/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 87 Write the area \(A\) of a square... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 87

Write the area \(A\) of a square as a function of its perimeter \(P\).

Short Answer

Expert verified
The area of a square can be written as a function of its perimeter as \(A = P^2/16\).

Step by step solution

01

Write down the equations for area and perimeter of a square

Firstly, we have the formula for the area of a square, which is \(A = s^2\). And we know that the perimeter is given by \(P = 4s\).
02

Solve the perimeter equation for \(s\)

To express \(A\) in terms of \(P\), we need to eliminate \(s\) from our area equation. Therefore, we'll solve the perimeter equation to give \(s\) in terms of \(P\), which makes \(s = P/4\).
03

Substitute \(s\) in terms of \(P\) into the area equation

Now we substitute \(s = P/4\) into our area equation. Thus \(A = (P/4)^2\).
04

Simplify the equation

Lastly, we simply simplify the equation to get \(A = P^2/16\).

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Most popular questions from this chapter

Find a mathematical model for the verbal statement. \(h\) varies inversely as the square root of \(s\).

Determine whether the function has an inverse function. If it does, find the inverse function. $$ q(x)=(x-5)^{2} $$

Use the given value of \(k\) to complete the table for the inverse variation model $$y=\frac{k}{x^{2}}$$ Plot the points on a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=\frac{k}{x^{2}} & & & & & \\ \hline \end{array}$$ $$ k=2 $$

Find a mathematical model representing the statement. (In each case, determine the constant of proportionality.) \(y\) varies inversely as \(x .(y=3\) when \(x=25\).

The total numbers of people (in thousands) in the U.S. civilian labor force from 1992 through 2007 are given by the following ordered pairs. $$\begin{array}{ll} (1992,128,105) & (2000,142,583) \\ (1993,129,200) & (2001,143,734) \\ (1994,131,056) & (2002,144,863) \\ (1995,132,304) & (2003,146,510) \\ (1996,133,943) & (2004,147,401) \\ (1997,136,297) & (2005,149,320) \\ (1998,137,673) & (2006,151,428) \\ (1999,139,368) & (2007,153,124) \end{array}$$ A linear model that approximates the data is \(y=1695.9 t+124,320,\) where \(y\) represents the number of employees (in thousands) and \(t=2\) represents 1992 . Plot the actual data and the model on the same set of coordinate axes. How closely does the model represent the data? (Source: U.S. Bureau of Labor Statistics)
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