formatted listlengths 2 2 |
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[
{
"content": "Statement:\n Determine whether $228$ is divisible by $3$.\n\n[embedded]\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
},
{
"content": "Determine whether $228$ is divisible by $3$.\n\n[embedded]\n",
"role": "assistant"
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] |
[
{
"content": "Statement:\n Find the smallest $x$ such that\n$x \\equiv 14 \\pmod{7}$\n$x \\equiv 16 \\pmod{9}$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
},
{
"content": "Find the smallest $x$ such that\n$x \\equiv 14 \\pmod{7}$\n$x \\equiv 16 \\pmod{9}$\n",
"r... |
[
{
"content": "Statement:\n If $x = \\frac{41098}{32823}$, then find $\\frac{1}{x+\\frac{1}{x+\\frac{1}{x+\\ddots}}$.\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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{
"content": "If $x = \\frac{41098}{32823}$, then find $\\frac{1}{x+\\frac{1}{x+\\frac{1}{x+\\ddots}}$... |
[
{
"content": "Statement:\n Find the least common multiple of $\\{13,-94\\}$.\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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{
"content": "Find the least common multiple of $\\{13,-94\\}$.\n",
"role": "assistant"
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[
{
"content": "Statement:\n Find the smallest $x$ such that $x \\equiv 35557 \\pmod{18}$.\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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{
"content": "Find the smallest $x$ such that $x \\equiv 35557 \\pmod{18}$.\n",
"role": "assistant"
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] |
[
{
"content": "Statement:\n Find the greatest common divisor of $\\{659,838\\}$.\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
},
{
"content": "Find the greatest common divisor of $\\{659,838\\}$.\n",
"role": "assistant"
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] |
[
{
"content": "Statement:\n Determine the $n=8$ $40$-gonal number.\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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{
"content": "Determine the $n=8$ $40$-gonal number.\n",
"role": "assistant"
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] |
[
{
"content": "Statement:\n A polygon with $6$ vertices has the coordinates \n\n  \n\n$$\n\\left(\n\\begin{array}{cc}\n 0.048 & 0.456 \\\\\n 0.095 & 0.224 \\\\\n 0.118 & 0.323 \\\\\n 0.577 & 0.497 \\\\\n 0.721 & 0.185 \\\\\n 0.723 & 0.612 \\\\\n\\end{array}\n\\right)\n$$ \nEstimate the polygon's int... |
[
{
"content": "Statement:\n 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.\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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{
... |
[
{
"content": "Statement:\n A polyhedron has vertices with the coordinates\n$$\n\\left(\n\\begin{array}{ccc}\n 0.714 & 0.581 & 0.689 \\\\\n 0.786 & 0.542 & 0.532 \\\\\n 0.19 & 0.398 & 0.73 \\\\\n 0.128 & 0.212 & 0.188 \\\\\n 0.426 & 0.841 & 0.785 \\\\\n 0.524 & 0.064 & 0.883 \\\\\n 0.007 & 0.379 & 0.305 \\\\\... |
[
{
"content": "Statement:\n Compute the rank of\n$$\n\\left(\n\\begin{array}{c}\n \\frac{37}{4} \\\\\n \\frac{91}{16} \\\\\n \\frac{23}{4} \\\\\n -\\frac{53}{16} \\\\\n\\end{array}\n\\right)\n$$\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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{
"content": "Compute the r... |
[
{
"content": "Statement:\n Find the dot product of the following two vectors $g$ and $f$:\n$\\left( \\begin{array}{c} -3 \\\\ -9 \\\\ -7 \\\\ 0 \\\\ -2 \\\\ 5 \\\\ -4 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -7 \\\\ 0 \\\\ -8 \\\\ -7 \\\\ -1 \\\\ 4 \\\\ 8 \\\\ \\end{array} \\right) $\... |
[
{
"content": "Statement:\n Find the plane defined by the following points:\n${\\left\\{\\frac{1}{2},3,-\\frac{1}{2}\\right\\}, \\left\\{-4,\\frac{1}{2},-\\frac{9}{2}\\right\\}, \\left\\{-\\frac{5}{2},\\frac{5}{2},-\\frac{3}{2}\\right\\}$.\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role"... |
[
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"content": "Statement:\n Find the eigenvectors of the following matrix (round your answer to three decimal places):\n$$\n\\left(\n\\begin{array}{ccc}\n \\frac{25}{3} & \\frac{17}{3} & \\frac{11}{3} \\\\\n -\\frac{29}{3} & \\frac{19}{3} & \\frac{25}{3} \\\\\n \\frac{11}{3} & -9 & -\\frac{29}{3} \\\\\n\\end{... |
[
{
"content": "Statement:\n Find the eigenvectors of the following matrix:\n$$\n\\left(\n\\begin{array}{cc}\n \\frac{24}{5} & -\\frac{46}{5} \\\\\n -\\frac{28}{5} & \\frac{26}{5} \\\\\n\\end{array}\n\\right)\n$$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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"conte... |
[
{
"content": "Statement:\n Subtract the second matrix from the first:\n$ \\left( \\begin{array}{ccc} 4 & -10 & -5 \\\\ 0 & -9 & 0 \\\\ 7 & 9 & 0 \\\\ \\end{array} \\right)$ from $\\left( \\begin{array}{ccc} -7 & 1 & 0 \\\\ 1 & -3 & -2 \\\\ -1 & -9 & 1 \\\\ \\end{array} \\right)$\n\n\n Task:\n Rewr... |
[
{
"content": "Statement:\n Multiply\n$\\left( \\begin{array}{ccccc} -3 & -3 & 1 & 1 & 0 \\\\ 2 & 1 & -2 & -2 & 1 \\\\ 2 & 0 & -2 & -2 & 2 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -3 \\\\ -1 \\\\ -2 \\\\ -2 \\\\ -2 \\\\ \\end{array} \\right)$.\n\n\n Task:\n Rewrite the statement ... |
[
{
"content": "Statement:\n Convert the following matrix to reduced row echelon form:\n$$\n\\left(\n\\begin{array}{cccc}\n 8 & -3 & -2 & 7 \\\\\n 10 & -4 & -10 & 7 \\\\\n\\end{array}\n\\right)\n$$\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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"content": "Convert the... |
[
{
"content": "Statement:\n Find the characteristic polynomial of the following matrix:\n$$\n\\left(\n\\begin{array}{ccc}\n \\frac{49}{16} & \\frac{57}{16} & \\frac{115}{16} \\\\\n -\\frac{21}{8} & -\\frac{13}{4} & \\frac{109}{16} \\\\\n \\frac{13}{4} & \\frac{123}{16} & \\frac{9}{16} \\\\\n\\end{array}\n\\ri... |
[
{
"content": "Statement:\n Find the distance between the following two vectors $\\bf{a}$ and $\\bf{b}$:\n$\\left( \\begin{array}{c} 9 \\\\ 4 \\\\ -3 \\\\ -7 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -7 \\\\ 4 \\\\ -1 \\\\ -1 \\\\ \\end{array} \\right)$.\n\n\n Task:\n Rewrite the ... |
[
{
"content": "Statement:\n Find the projection of the first vector $\\bf{a}$ onto the second $\\bf{b}$:\n$\\left( \\begin{array}{c} -\\frac{1}{5} \\\\ -\\frac{1}{5} \\\\ -\\frac{8}{5} \\\\ \\frac{1}{5} \\\\ \\end{array} \\right)$, $\\left( \\begin{array}{c} \\frac{6}{5} \\\\ -2 \\\\ \\frac{3}{5} \\\\ -\\... |
[
{
"content": "Statement:\n Subtract the second matrix from the first:\n$\\left( \\begin{array}{cc} -7 & -6 \\\\ 0 & 6 \\\\ \\end{array} \\right)$ - $\\left( \\begin{array}{cc} 3 & -9 \\\\ 1 & 4 \\\\ \\end{array} \\right)$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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... |
[
{
"content": "Statement:\n Compute the (pseudo)inverse of\n$$\n\\left(\n\\begin{array}{ccc}\n 1 & 1 & -4 \\\\\n -3 & -2 & -4 \\\\\n -3 & -1 & -3 \\\\\n\\end{array}\n\\right)\n$$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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"content": "Compute the (pseudo)inverse... |
[
{
"content": "Statement:\n Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):\n$$\n\\left(\n\\begin{array}{ccc}\n 6 & -4 & -4 \\\\\n -9 & 4 & 1 \\\\\n -8 & -2 & 0 \\\\\n 5 & -10 & 9 \\\\\n\\end{array}\n\\right)\n$$\n\n\n Task:\... |
[
{
"content": "Statement:\n Find the distance from the point ${-\\frac{10}{3}, -\\frac{13}{3}, -\\frac{5}{3}$ to the plane $-\\frac{7 x}{3}-\\frac{2 y}{3}-\\frac{4 z}{3}+\\frac{7}{3}=0$.\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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"content": "Find the distance fro... |
[
{
"content": "Statement:\n Normalize the following vector $\\bf{d}$: \n$$\n\\left(\n\\begin{array}{c}\n -1 \\\\\n 2 \\\\\n\\end{array}\n\\right)$$.\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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{
"content": "Normalize the following vector $\\bf{d}$: \n$$\n\\left(\n... |
[
{
"content": "Statement:\n Orthogonalize the following sets:\n${\\{0,2,-1\\}, \\{0,-1,3\\}, \\left\\{-\\frac{3}{2},\\frac{5}{2},-\\frac{5}{2}\\right\\}$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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{
"content": "Orthogonalize the following sets:\n${\\{0,2,-1\\}, \... |
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"content": "Statement:\n Compute the (pseudo)inverse of\n$$\n\\left(\n\\begin{array}{ccc}\n -\\frac{43}{16} & -\\frac{65}{16} & -\\frac{59}{16} \\\\\n -\\frac{19}{8} & -\\frac{79}{16} & -\\frac{29}{16} \\\\\n -\\frac{15}{4} & \\frac{5}{16} & -\\frac{73}{16} \\\\\n\\end{array}\n\\right)$$\n\n\n Task:\n ... |
[
{
"content": "Statement:\n Find the determinant of the matrix\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n -\\frac{3}{2} & -5 & -4 \\\\\n \\frac{9}{2} & 3 & -5 \\\\\n -\\frac{1}{2} & 5 & -4 \\\\\n\\end{array}\n\\right)\n$$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user... |
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{
"content": "Statement:\n Add the two matrices\n$ \\left( \\begin{array}{cc} -1 & -4 \\\\ 6 & -1 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{cc} -3 & 8 \\\\ 4 & -3 \\\\ \\end{array} \\right)$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
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"content"... |
[
{
"content": "Statement:\n Multiply the scalar $\\frac{13}{6}$ and the matrix\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n 9 & 3 & -3 \\\\\n -5 & -5 & -5 \\\\\n -7 & -3 & 1 \\\\\n\\end{array}\n\\right)\n$$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
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"c... |
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"content": "Statement:\n Compute\n\n  \n\n$$\ne^\\left(\n\\begin{array}{cc}\n 1 & -1 \\\\\n 1 & -1 \\\\\n\\end{array}\n\\right)\n$$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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"content": "Compute\n\n  \n\n$$\ne^\\left(\n\\begin{array}{cc}\... |
[
{
"content": "Statement:\n Give a list of vectors that forms a basis for the null space of the following matrix:\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n 4 & 7 & 3 \\\\\n -4 & 5 & -7 \\\\\n 9 & 8 & -4 \\\\\n 4 & 4 & -1 \\\\\n\\end{array}\n\\right)\n$$\n\n\n Task:\n Rewrite the statement in... |
[
{
"content": "Statement:\n Find the cross product of the following vectors $\\bf{a}$ and $\\bf{g}$:\n$\\left( \\begin{array}{c} -9 \\\\ 3 \\\\ 7 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} 6 \\\\ 0 \\\\ 3 \\\\ \\end{array} \\right)$\n\n\n Task:\n Rewrite the statement in LaTeX.\n "... |
[
{
"content": "Statement:\n Multiply the scalar $-\\frac{7}{4}$ and the matrix\n\n  \n\n$$\n\\left( \\begin{array}{cccc}\n -8 & 3 & -1 & 0 \\\\\n 8 & -6 & 8 & -6 \\\\\n -6 & -6 & 1 & -6 \\\\\n\\end{array}\n\\right)\n$$\n\n  \n\n[embedded]\n\n\n Task:\n Rewrite the statement in LaTeX.... |
[
{
"content": "Statement:\n Add the two matrices\n$\\left( \\begin{array}{c} -3 \\\\ \\frac{8}{5} \\\\ 9 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} \\frac{22}{5} \\\\ \\frac{19}{5} \\\\ \\frac{18}{5} \\\\ \\end{array} \\right)$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
... |
[
{
"content": "Statement:\n Compute the trace of\n\n  \n\n$$\n\\left(\n\\begin{array}{cccc}\n 6 & 1 & -10 & -7 \\\\\n -10 & 4 & -8 & 1 \\\\\n -8 & -9 & 1 & 9 \\\\\n -10 & 8 & -7 & 3 \\\\\n\\end{array}\n\\right)\n$$\n\n  \n\n[embedded]\n\n\n Task:\n Rewrite the statement in LaTeX.\n ... |
[
{
"content": "Statement:\n Find the characteristic polynomial of the following matrix:\n\n  \n\n$$\n\\left(\n\\begin{array}{cc}\n -3 & -\\frac{4}{5} \\\\\n -\\frac{3}{5} & \\frac{18}{5} \\\\\n\\end{array}\n\\right)\n$$\n\n  \n\n[embedded]\n\n\n Task:\n Rewrite the statement in LaTeX... |
[
{
"content": "Statement:\n Find the least squares vector given the matrix\n$\\bf{A} = \\left( \\begin{array}{cc} 1 & 1 \\\\ 0 & -2 \\\\ 1 & -2 \\\\ -3 & 0 \\\\ \\end{array} \\right)$ and the vector $\\bf{b} = \\left( \\begin{array}{c} -2.65 \\\\ 2.69 \\\\ -2.86 \\\\ -0.45 \\\\ \\end{array} \\right)$.... |
[
{
"content": "Statement:\n Convert the following matrix to reduced row echelon form:\n\n  \n\n$$\n\\left(\n\\begin{array}{ccccc}\n 10 & -8 & 6 & 0 & -1 \\\\\n -1 & 1 & -1 & -1 & -2 \\\\\n -4 & -1 & -5 & 0 & -10 \\\\\n\\end{array}\n\\right)\n$$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ... |
[
{
"content": "Statement:\n Find the dot product of the following two vectors $\\bf{m}$ and $\\bf{n}$:\n$\\left( \\begin{array}{c} 3 \\sqrt{2} \\\\ -6 \\sqrt{2} \\\\ -\\sqrt{2} \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -\\sqrt{2} \\\\ 0 \\\\ -\\frac{9}{\\sqrt{2} \\\\ \\end{array} \\righ... |
[
{
"content": "Statement:\n Multiply\n$\\left( \\begin{array}{ccc} 1 & 2 & 0 \\\\ -2 & 2 & -2 \\\\ -2 & -1 & 0 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{ccc} -3 & 2 & -1 \\\\ -1 & 2 & 2 \\\\ -1 & -1 & 2 \\\\ \\end{array} \\right)$.\n\n\n Task:\n Rewrite the statement in LaTeX.\n "... |
[
{
"content": "Statement:\n Find the determinant of the matrix\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n \\frac{7}{6} & \\frac{23}{6} & -\\frac{23}{6} \\\\\n -2 & -\\frac{1}{3} & -\\frac{11}{6} \\\\\n \\frac{5}{3} & \\frac{14}{3} & \\frac{3}{2} \\\\\n\\end{array}\n\\right)\n$$\n\n\n Task:\n ... |
[
{
"content": "Statement:\n Find the $\\ell_\\infty$ norm of the following vector $\\bf{y}$:\n\n  \n\n$$\n\\left(\n\\begin{array}{c}\n \\frac{40}{7} \\\\\n -5 \\\\\n\\end{array}\n\\right)\n$$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
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"content": "Find... |
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"content": "Statement:\n Find the eigenvalues of the following matrix:\n\n  \n\n$$\n\\left(\n\\begin{array}{cc}\n -\\frac{20}{3} & \\frac{11}{3} \\\\\n -7 & 8 \\\\\n\\end{array}\n\\right)\n$$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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"content": "F... |
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{
"content": "Statement:\n Find the eigenvalues of the following matrix (round your answer to three decimal places):\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n -1 & 9 & 8 \\\\\n 1 & 10 & 2 \\\\\n 8 & -8 & -9 \\\\\n\\end{array}\n\\right)\n$$\n\n\n Task:\n Rewrite the statement in LaTeX.\n ... |
[
{
"content": "Statement:\n Find the $\\ell_2$ norm of the following vector $\\bf{x}$:\n\n  \n\n$$\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\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user... |
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{
"content": "Statement:\n Find the cross product of the following vectors $\\bf{p}$ and $\\bf{q}$:\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} \... |
[
{
"content": "Statement:\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 Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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"content": "Solve for $y=f(x)$ given the following ... |
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"content": "Statement:\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 Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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"content": "Solve the following system of three equations: \n$14 x+15 y-24 ... |
[
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"content": "Statement:\n The code chunks below contain examples of creating objects (or, assigning variables) in R.\n student_name <- \"Jay\"\n\n _age <- 23\n\n 1st_line_address <- \"56 Exhibition Road\"\n\nWhich *one* of these variable names correctly follows variable naming rules in R?\n\n\n ... |
[
{
"content": "Statement:\n Much of our analysis work involves data cleaning and preparation.\n\nYou may find it helpful to read through the **Supplement** at the end of *Handout03.Rmd* if you are stuck on any questions.\n > head(stocks)\n Date GOOG.Close AAPL.Close\n 1 08/09/2021 144.8835... |
[
{
"content": "Statement:\n Below is an image of a current clamp meter. You can open the loop with the red button on the side, and place a wire inside the loop. There are Hall sensors in the red loop, which measure the magnetic field. \n\n[embedded]\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
... |
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"content": "Statement:\n What is the correct reading on this vernier caliper?\n[embedded]\n\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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"content": "What is the correct reading on this vernier caliper?\n[embedded]\n\n",
"role": "assistant"
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"content": "Statement:\n Some questions on regression and the `lm()` function...\n Assume that the variable `model` is a properly implemented linear regression model created with `lm()`. \n\nWhat function could we use to get detail on the properties of the model?\n\n\n Task:\n Rewrite the statement i... |
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"content": "Statement:\n A fuel is burnt first with the stoichiometric amount of air and then with the stoichiometric amount of pure oxygen. \n\n For which case will the adiabatic flame temperature be higher?\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
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"conte... |
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"content": "Statement:\n [embedded]\n\n \n\nYou are building a toy car to race in a miniature version of Formula 1. In this racing series, car weight is set at 8kg. You are required to use a small motor with a speed vs torque curve shown below.\n\n \n\n[embedded]\n Given that the regulations for Formula ... |
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"content": "Statement:\n The *diagram* below illustrates the operation of a **4-bit** optical encoder for angular position. The encoder is attached to a lead screw of **0.8mm** pitch, which controls the linear position of a slider.\n\n[embedded]\n If a computer is to be used to count the **number of comple... |
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{
"content": "Statement:\n ### Playtime:\n\nAs you do so, smoothly turn corners at a constant speed, and note down your prediction as to whether the wheels and the ring gear speed up, slow down or maintain the same angular velocity.\n\n***\n\n### Test your understanding:\n\nText here\n\n\n Task:\n Rewr... |
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"content": "Statement:\n ### Introduction:\n\nTo make a bearing assembly functional, the bearings must be correctly constrained\n\nIn most cases, the rotating element is the shaft, and the stationary element is the housing. A case in which the housing is rotating and the shaft is stationary would be an idl... |
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"content": "Statement:\n **What are fits and tolerances?**\n\n* Up until last week, all dimensions that you had considered previously were **nominal**.\n* As you saw last week, ***tolerances*** are numerical bands or margins that are applied to nominal dimensions to allow for **real-world manufacturing... |
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{
"content": "Statement:\n ### Introduction:\n\nIn ME1 Materials, you have learned about tensile (brittle/ductile) fracture, fatigue failure and creep failure. Compressive buckling and shear failure were also touched upon.\n\n[embedded]\n\n***\n\n### Playtime:\n\nOn CES Granta EduPack, generate Ashby maps of... |
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{
"content": "Statement:\n The pilot of a Beechcraft King Air C90 intends to take off from runway 21L of Stapleford Aerodrome (ICAO EGSG). Consulting the Pilot Operating Handbook (POH), they have calculated a TakeOff Distance Required (TODR) of 3,900 ft. Data on the runway, TakeOff Distance Available (TOTA) ... |
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"content": "Statement:\n ### Introduction:\n\n***\n\n### Playtime:\n\n\n***\n\n### Test your understanding:\n\n Calculate the critical diameter for a solid shaft of the same material such that it can take the same torque. Also, calculate the weight saving afforded.\n\n\n Task:\n Rewrite the statement... |
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"content": "Statement:\n \n(**Note**: there is no response area for this question. Think about an explanation in words.)\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
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"content": "\n(**Note**: there is no response area for this question. Think about an explana... |
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"content": "Statement:\n Consider a plane that passes through the points A=(1, -1, 2), B=(-2, 2, -1), and C=(3, 3, 0).\n\nWhich of the following vectors is normal to the plane described by the points A, B and C?\n \n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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... |
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"content": "Statement:\n A series of questions on working with big data in R.\n Which package in R enables use of dplyr verbs and pipe operators on the `data.table` type?\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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"content": "A series of questions on working... |
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"content": "Statement:\n If you need to look up properties you can use *Table E.3* of the Data book or any reliable source Can you explain why a person who has inhaled helium speaks with a high-pitched voice?\n\n[embedded]\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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... |
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"content": "Statement:\n Some questions on multiple regression with FF3...\n model_A <- lm(formula = DailyReturns ~ RF + SMB + HML, data = merged_data)\n\n model_B <- lm(formula = DailyReturns ~ Mkt.RF + SMB + HML, data = merged_data)\n\n model_C <- lm(formula = ExcessReturns ~ RF + SMB + HML, da... |
[
{
"content": "Statement:\n The following graph shows a shape before (blue) and after (orange) a linear transform has been applied to it. What was the linear transform?\n\n[embedded]\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
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"content": "The following graph sho... |
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{
"content": "Statement:\n You may find it helpful to read through the **Supplement** at the end of *Handout03.Rmd* if you are stuck on any questions.\n > head(trading)\n Date Ticker Return\n 1 2022-08-30 GOOG -0.003896973\n 2 2022-08-31 GOOG -0.006914766\n\nGiven the `trading`... |
[
{
"content": "Statement:\n According to a pointless report from a made up survey, in a class of 100 students, the mean length of their index fingers was 65 mm, with a standard deviation of 8 mm. \n\n [embedded]\n\nWhich expression describes the shaded region on the above distribution?\n \n\n\n Task:\n ... |
[
{
"content": "Statement:\n Calculate the power dissipated in all components of the circuit below.\n [embedded]\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
},
{
"content": "Calculate the power dissipated in all components of the circuit below.\n [embedded]\n",
"r... |
[
{
"content": "Statement:\n Suppose that you were lucky enough to take the following picture of a Super Hornet flying slightly above the speed of sound at sea level. The weather conditions are just perfect so that a Mach cone is made visible thanks to a condensation phenomenon.\n\n[embedded]\n\n\n Task:\n ... |
[
{
"content": "Statement:\n * You will need access to the library resources in parts (a) to (c) below.\n* To access the books click on the thumbnail image or the link in the reference at the bottom.\n\n[embedded] [embedded]\n\nReference:\n\n**Simmons, C.H., Maguire, D.E., and Phelps, N. (2020) *Manual of ... |
[
{
"content": "Statement:\n * You should read the first four pages of Simmons et al., 2020 **Chapter 16: Dimensioning principles**.\n* Answer the questions in parts (a) to (c) below.\n How many dimensions would you need to add to the drawing below before it could be manufactured?\n\n[embedded]\n\n Task... |
[
{
"content": "Statement:\n You are now tasked with building a go-kart capable of travelling at a max speed of between 12 and 14 m/s. The car has a wheel diameter of 0.3m and a weight of 500kg.\n\nThe engine you have been supplied to work with operates at a maximum of 6000rpm and 15Nm (you may assume these ar... |
[
{
"content": "Statement:\n You should now proceed to read:\n\n[embedded]\n\n* Branoff, **Unit 13: INTRODUCTION TO CONVENTIONAL TOLERANCING**\n* The first pages of Simmons et al., **Chapter 21: Limits and Fits**\n* Then answer the questions in parts (a) to (e).\n\n Task:\n Rewrite the statement i... |
[
{
"content": "Statement:\n Some questions on quantiles!\nwe can use `seq()` and `paste()` / `paste0()` together. Please select all correct options.\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
},
{
"content": "Some questions on quantiles!\nwe can use `seq()` and `pas... |
[
{
"content": "Statement:\n Two trusses are shown below:\n\n| | |\n| :---- | :-------------------------------------------------------------... |
[
{
"content": "Statement:\n ### Playtime:\n\n\nThe most common bearing type is the rolling element bearing. Here is a quick video analysing them.\n\n***\n\n[embedded]\n\n### Test your understanding:\n\nAnswer the questions below about the bearings you have interacted with.\n Which bearings can be disassembled... |
[
{
"content": "Statement:\n ### Challenge:\n\nIn this section, you will calculate the speed ratios between the spinning raceway (inner and outer) and the speed of the roller and the cage for NU 216 ECP. To help you visualise this, spin the inner race of NU 216 ECP while keeping the outer race still, then do t... |
[
{
"content": "Statement:\n * You have now completed this week's pre-class learning. Well done!\n* You should now have the basic understanding necessary to undertake this week's practical task..\n* Finally here's an interesting example of some *very* low-tolerance machining:\n\n[embedded]\n \n\n Task... |
[
{
"content": "Statement:\n ### Introduction:\n\n***\n\n### Test your understanding:\n\n What is the maximum applicable torque for the shaft?\n\n \n\n \n\nWhat is the total torsional stiffness of the shaft?\n\nOut of all of the transmission sets you assembled, what is the lowest safety factor experienced by... |
[
{
"content": "Statement:\n The code chunks below create vectors, and then index them. Below the code chunks, you will see the R Notebook output, starting with a `[1]` as usual.\n\n\n\nRead the questions carefully and provide either the value used to index the vector, or the output that you expect.\n y_ve... |
[
{
"content": "Statement:\n Consider the direction of the flow (to the right) as positive. Assume the following:\n\n1. steady\n2. Constant\n3. reference\n4. neglible\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
},
{
"content": "Consider the direction of the flow (to... |
[
{
"content": "Statement:\n The code chunks below contain examples of creating objects (or, assigning variables) in R.\n op_bal <- 1200\n\n openingbalancegbp <- 1200\n\n opening_balance_sterling <- 1200\n\nWhich *one* of these variable names most closely follows ***best practices*** in naming R vari... |
[
{
"content": "Statement:\n * You can't dimension a drawing without understanding the basics of tolerancing.\n* We'll look at tolerancing in more detail next week.\n* **Unit 13: Introduction to Conventional Tolerancing**.\n* Then consult the resources below.\n\n[embedded]\n\n Task:\n Rewrite the... |
[
{
"content": "Statement:\n A fairground ride involves attaching a person between two *opposin*g horizontal springs of stiffness 6 N/m each (i.e. 12 N/m combined), while standing on a skateboard. The person is then pulled 5 meters to one side and released from rest.\n\n\n[embedded]\n \n\n\n Task:\n Rewr... |
[
{
"content": "Statement:\n \n\nNote that the values for torque given in the table below are values at the output shaft.\n\n| Operating point | Torque (Nm) |\n| :-------------- | :---------- |\n| 1 | 6 |\n| 2 | 7 |\n| 3 | 8 |\n Given that... |
[
{
"content": "Statement:\n There are two supported conventions:\n\n1: Implicit multiplication have the same precedence as explicit multiplication, i.e. both `1/ab` and `1/a*b` will be equal to `(1/a)*b`.\n\n2: Implicit multiplication have precedence than explicit multiplication, i.e. `1/ab` will be equal to ... |
[
{
"content": "Statement:\n ### Introduction:\n\nA clutch relies upon friction to engage or disengage two components.\n\nMaria taught you the derivations for flat and conical clutches in uniform pressure and wear conditions. The equations are below:\n\n| | Flat ... |
[
{
"content": "Statement:\n Water from a tap with a diameter of 2 cm flows with an average velocity of 2 m/s. Calculate the Reynolds number for this flow assuming the dynamic viscosity of water is 0.001 $\\rm{Pa \\cdot s}$ . Is the flow laminar or turbulent?\n \n\n\n Task:\n Rewrite the statement in LaT... |
[
{
"content": "Statement:\n Show how dislocations can account for the following observations:\n\n1. Cold working makes aluminium harder\n2. Adding 20% Zn into Cu makes the alloy harder than pure copper\n3. The hardness of nickel is increased by adding particles of thorium oxide\n \n\n\n Task:\n Rewri... |
[
{
"content": "Statement:\n Some questions on auto-correlation.\n > head(dis_data)\n\n datadate tic conm cshtrd prccd return\n 1 01/09/2020 DIS DISNEY (WALT) CO 7350214 133.55 NA\n 2 02/09/2020 DIS DISNEY (WALT) CO 8159343 135.39 0.013777611\n 3 03/09/2020... |
[
{
"content": "Statement:\n Calculate the resistor nominal value and upper and lower limits for each of the following parameters:\n The resistor parameters are given in the table below:\n\n| *a* | *b* | *c* | *tol* |\n| :------- | :------- | :---- | :-------- |\n| *Yellow* | *Orange* | *Red* |... |
[
{
"content": "Statement:\n In each of the code chunks below, two vectors will be created. Determine if they are equal.\n i_vector <- c(2, 4, 6, 8, 10)\n\n j_vector <- c(0, 4, 6, 8, 10)\n j_vector[1] <- 2\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
},
{
"co... |
[
{
"content": "Statement:\n Some questions on regression and the `lm()` function...\n How many response variables can we have in the formula for multiple regression?\n\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
},
{
"content": "Some questions on regression and the `lm... |
[
{
"content": "Statement:\n When the separating piston of mass 2kg is placed in the cylinder and the hydraulic side is pressurised to 2 bar, the trapped air is at 298K.\n\n\n\nFind the air pressure inside the cylinder in this state, and hence the volume. Find also the distance x in this state\n\n\n Task:\n... |
[
{
"content": "Statement:\n Give the expression, define terms and explain the physical meaning of the following laws and variables. Add sketched to each of your explanations.\n\na) Fourier's Law\n\nb) Newton's Law of cooling\n\n Task:\n Rewrite the statement in LaTeX.\n ",
"role": "user"
},
{... |
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