Intermediate Algebra (11th edition)

OBJECTIVE 4 Use the power rule to solve a formula for a specified variable.

Solving a Formula from Electronics for a Variable

An important property of a radio-frequency transmission line is its characteristic

impedance,represented by Zand measured in ohms. If Land Care the inductance

and capacitance, respectively, per unit of length of the line, then these quantities are

related by the formula. Solve this formula for C.

Given formula

Square each side.

Multiply by C.

C= Divide by .Z^2

L

Z^2

CZ^2 = L

Z 2 = A 2 aB^2 =a

L

C

Z^2 = a

B

L

C

b

2

Z=

B

L

C

Z= 2

L C

EXAMPLE 7

472 CHAPTER 8 Roots, Radicals, and Root Functions

NOW TRY

NOW TRY
EXERCISE 7
Solve the formula for a.

x= B

y+ 2 a

NOW TRY ANSWER

a=

y+ 2 x^2

Complete solution available
on the Video Resources on DVD

8.6 EXERCISES

Concept Check Check each equation to see if the given value for x is a solution.

1. (a) 6 (b)

2.

(a) 1 (b) 4

23 x- 3 - x+ 1 = 0

3

23 x+ 18 - x= 0

3.

(a) 2 (b) 7

4.

(a) (b)

1

2

3

2

2 x+ 2 - 29 x- 2 =- 22 x- 1 28 x- 3 - 2 x= 0

5.Is 9 a solution of the equation? If not, what is the solution of this equation? Explain. 6.Before even attempting to solve , how can you be sure that the equation cannot have a negative solution?

Solve each equation. See Examples 1–4.

4 - 2 x- 2 = 0 16. 9 - 24 x+ 1 = 0

23 x+ 1 - 4 = 0 25 x+ 1 - 11 = 0

24 r+ 3 + 1 = 0 25 k- 3 + 2 = 0

26 k- 1 = 1 27 x- 3 = 6

2 x- 2 = 3 2 x+ 1 = 7

23 x+ 18 =x

2 x=- 3

Our goal is to isolate Con one side of the equals symbol.