\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Find the distance between the points \(\displaystyle \left( 85, \ 72\right)\) and \(\displaystyle \left( 157, \ 126\right)\).
The distace formula gives \(\displaystyle d=\sqrt{ ((157)-(85))^2 + ((126)-(72))^2 }=\sqrt{ 5184 + 2916 }\). Simplifying gives \(\displaystyle d = 90\).
\begin{question}Find the distance between the points $\left( 85, \ 72\right)$ and $\left( 157, \ 126\right)$.
\soln{9cm}{The distace formula gives $d=\sqrt{ ((157)-(85))^2 + ((126)-(72))^2 }=\sqrt{ 5184 + 2916 }$. Simplifying gives $d = 90$. }
\end{question}
\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}<p> <p>Find the distance between the points <img class="equation_image" title=" \displaystyle \left( 85, \ 72\right) " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%28%2085%2C%20%5C%20%2072%5Cright%29%20" alt="LaTeX: \displaystyle \left( 85, \ 72\right) " data-equation-content=" \displaystyle \left( 85, \ 72\right) " /> and <img class="equation_image" title=" \displaystyle \left( 157, \ 126\right) " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%28%20157%2C%20%5C%20%20126%5Cright%29%20" alt="LaTeX: \displaystyle \left( 157, \ 126\right) " data-equation-content=" \displaystyle \left( 157, \ 126\right) " /> . </p> </p>
<p> <p>The distace formula gives <img class="equation_image" title=" \displaystyle d=\sqrt{ ((157)-(85))^2 + ((126)-(72))^2 }=\sqrt{ 5184 + 2916 } " src="/equation_images/%20%5Cdisplaystyle%20d%3D%5Csqrt%7B%20%28%28157%29-%2885%29%29%5E2%20%2B%20%28%28126%29-%2872%29%29%5E2%20%7D%3D%5Csqrt%7B%205184%20%2B%202916%20%7D%20" alt="LaTeX: \displaystyle d=\sqrt{ ((157)-(85))^2 + ((126)-(72))^2 }=\sqrt{ 5184 + 2916 } " data-equation-content=" \displaystyle d=\sqrt{ ((157)-(85))^2 + ((126)-(72))^2 }=\sqrt{ 5184 + 2916 } " /> . Simplifying gives <img class="equation_image" title=" \displaystyle d = 90 " src="/equation_images/%20%5Cdisplaystyle%20d%20%3D%2090%20" alt="LaTeX: \displaystyle d = 90 " data-equation-content=" \displaystyle d = 90 " /> . </p> </p>