Intermediate Algebra (11th edition)

SECTION 9.4 Formulas and Further Applications 523

2 a# 2 a=a

2 a# 2 b= 2 ab;

OBJECTIVES

Formulas and Further Applications

9.4

1 Solve formulas for

variables involving

squares and square

roots.

2 Solve applied

problems using the

Pythagorean

theorem.

3 Solve applied

problems using

area formulas.

4 Solve applied

problems using

quadratic functions

as models.

OBJECTIVE 1 Solve formulas for variables involving squares and square

roots.

Solving for Variables Involving Squares or Square Roots

Solve each formula for the given variable. Keep in the answer in part (a).

(a) for v

Multiply by

Divide by w.

Square root property

Rationalize the denominator.

(b) for

Square both sides.

Multiply by

or a = Divide by 4. NOW TRY

pd^2

4

pd^2

4

=a,

pd^2 = 4 a p.

d^2 =

4 a

p

d=

B

4 a

p

d= a

B

4 a

p

v=

 2 kFrw

w

v=

 2 kFr

2 w

#^2 w

2 w

v=

B

kFr

w

v^2 =

kFr

w

v^2 w =kFr v 2.

w =

kFr

v^2

w=

kFr

v^2



EXAMPLE 1

The goal is to isolate

von one side.

The goal is to isolate

aon one side.

NOTE In formulas like in Example 1(a),we include both positive and

negative values.

Solving for a Variable That Appears in First- and

Second-Degree Terms

Solve for t.

Since the given equation has terms with and t, write it in standard form

with tas the variable instead of x.

Subtract s.

2 t^2 +k t-s= 0 Standard form

0 = 2 t^2 +k t-s

s= 2 t^2 +k t

ax^2 +bx+ c=0,

t^2

s= 2 t^2 +kt

EXAMPLE 2

 2 kFrw

w

v=

NOW TRY
EXERCISE 1
Solve each formula for the
given variable. Keep in
the answer in part (a).

(a) for E

(b)S= for p
B

pq

n

n=

ab

E^2



NOW TRY ANSWERS

1. (a)

(b)p=

nS 2

q

E=

 2 abn

n