\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus

Please login to create an exam or a quiz.

Algebra
Polynomials
New Random

The breaking distance, \(\displaystyle d\), of a car is proportional to the square of the speed, \(\displaystyle r\). If a car traveling at \(\displaystyle 56\) miles per hour can stop in \(\displaystyle 158\) feet. What is the stopping distance of a car traveling 36 miles per hour? Round the solution to the nearest foot.

The equation of variation is \(\displaystyle d=kr^2\). Evaluating at the known values and solving for \(\displaystyle k\) gives \(\displaystyle 158=k(56)^2 \iff k=\frac{79}{1568}\). The model is \(\displaystyle d=\frac{79}{1568}r\) evaluating at \(\displaystyle r=36\) gives \(\displaystyle d=\frac{6399}{98}\approx 65\) feet

Download \(\LaTeX\) 

\begin{question}The breaking distance, $d$, of a car is proportional to the square of the speed, $r$. If a car traveling at $56$ miles per hour can stop in $158$ feet. What is the stopping distance of a car traveling 36 miles per hour? Round the solution to the nearest foot.
    \soln{9cm}{The equation of variation is $d=kr^2$.  Evaluating at the known values and solving for $k$ gives $158=k(56)^2 \iff k=\frac{79}{1568}$. The model is $d=\frac{79}{1568}r$ evaluating at $r=36$ gives $d=\frac{6399}{98}\approx 65$ feet}

\end{question}

Download Question and Solution Environment\(\LaTeX\)
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}

\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}

\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}

\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue

\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

\end{question}\end{document}
HTML for Canvas 
<p> <p>The breaking distance,  <img class="equation_image" title=" \displaystyle d " src="/equation_images/%20%5Cdisplaystyle%20d%20" alt="LaTeX:  \displaystyle d " data-equation-content=" \displaystyle d " /> , of a car is proportional to the square of the speed,  <img class="equation_image" title=" \displaystyle r " src="/equation_images/%20%5Cdisplaystyle%20r%20" alt="LaTeX:  \displaystyle r " data-equation-content=" \displaystyle r " /> . If a car traveling at  <img class="equation_image" title=" \displaystyle 56 " src="/equation_images/%20%5Cdisplaystyle%2056%20" alt="LaTeX:  \displaystyle 56 " data-equation-content=" \displaystyle 56 " />  miles per hour can stop in  <img class="equation_image" title=" \displaystyle 158 " src="/equation_images/%20%5Cdisplaystyle%20158%20" alt="LaTeX:  \displaystyle 158 " data-equation-content=" \displaystyle 158 " />  feet. What is the stopping distance of a car traveling 36 miles per hour? Round the solution to the nearest foot.</p> </p>
HTML for Canvas
<p> <p>The equation of variation is  <img class="equation_image" title=" \displaystyle d=kr^2 " src="/equation_images/%20%5Cdisplaystyle%20d%3Dkr%5E2%20" alt="LaTeX:  \displaystyle d=kr^2 " data-equation-content=" \displaystyle d=kr^2 " /> .  Evaluating at the known values and solving for  <img class="equation_image" title=" \displaystyle k " src="/equation_images/%20%5Cdisplaystyle%20k%20" alt="LaTeX:  \displaystyle k " data-equation-content=" \displaystyle k " />  gives  <img class="equation_image" title=" \displaystyle 158=k(56)^2 \iff k=\frac{79}{1568} " src="/equation_images/%20%5Cdisplaystyle%20158%3Dk%2856%29%5E2%20%5Ciff%20k%3D%5Cfrac%7B79%7D%7B1568%7D%20" alt="LaTeX:  \displaystyle 158=k(56)^2 \iff k=\frac{79}{1568} " data-equation-content=" \displaystyle 158=k(56)^2 \iff k=\frac{79}{1568} " /> . The model is  <img class="equation_image" title=" \displaystyle d=\frac{79}{1568}r " src="/equation_images/%20%5Cdisplaystyle%20d%3D%5Cfrac%7B79%7D%7B1568%7Dr%20" alt="LaTeX:  \displaystyle d=\frac{79}{1568}r " data-equation-content=" \displaystyle d=\frac{79}{1568}r " />  evaluating at  <img class="equation_image" title=" \displaystyle r=36 " src="/equation_images/%20%5Cdisplaystyle%20r%3D36%20" alt="LaTeX:  \displaystyle r=36 " data-equation-content=" \displaystyle r=36 " />  gives  <img class="equation_image" title=" \displaystyle d=\frac{6399}{98}\approx 65 " src="/equation_images/%20%5Cdisplaystyle%20d%3D%5Cfrac%7B6399%7D%7B98%7D%5Capprox%2065%20" alt="LaTeX:  \displaystyle d=\frac{6399}{98}\approx 65 " data-equation-content=" \displaystyle d=\frac{6399}{98}\approx 65 " />  feet</p> </p>