Question

example 3

1. rectangles the formula ( p = 2l + 2w ) represents the perimeter of a rectangle. in this formula,

( l ) is the length of the rectangle and ( w ) is the width.

a. solve the formula for ( l ).
b. find the length when the width is 4 meters and the perimeter is 36 meters.

1. baseball the formula ( a=\frac{h}{b} ) can be used to find the batting average ( a ) of a batter who has

( h ) hits in ( b ) times at bat.

a. solve the formula for ( b ).
b. if a batter has a batting average of 0.325 and has 39 hits, how many times has the player
been at bat?

Explanation:

19.

a.

Step1: Solve the formula for \(L\)

Given \(P = 2L+2w\).
Subtract \(2w\) from both sides: \(P - 2w=2L\).
Divide both sides by \(2\): \(L=\frac{P - 2w}{2}\).

b.

Step1: Substitute values into the formula

We know \(P = 36\) meters and \(w = 4\) meters.
Use the formula \(L=\frac{P - 2w}{2}\).
Substitute \(P = 36\) and \(w = 4\): \(L=\frac{36-2\times4}{2}\).

Step2: Simplify the expression

First, calculate \(2\times4 = 8\). Then \(36-8=28\).
Now, \(\frac{28}{2}=14\) meters.

20.

a.

Step1: Solve the formula for \(b\)

Given \(a=\frac{h}{b}\).
Multiply both sides by \(b\): \(ab = h\).
Divide both sides by \(a\): \(b=\frac{h}{a}\).

b.

Step1: Substitute values into the formula

We know \(a = 0.325\) and \(h = 39\).
Use the formula \(b=\frac{h}{a}\).
Substitute \(h = 39\) and \(a=0.325\): \(b=\frac{39}{0.325}\).

Step2: Simplify the expression

\(\frac{39}{0.325}=\frac{39\times1000}{0.325\times1000}=\frac{39000}{325}=120\) times.

Answer:

19.
a. \(L=\frac{P - 2w}{2}\)
b. \(14\) meters
20.
a. \(b=\frac{h}{a}\)
b. \(120\) times