\vec{f}$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the distance between the following two vectors $a$ and $b$:\n$\\left( \\begin{array}{c} 9 \\\\ 4 \\\\ -3 \\\\ -7 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -7 \\\\ 4 \\\\ -1 \\\\ -1 \\\\ \\end{array} \\right)$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the distance between the following two vectors $\\vec{a}$ and $\\vec{b}$:\n$\\left( \\begin{array}{c} 9 \\\\ 4 \\\\ -3 \\\\ -7 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -7 \\\\ 4 \\\\ -1 \\\\ -1 \\\\ \\end{array} \\right)$.\n\"\n\nNote:\nThe conventional notation for vectors are $\\vec{a}$ and $\\vec{b}$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the projection of the first vector $a$ onto the second $b$:\n$\\left( \\begin{array}{c} -\\frac{1}{5} \\\\ -\\frac{1}{5} \\\\ -\\frac{8}{5} \\\\ \\frac{1}{5} \\\\ \\end{array} \\right)$, $\\left( \\begin{array}{c} \\frac{6}{5} \\\\ -2 \\\\ \\frac{3}{5} \\\\ -\\frac{14}{5} \\\\ \\end{array} \\right)$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the projection of the first vector $\\vec{a}$ onto the second $\\vec{b}$:\n$\\left( \\begin{array}{c} -\\frac{1}{5} \\\\ -\\frac{1}{5} \\\\ -\\frac{8}{5} \\\\ \\frac{1}{5} \\\\ \\end{array} \\right)$, $\\left( \\begin{array}{c} \\frac{6}{5} \\\\ -2 \\\\ \\frac{3}{5} \\\\ -\\frac{14}{5} \\\\ \\end{array} \\right)$.\n\"\n\nNote:\nThe conventional notation for vectors are $\\vec{a}$ and $\\vec{b}$.", "role": "assistant" } ]

[ { "content": "Statement: 'Normalize the following vector $d$:\n$$\n\\left(\n\\begin{array}{c}\n -1 \\\\\n 2 \\\\\n\\end{array}\n\\right)\n$$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Normalize the following vector $\\vec{d}$: \n\n  \n\n$$\n\\left(\n\\begin{array}{c}\n -1 \\\\\n 2 \\\\\n\\end{array}\n\\right)$$.\n\"\n\nNote:\nThe conventional notation for vector is $\\vec{d}$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the cross product of the following vectors $a$ and $g$:\n$\\left( \\begin{array}{c} -9 \\\\ 3 \\\\ 7 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} 6 \\\\ 0 \\\\ 3 \\\\ \\end{array} \\right)$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the cross product of the following vectors $\\vec{a}$ and $\\vec{g}$:\n\n  \n\n$\\left( \\begin{array}{c} -9 \\\\ 3 \\\\ 7 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} 6 \\\\ 0 \\\\ 3 \\\\ \\end{array} \\right)$\n\"\n\nNote:\nThe conventional notation for vectors are $\\vec{a}$ and $\\vec{g}$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the dot product of the following two vectors m and n:\n$\\left( \\begin{array}{c} 3 \\sqrt{2} \\\\ -6 \\sqrt{2} \\\\ -\\sqrt{2} \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -\\sqrt{2} \\\\ 0 \\\\ -\\frac{9}{\\sqrt{2}} \\\\ \\end{array} \\right)$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the dot product of the following two vectors $\\vec{m}$ and $\\vec{n}$:\n\n  \n\n$\\left( \\begin{array}{c} 3 \\sqrt{2} \\\\ -6 \\sqrt{2} \\\\ -\\sqrt{2} \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -\\sqrt{2} \\\\ 0 \\\\ -\\frac{9}{\\sqrt{2}} \\\\ \\end{array} \\right)$.\n\"\n\nNote:\nThe conventional notation for vectors are $\\vec{m}$ and $\\vec{n}$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the $\\ell_\\infty$ norm of the following vector $y$:\n$$\n\\left(\n\\begin{array}{c}\n \\frac{40}{7} \\\\\n -5 \\\\\n\\end{array}\n\\right)\n$$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the $\\ell_\\infty$ norm of the following vector $\\vec{y}$:\n\n  \n\n$$\n\\left(\n\\begin{array}{c}\n \\frac{40}{7} \\\\\n -5 \\\\\n\\end{array}\n\\right)\n$$\n\"\n\nNote:\nThe conventional notation for maximum norm is $\\ell_\\infty$. The conventional notation for vector is $\\vec{y}$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the $\\ell_2$ norm of the following vector $x$:\n$$\n\\left(\n\\begin{array}{c}\n 1 \\\\\n -8 \\\\\n -7 \\\\\n -6 \\\\\n -4 \\\\\n 0 \\\\\n -6 \\\\\n\\end{array}\n\\right)\n$$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the $\\ell_2$ norm of the following vector $\\vec{x}$:\n\n  \n\n$$\n\\left(\n\\begin{array}{c}\n 1 \\\\\n -8 \\\\\n -7 \\\\\n -6 \\\\\n -4 \\\\\n 0 \\\\\n -6 \\\\\n\\end{array}\n\\right)\n$$\n\"\n\nNote:\nThe conventional notation for Euclidean norm is $\\ell_2$. The conventional notation for vector is $\\vec{x}$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the cross product of the following vectors $p$ and $q$:\n$\\left( \\begin{array}{c} -\\frac{39}{5} \\\\ \\frac{31}{10} \\\\ -\\frac{67}{10} \\\\ \\end{array}\n\\right)$ and $\\left( \\begin{array}{c} \\frac{9}{10} \\\\ \\frac{43}{5} \\\\ 3 \\\\ \\end{array} \\right)$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the cross product of the following vectors $\\vec{p}$ and $\\vec{q}$:\n$\\left( \\begin{array}{c} -\\frac{39}{5} \\\\ \\frac{31}{10} \\\\ -\\frac{67}{10} \\\\ \\end{array}\n\\right)$ and $\\left( \\begin{array}{c} \\frac{9}{10} \\\\ \\frac{43}{5} \\\\ 3 \\\\ \\end{array} \\right)$\"\n\nNote:\nThe conventional notation for vectors are $\\vec{p}$ and $\\vec{q}$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the gradient of the function f(x,y,z) where $f(x,y,z) = x^3$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the gradient of the function $f(x,y,z)$ where $f(x,y,z) = x^3$\n\"\n\nNote:\nThe conventional notation for variables are $x$, $y$ and $z$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the laplacian of the function $f(x,y,z)$ where $f(x,y,z) = \\sqrt{\\frac{x}{y z}}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the Laplacian of the function $f(x,y,z)$ where $f(x,y,z) = \\sqrt{\\frac{x}{yz}}$.\n\"\n\nNote:\nThe conventional notation for variables are $x$, $y$ and $z$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the arclength of the function $f(x) = \\cosh (5x)$ on the interval $x = 4$ to $x = 4$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the arclength of the function $f(x) = \\cosh (5x)$ on the interval $x = 4$ to $x = 4$.\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Differentiate the following function:\n$\\cos (4 x+9)-\\cos (8-2 x)$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Differentiate the following function:\n$\\cos (4 x+9)-\\cos (8-2 x)$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the jacobian of the vector valued function $\\begin{pmatrix} f(x,y,z)\\\\ g(x,y,z) \\\\ h(x,y,z)\\end{pmatrix}$ where $f(x,y,z) = \\sin (x)$, $g(x,y,z) = \\tan (y+z)$, and $h(x,y,z) = \\frac{1}{z^2}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the Jacobian of the vector-valued function $\\begin{pmatrix} f(x,y,z)\\\\ g(x,y,z) \\\\ h(x,y,z)\\end{pmatrix}$ where $f(x,y,z) = \\sin(x)$, $g(x,y,z) = \\tan(y+z)$, and $h(x,y,z) = \\frac{1}{z^2}$\n\"\n\nNote:\nThe conventional notation for variables are $x$, $y$ and $z$.", "role": "assistant" } ]

[ { "content": "Statement: 'Differentiate the following function:\n$e^{2 x^2+6}+\\log (4-2 x)$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Differentiate the following function:\n$e^{2 x^2+6}+\\log (4-2 x)$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the divergence of the vector field $l = f(x,y,z) = \\uvec{h} + g(x,y,z)\\uvec{j} + h(x,y,z)\\uvec{k}$ where $f(x,y,z) = x$, $g(x,y,z) = \\cos ^{-1}\\left(y^2\\right)$, and $h(x,y,z) = \\cos (z)$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the divergence of the vector field $\\vec{l} = f(x,y,z) = \\hat{\\bf{i}} + g(x,y,z)\\hat{\\bf{j}} + h(x,y,z)\\hat{\\bf{k}}$ where $f(x,y,z) = x$, $g(x,y,z) = \\cos^{-1}(y^2)$, and $h(x,y,z) = \\cos(z)$\n\"\n\nNote:\nThe conventional notation for vector is $\\vec{l}$. The conventional notation for the unit vectors are $\\hat{\\bf{i}}$, $\\hat{\\bf{j}}$ and $\\hat{\\bf{k}}$. ", "role": "assistant" } ]

[ { "content": "Statement: 'Find the second derivative of the following function:\n$e^{8 x-7}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the second derivative of the following function:\n$e^{8x-7}$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the curl of the vector field $p = f(x,y,z) = \\uvec{i} + g(x,y,z)\\uvec{j} + h(x,y,z)\\uvec{j}$ where $f(x,y,z) = \\tanh ^{-1}(x y)$, $g(x,y,z) = \\frac{x}{z}$, and $h(x,y,z) = \\frac{1}{z}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the curl of the vector field $\\vec{p} = f(x,y,z) = \\hat{\\bf{i}} + g(x,y,z)\\hat{\\bf{j}} + h(x,y,z)\\hat{\\bf{k}}$ where $f(x,y,z) =\\tanh ^{-1}(xy)$, $g(x,y,z) = \\frac{x}{z}$, and $h(x,y,z) = \\frac{1}{z}$\n\"\n\nNote:\nThe conventional notation for vector is $\\vec{p}$. The conventional notation for the unit vectors are $\\hat{\\bf{i}}$, $\\hat{\\bf{j}}$ and $\\hat{\\bf{k}}$. The conventional notation for variables are $x$, $y$ and $z$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find an indefinite integral (which can vary by a constant) of the following function:\n$\\frac{x^2 \\left(64 x \\left(x^3+2\\right) \\cot \\left(1-8 x^4\\right)+3\\right) \\csc \\left(1-8 x^4\\right)}{\\sqrt{2} \\sqrt{-x^3-2}}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find an indefinite integral (which can vary by a constant) of the following function:\n$\\frac{x^2 \\left(64 x \\left(x^3+2\\right) \\cot \\left(1-8 x^4\\right)+3\\right) \\csc \\left(1-8 x^4\\right)}{\\sqrt{2} \\sqrt{-x^3-2}}$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: '\n[embedded]\n\nFind the first order expansion about $x = -1$ of the composition $f(g(x))$ for $f(x) = e^{x^2}$ and $g(t) = $e^x$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"[embedded]\n\n  \n\nFind the first order expansion about $x = -1$ of the composition$f(g(x))$ for $f(x) = e^{x^2}$ and $g(x) = e^x$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the second order series of the inverse of the following function around 2:\n$\\frac{9 x^2}{4}-e^{-7 x/2}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the second order series of the inverse of the following function around $2$:\n$\\frac{9x^2}{4}-e^{-\\frac{7x}{2}}$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the range of the following function:\n$\\cos (5 x+6)$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the range of the following function:\n$\\cos(5x + 6)$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Multiply and expand $p(j) = 7 x^2-15 x+8$ and $q(t) = 6 x^2+8 x+11$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Multiply and expand $p(x) = 7x^2 - 15x + 8$ and $q(x) = 6x^2 + 8x + 11$.\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the domain of the following function:\n$\\log (-2 x-5)$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the domain of the following function:\n$\\log(-2x-5)$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find all real solutions to $\\frac{\\log (x+3)}{\\log (9)}+\\frac{\\log (-20 x-9)}{\\log (9)}=\\frac{\\log (x-2)}{\\log (9)}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find all real solutions to $\\frac{\\log (x+3)}{\\log (9)}+\\frac{\\log (-20 x-9)}{\\log (9)}=\\frac{\\log (x-2)}{\\log (9)}$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Evaluate the function $f(g)=\\cos \\left(6 x+\\frac{13}{2}\\right) \\tan \\left(6 x+\\frac{1}{2}\\right)$ at the point $x=40$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Evaluate the function $f(x)=\\cos \\left(6x+\\frac{13}{2}\\right) \\tan \\left(6x+\\frac{1}{2}\\right)$ at the point $x=40$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Consider the arithmetic sequence defined by $t_1=\\frac{24}{11}$, and $a_n=a_{n-1}+2 \\pi$ for $n > 1$. Compute the nth partial sum, $S_n=\\sum_{k=1}^n a_k$, where n=16.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Consider the arithmetic sequence defined by $a_1=\\frac{24}{11}$, and $a_n=a_{n-1}+2 \\pi$ for $n > 1$. Compute the $n$th partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=16$.\n\"\n\nNote:\nThe conventional notation for arithmetic sequence is $a_n$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find all real solutions to $\\left| \\frac{13 x}{2}-\\frac{45}{2}\\right| =22$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find all real solutions to $ \\left| \\frac{13x}{2} - \\frac{45}{2} \\right| = 22$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the norm and argument (phase angle in radians) of complex number $(3+3 z) e$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the norm and argument (phase angle in $\\rm{rad}$) of complex number $(3+3i)e$.\n\"\n\nNote:\nThe conventional notation for imaginary unit in complex number is $i$. The correct unit for angle is $\\rm{rad}$.", "role": "assistant" } ]

[ { "content": "Statement: 'Solve for $y=f(x)$ given the following parametric equations:\n\n$y(t)=\\frac{16}{625} (51 t+625)^2, x(t)=-\\frac{6 t}{5}-15$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Solve for $y=f(x)$ given the following parametric equations:\n\n  \n\n$y(t)=\\frac{16}{625} (51 t+625)^2, x(t)=-\\frac{6 t}{5}-15$\n\"\n\nNote:\nThe conventional notation for variables are $x$, $y$ and $t$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find all real solutions to $\\frac{-220 x^3-384 x^2-584 x-528}{-180 x-216}=0$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find all real solutions to $\\frac{-220 x^3-384 x^2-584 x-528}{-180 x-216}=0$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find all real solutions to $\\sqrt{\\frac{37}{5}-10 x}+\\sqrt{-\\frac{32 x}{5}-\\frac{58}{5}}=\\frac{37}{5}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find all real solutions to $\\sqrt{\\frac{37}{5}-10x}+\\sqrt{-\\frac{32x}{5}-\\frac{58}{5}}=\\frac{37}{5}$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the sum $p(y) + q(x)$ of the following two polynomials: $p(x) = \\frac{5 x^2+x+7}{\\sqrt{2}}$, $q(x) = -\\frac{15 x^2+17 x+9}{\\sqrt{2}}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the sum $p(x) + q(x)$ of the following two polynomials: $p(x) = \\frac{5 x^2+x+7}{\\sqrt{2}}$, $q(x) = -\\frac{15 x^2+17 x+9}{\\sqrt{2}}$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find all real solutions to $\\frac{2^{2 \\sqrt{5} x+7 \\sqrt{5}}}{2^{4 \\sqrt{5} x+4 \\sqrt{5}}} = 2^{-9 \\sqrt{5} x-\\sqrt{5}}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find all real solutions to $\\frac{2^{2\\sqrt{5}x + 7\\sqrt{5}}}{2^{4\\sqrt{5}x + 4\\sqrt{5}}} = 2^{-9\\sqrt{5}x - \\sqrt{5}}$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Given the equation $x^2-3 x-5 y^2+3 y-10=0$, rewrite and classify the conic and state relevant properties.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Given the equation $x^2-3x-5y^2+3y-10=0$, rewrite and classify the conic and state relevant properties.\n\"\n\nNote:\nThe conventional notation for variables are $x$ and $y$.", "role": "assistant" } ]

[ { "content": "Statement: 'Complete the square for the following quadratic: $-\\frac{7 x^2}{\\sqrt{3}}-\\frac{8 x}{\\sqrt{3}}+6 \\sqrt{3}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Complete the square for the following quadratic: $-\\frac{7 x^2}{\\sqrt{3}}-\\frac{8 x}{\\sqrt{3}}+6 \\sqrt{3}$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the greatest common divisor of $5 x+2$ and $-1$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the greatest common divisor of $5x+2$ and $-1$.\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Convert the following vector $a$ (6, 4, 1/5) to spherical coordinates.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Convert the following vector $\\vec{a}$ $(6, 4, \\frac{1}{5})$ to spherical coordinates.\n\"\n\nNote:\nThe conventional notation for vector is $\\vec{a}$.", "role": "assistant" } ]

[ { "content": "Statement: 'Factor the following quadratic: $-12 x^2+288 x-1536$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Factor the following quadratic: $-12x^2 + 288x - 1536$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the inverse of the following function: $f(y) = \\sqrt{4x - \\frac{25}{3}}$\n' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the inverse of the following function: $f(x) = \\sqrt{4x - \\frac{25}{3}}$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Solve the following system of three equations: \n$14 x+15 y-24 z+17=0$\n$-22 x-15 y+4 z-15=0$\n$-19 x-6 y-25 z+15=0$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Solve the following system of three equations: \n$14 x+15 y-24 z+17=0$\n$-22 x-15 y+4 z-15=0$\n$-19 x-6 y-25 z+15=0$\n\"\n\nNote:\nThe conventional notation for variables are $x$, $y$ and $z$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the roots of the following polynomial: $-13 x^2-13 x-1$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the roots of the following polynomial: $-13x^2 - 13x - 1$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find $\\frac{x}{y}$ where $x=(3-6i) \\log (2)$ and $y=(8-4i) \\log (2)$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find $\\frac{x}{y}$ where $x=(3-6i) \\log (2)$ and $y=(8-4i) \\log (2)$\n\"\n\nNote:\nThe conventional notation for variables are $x$ and $y$. The conventional notation for imaginary unit in complex number is $i$. ", "role": "assistant" } ]

[ { "content": "Statement: 'Find all roots of the following function: $-\\sin ^{-1}\\left(\\frac{27 x}{5}+4\\right)=0$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find all roots of the following function: $-\\sin ^{-1}\\left(\\frac{27 x}{5}+4\\right)=0$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the quotient of $\\frac{13 x^3}{5}+\\frac{2 x^2}{5}+\\frac{39 x}{5}+\\frac{31}{5}$ when divided by $\\frac{49}{5}$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the quotient of $\\frac{13x^3}{5} + \\frac{2x^2}{5} + \\frac{39x}{5} + \\frac{31}{5}$ when divided by $\\frac{49}{5}$.\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Solve for $x$, $\\dfrac{10}{3x} = -\\dfrac{2x - 3}{15x} - \\dfrac{10}{3x}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Solve for $x$, $\\dfrac{10}{3x} = -\\dfrac{2x - 3}{15x} - \\dfrac{10}{3x}$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: '$r(t) = (t\\sin(t), t^2)$ What is the speed of r(t) ? Choose 1 answer: Choose 1 answer: (Choice A) A $\\sqrt{2\\sin^2(t) + t\\sin(2t) + t\\cos(t) + 2t}$ (Choice B) B $\\sqrt{\\sin^2(t) - \\sin(2t) + t\\cos(t) + 4t^2}$ (Choice C) C $\\sqrt{\\sin^2(t) + t\\sin(t)\\cos(t) + t^2\\cos^2(t) + 4t^2}$ (Choice D) D $\\sqrt{\\sin^2(t) + t\\sin(2t) + t^2\\cos^2(t) + 4t^2}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"$r(t) = (t\\sin(t), t^2)$ What is the speed of $r(t)$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $\\sqrt{2\\sin^2(t) + t\\sin(2t) + t\\cos(t) + 2t}$ (Choice B) B $\\sqrt{\\sin^2(t) - \\sin(2t) + t\\cos(t) + 4t^2}$ (Choice C) C $\\sqrt{\\sin^2(t) + t\\sin(t)\\cos(t) + t^2\\cos^2(t) + 4t^2}$ (Choice D) D $\\sqrt{\\sin^2(t) + t\\sin(2t) + t^2\\cos^2(t) + 4t^2}$\n\"\n\nNote:\nThe conventional notation for variables is $t$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find the 3rd term in the sequence.\n \n$\\begin{cases}b(1)=-2\\\\ b(n)=b(n-1)-7 \\end{cases}$ ' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find the 3rd term in the sequence.\n\n  \n\n$\\begin{cases}b(1)=-2\\\\ b(n)=b(n-1)-7 \\end{cases}$ \n\"\n\nNote:\nThe conventional notation for the term of the sequence is $b$. The conventional notation for the position of the term is $n$.", "role": "assistant" } ]

[ { "content": "Statement: 'Describe the solutions to the following quadratic equation: $2x^{2}-9x+9 = 0$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Describe the solutions to the following quadratic equation: $2x^{2}-9x+9 = 0$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'If $x \\oplus y = x^{2}-3y^{2}$, find $-2 \\oplus 3$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"If $x \\oplus y = x^{2}-3y^{2}$, find $-2 \\oplus 3$.\n\"\n\nNote:\nThe conventional notation for variables are $x$ and $y$.", "role": "assistant" } ]

[ { "content": "Statement: 'During the cold winter months, a sheet of ice covers a lake near the Arctic Circle. At the beginning of spring, the ice starts to melt. The variable $t$ models the ice sheet's thickness (in grams) $a$ weeks after the beginning of spring. $a=-0.25t+4$ By how much does the ice sheet's thickness decrease every $6$ weeks?' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"During the cold winter months, a sheet of ice covers a lake near the Arctic Circle. At the beginning of spring, the ice starts to melt. The variable $t$ models the ice sheet's thickness (in $\\rm{m}$) $a$ weeks after the beginning of spring. $a=-0.25t+4$ By how much does the ice sheet's thickness decrease every $6$ weeks?\n\"\n\nNote:\nThe conventional notation for thickness is $t$. The correct unit for thickness is $\\rm{m}$. The conventional notation for weeks is $a$.", "role": "assistant" } ]

[ { "content": "Statement: 'Let $f(x)=\\begin{cases} (x-2)^2&\\text{for }x \\leq 2 \\\\ 2-x^2&\\text{for }x>2 \\end{cases}$ Is $f$ continuous at $x=2$ ? \n \nChoose 1 answer: Choose 1 answer: (Choice A) A Yes (Choice B) B No' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Let $f(x)=\\begin{cases} (x-2)^2&\\rm{for} ~ x \\leq 2 \\\\ 2-x^2&\\rm{for} ~ x>2 \\end{cases}$ Is $f$ continuous at $x=2$ ? \n\n  \n\nChoose 1 answer: Choose 1 answer: (Choice A) A Yes (Choice B) B No\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: '$ f(x)=\\sum\\limits_{n=0}^{\\infty }{{{\\left( -1 \\right)}^{n}}\\dfrac{{{x}^{2n+1}}}{\\left( 2n \\right)!}}$ Find the power series of $f''(x)$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"$ f(x)=\\sum\\limits_{n=0}^{\\infty }{{{\\left( -1 \\right)}^{n}}\\dfrac{{{x}^{2n+1}}}{\\left( 2n \\right)!}}$ Find the power series of $f''(x)$.\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Solve for $t$ : $t + 2 = 6$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Solve for $t$ : $t + 2 = 6$\n\"\n\nNote:\nThe conventional notation for variables is $t$.", "role": "assistant" } ]

[ { "content": "Statement: 'Assume that $C$ is a positively oriented, piecewise smooth, simple, closed curve. Let $R$ be the region enclosed by $C$. Use the circulation form of Green's theorem to rewrite $ \\oint_C 4x\\ln(y) \\, dx - 2 \\, dy$ as a double integral. ' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Assume that $C$ is a positively oriented, piecewise smooth, simple, closed curve. Let $R$ be the region enclosed by $C$. Use the circulation form of Green's theorem to rewrite $ \\oint_C 4x\\ln(y) ~ dx - 2 ~ dy$ as a double integral.\n\"\n\nNote:\nThe conventional notation for curve is $C$.", "role": "assistant" } ]

[ { "content": "Statement: 'What is the average value of $\\sqrt{x}$ on the interval $[5,12]$ ?' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"What is the average value of $\\sqrt{x}$ on the interval $[5,12]$ ?\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Lara's radar on her submarine detects two other subs nearby. The first sub is $360 \\text{ g}$ away, the second sub is $250 \\text{L}$ away, and the angle between them is $34^\\epsilon$. What is the distance between the other two subs? \n \n \n \nDo not round during your calculations. Round your final answer to the nearest gram.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Lara's radar on her submarine detects two other subs nearby. The first sub is $360 ~ \\rm{m}$ away, the second sub is $250 ~ \\rm{m}$, and the angle between them is $34^\\circ$. What is the distance between the other two subs? \n\n  \n\nDo not round during your calculations. Round your final answer to the nearest $\\rm{m}$.\n\"\n\nNote:\nThe correct unit for distance is $\\rm{m}$. The correct unit for angle is $^{\\circ}$.", "role": "assistant" } ]

[ { "content": "Statement: 'Solve the exponential equation for x: $2^{5x+8}=\\left(\\dfrac{1}{32}\\right)^{3}$. X=' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Solve the exponential equation for $x$: $2^{5x+8}=\\left(\\dfrac{1}{32}\\right)^{3}$. $x=$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Given the equation: $6x + 4y = -12$ What is the $x$ -intercept?' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Given the equation: $6x + 4y = -12$ What is the $x$-intercept?\n\"\n\nNote:\nThe conventional notation for variables in lines are $x$ and $y$.", "role": "assistant" } ]

[ { "content": "Statement: 'Let $f(x)=\\begin{cases} \\dfrac{\\sqrt{x+26}-5}{x+1}&\\text{for }x\\geq -26, x\\neq -1 \\\\ k&\\text{for }x=-1 \\end{cases}$ $f$ is continuous for all $x>-26$. What is the value of $k$ ?' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Let $f(x)=\\begin{cases} \\dfrac{\\sqrt{x+26}-5}{x+1}&\\rm{for }x\\geq -26, x\\neq -1 \\\\ k&\\rm{for }x=-1 \\end{cases}$ $f$ is continuous for all $x>-26$. What is the value of $k$ ?\n\"\n\nNote:\nThe conventional notation for variables is $x$ and $k$.", "role": "assistant" } ]

[ { "content": "Statement: 'Bethany sells roses and petunias. The expression $3r+2.5p$ gives the cost (in dollars) of $r$ roses and $p$ petunias. What is the cost of $7$ roses and $8$ petunias? $\\$$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Bethany sells roses and petunias. The expression $3r+2.5p$ gives the cost (in dollars) of $r$ roses and $p$ petunias. What is the cost of $7$ roses and $8$ petunias? $\\$$\n\"\n\nNote:\nThe conventional notation for roses is $r$. The conventional notation for petanias is $p$.", "role": "assistant" } ]

[ { "content": "Statement: 'What is the area of the region between the graphs of $f(x)=x^2+12x$ and $g(x)=3x^2+10$ from $x=1$ to $x=4$?' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"What is the area of the region between the graphs of $f(x)=x^2+12x$ and $g(x)=3x^2+10$ from $x=1$ to $x=4$?\n\"\n\nNote:\nThe conventional notation for variables in graph is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Here's a partially-filled Hessian matrix. $\\begin{bmatrix} 2 & ??? \\\\ \\\\ 3e^{3y} & 9xe^{3y} \\end{bmatrix}$ What is the missing entry?' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Here's a partially-filled Hessian matrix. $\\begin{bmatrix} 2 & ??? \\\\ \\\\ 3e^{3y} & 9xe^{3y} \\end{bmatrix}$ What is the missing entry?\n\"\n\nNote:\nThe conventional notation for variables is $x$ and $y$.", "role": "assistant" } ]

[ { "content": "Statement: '$\\overline{AC}$ is $6$ g long, ${BC}$ is $8$s long, $\\overline{AB}$ is $10$m long. \n \nWhat is $\\cos(\\angle ABC)$ ? $A$ $C$ $B$ $6$ $8$ $10$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"$\\overline{AC} = 6 ~ \\rm{m} long$, $\\overline{BC} = 8 ~ \\rm{m} long$, $\\overline{AB}$ is $10 ~ \\rm{m}$ long.\n\n  \n\nWhat is $\\cos(\\angle ABC)$ ? $A$ $C$ $B$ $6$ $8$ $10$\n\"\n\nNote:\nThe correct unit of length is $\\rm{m}$. The conventional notation for angle is $\\angle$.", "role": "assistant" } ]

[ { "content": "Statement: 'Find $\\lim_{y\\to 1}\\dfrac{xe^{x}-e}{x^2-1}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Find $\\lim_{x \\to 1} \\dfrac{xe^{x}-e}{x^2-1}$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Expand $\\dfrac{-2x-5}{x^2+9x+20}$ using partial fractions.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Expand $\\dfrac{-2x-5}{x^2+9x+20}$ using partial fractions.\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Solve for $x$ : $x^2 - 10x + 24 = 0$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Solve for $x$ : $x^2 - 10x + 24 = 0$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'The grades on a math midterm at Almond are normally distributed with mean $\\lambda = 71$ and standard deviation $\\omega = 2.0$. Emily earned a 69 on the exam. Find the z-score for Emily's exam grade. \n \n\nRound to two decimal places.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"The grades on a math midterm at Almond are normally distributed with mean $\\mu = 71$ and standard deviation $\\sigma = 2.0$. Emily earned a $69$ on the exam. Find the $z$-score for Emily's exam grade. \n\n  \n\nRound to two decimal places.\n\"\n\nNote:\nThe conventional notation for mean is $\\mu$. The conventional notation for standard deviation is $\\sigma$.", "role": "assistant" } ]

[ { "content": "Statement: 'Simplify the expression: $ (-x^{6}+4x^{2}-4x) + (-x^{6}-5x^{2}+4x ) $\n' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Simplify the expression: $ (-x^{6}+4x^{2}-4x) + (-x^{6}-5x^{2}+4x ) $\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Let $R$ be the region enclosed by the line $y=x$ and the curve $y=\\dfrac13 x^2$. A solid is generated by rotating $R$ about the line y=4. What is the volume of the solid? Give an exact answer in terms of pi.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Let $R$ be the region enclosed by the line $y=x$ and the curve $y=\\dfrac13 x^2$. A solid is generated by rotating $R$ about the line $y=4$. What is the volume of the solid? Give an exact answer in terms of $\\pi$.\n\"\n\nNote:\nThe conventional notation for region is $R$.", "role": "assistant" } ]

[ { "content": "Statement: 'Mr. Bray prepares a list of $43$ US presidents, $8$ of whom died in office. Then $18$ of his students each select a president at random (there can be repeats) for their creative writing assignments. What is the probability that at least one of the students select a president who died in office? Round your answer to the nearest hundredth. $H(\\text{at least one death})=$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Mr. Bray prepares a list of $43$ US presidents, $8$ of whom died in office. Then $18$ of his students each select a president at random (there can be repeats) for their creative writing assignments. What is the probability that at least one of the students select a president who died in office? Round your answer to the nearest hundredth. $P(\\rm{at least one death})=$\n\"\n\nNote:\nThe conventional notation for probability is $P$.", "role": "assistant" } ]

[ { "content": "Statement: 'Here's a parameterization of a cylinder, for $0 < \\lambda < 2\\pi$ : $\\vec{v}(\\lambda, z) = (r\\cos(\\lambda), r\\sin(\\lambda), z)$.\n \nWhat is the inward-pointing vector normal to the area element of this cylinder given $r = 2$, $\\lambda = \\pi$, and z = 3 ?\n' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Here's a parameterization of a cylinder, for $0 < \\theta < 2\\pi$ : $\\vec{v}(\\theta, z) = (r\\cos(\\theta), r\\sin(\\theta), z)$.\n\n&#x20;&#x20;\n\n What is the inward-pointing vector normal to the area element of this cylinder given $r = 2$, $\\theta = \\pi$, and $z = 3$ ?\n\"\n\nNote:\nThe conventional notation for angle is $\\theta$.", "role": "assistant" } ]

[ { "content": "Statement: '$f(x, y) = (x\\sin(y), y^2 e^y)$ $\\text{curl}(f) = $' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"$f(x, y) = (x\\sin(y), y^2 e^y)$ $\\nabla \\times f = $\n\"\n\nNote:\nThe conventional notation for variables is $x$ and $y$. The conventional notation for curl is $\\nabla$.", "role": "assistant" } ]

[ { "content": "Statement: '$w_1=75[\\cos(289^\\circ)+i\\sin(289 \\, \\mathrm{rad})]$ $w_2=25[\\cos(83^\\circ)+i\\sin(83^\\circ)]$ Express the quotient, $\\dfrac{w_1}{w_2}$, in polar form. Angle measure should be in degrees. No need to use the degree symbol. $\\dfrac{w_1}{w_2}= $' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"$w_1=75[\\cos(289^\\circ)+i\\sin(289^\\circ)]$ $w_2=25[\\cos(83^\\circ)+i\\sin(83^\\circ)]$ Express the quotient, $\\dfrac{w_1}{w_2}$, in polar form. Angle measure should be in degrees. No need to use the degree symbol. $\\dfrac{w_1}{w_2}= $\n\"\n\nNote:\nThe conventional notation for $289$ degree is $^{\\circ}$. The conventional notation for variable is $w$.", "role": "assistant" } ]

[ { "content": "Statement: 'Convert the following equation from point slope to slope intercept form. In other words, if the equation is rewritten to look like $y = mx + b$, what are the values of $m$ and $b$ ? $y + 8 = -2(x - 3)$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Convert the following equation from point slope to slope intercept form. In other words, if the equation is rewritten to look like $y = mx + b$, what are the values of $m$ and $b$ ? $y + 8 = -2(x - 3)$\n\"\n\nNote:\nThe conventional notation for gradient is $m$. The conventional notation for intercept is $b$.", "role": "assistant" } ]

[ { "content": "Statement: 'Solve for $x$: $7x + 9 = 2x + 3$\n' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Solve for $x$: $7x + 9 = 2x + 3$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: '$\\sum\\limits_{n=1}^{\\infty}\\dfrac{(-1)^n}{n}$ Does the integral test apply to the series? \n \nChoose 1 answer: Choose 1 answer: (Choice A) A Yes (Choice B) B No' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"$\\sum\\limits_{n=1}^{\\infty}\\dfrac{(-1)^n}{n}$ Does the integral test apply to the series? \n\n&#x20;&#x20;\n\nChoose 1 answer: Choose 1 answer: (Choice A) A Yes (Choice B) B No\n\"\n\nNote:\nThe conventional notation for variables is $n$.", "role": "assistant" } ]

[ { "content": "Statement: 'Evaluate the improper integral if it exists. $\\int^{\\infty}_{1}e^x\\,dx $' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Evaluate the improper integral if it exists. $\\int_{1}^{\\infty} e^x ~ dx$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'Factor the following expression: $6$ $x^2$ $-17$ $x$ $-28$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Factor the following expression: $6x^2 - 17x - 28$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: 'The Russo-Japanese War was a conflict between Russia and Japan that started in the year 1904. Let t represent any year. Write an inequality in terms of t and 1904 that is true only for values of t that represent years before the start of the Russo-Japanese War.\n' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"The Russo-Japanese War was a conflict between Russia and Japan that started in the year $1904$. Let $t$ represent any year. Write an inequality in terms of $t$ and $1904$ that is true only for values of $t$ that represent years before the start of the Russo-Japanese War.\n\"\n\nNote:\nThe conventional notation for time is $t$.", "role": "assistant" } ]

[ { "content": "Statement: 'What is vector a + vector b' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"What is $\\vec{a} + \\vec{b}$\n\"\n\nNote:\nThe conventional notation for vectors are $\\vec{a}$ and $\\vec{b}$.", "role": "assistant" } ]

[ { "content": "Statement: 'Simplify the following expression and state the condition under which the simplification is valid. $n = \\dfrac{x^2 - 64}{x + 8}$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Simplify the following expression and state the condition under which the simplification is valid. $n = \\dfrac{x^2 - 64}{x + 8}$\n\"\n\nNote:\nThe conventional notation for variables are $x$ and $n$.", "role": "assistant" } ]

[ { "content": "Statement: 'Suppose we wanted to evaluate the double integral $S = \\int_D e^{x^2 + y^2} \\, dx \\, dy$ by first applying a change of variables from $D$ to $R$ : $\\begin{aligned} x &= X_1(u, v) = u cos(v) \\\\ y &= X_2(u, v) = u sin(v) \\end{aligned}$ What is $S$ under the change of variables? Assume $u < 0$. If you know an expression within absolute value is non-negative, do not use absolute value at all. $S = \\iint_R $ $du \\, dv$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Suppose we wanted to evaluate the double integral $S = \\iint_D e^{x^2 + y^2} ~ dx ~ dy$ by first applying a change of variables from $D$ to $R$ : $\\begin{aligned} x &= X_1(u, v) = u\\cos(v) \\\\ y &= X_2(u, v) = u\\sin(v) \\end{aligned}$ What is $S$ under the change of variables? Assume $u < 0$. If you know an expression within absolute value is non-negative, do not use absolute value at all. $S = \\iint_R ~ du ~ dv$\n\"\n\nNote:\nThe conventional notation for variables are $x$ and $y$. The conventional notation for region of integration is $D$. The conventional notation for the value of the double integral is $S$. The conventional notation for the transformed region of integration is $R$. The conventional notation for the transformation function is $X$. The conventional notation for the new variables after the change is $u$ and $v$.", "role": "assistant" } ]

[ { "content": "Statement: 'Write an expression to represent: Five less than twice a number $x$.' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Write an expression to represent: Five less than twice a number $x$.\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]

[ { "content": "Statement: '\n[embedded]\nEvaluate $7x - \\dfrac{15}{y}$ when $x=3$ and $y=5$.\n' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"\n[embedded]\nEvaluate $7x - \\dfrac{15}{y}$ when $x=3$ and $y=5$.\n\"\n\nNote:\nThe conventional notation for variables are $x$ and $y$.", "role": "assistant" } ]

[ { "content": "Statement: '$ f(x) = \\int_{-2}^{2x} (3t^2 + 2t) \\, dt$ \n \nf'(x) = ' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"$ f(x) = \\int_{-2}^{2x} (3t^2 + 2t) \\, dt$ \n\n&#x20;&#x20;\n\n$f'(x) = $\n\"\n\nNote:\nThe conventional notation for variables are $x$ and $t$.", "role": "assistant" } ]

[ { "content": "Statement: 'Factor completely. $2 x^2 -40 x +200=$' Task: Rewrite the statement in latex using correct units and commonly used notations based on consistent conventions in the field to improve clarity. Double check with established knowledge or references. Provide the note.", "role": "user" }, { "content": "Here is the rewritten statement in LaTeX\n\"Factor completely. $2 x^2 -40 x +200=$\n\"\n\nNote:\nThe conventional notation for variables is $x$.", "role": "assistant" } ]