Solve each formula for the indicated variable. See Example 7.(Source:Cooke, Nelson M.,
and Joseph B. Orleans, Mathematics Essential to Electricity and Radio,McGraw-Hill.)- for L 64. for 65. for K
- for m 67. for M 68. for F
The formulais used to find the rotational rate N of a space
station. Here, a is the acceleration and r repre-
sents the radius of the space station, in meters.
To find the value of r that will make N simulate
the effect of gravity on Earth, the equation must
be solved for r, using the required value of N.
(Source: Kastner, Bernice, Space Mathematics,
NASA.)
69.Solve the equation for r.- (a)Approximate the value of rso that rotation per sec if m per.
(b)Approximate the value of rso that N=0.04rotation per sec if a=9.8m per sec^2.
N=0.063 a=9.8 sec^2N=
1
2 p
Ba
rr=
BMm
Fr=
BMm
FV=
B
2 K
mV=
B
2 K
mr= a
Ba
pZ=
B
L
C
474 CHAPTER 8 Roots, Radicals, and Root Functions
Perform the indicated operations. See Sections 5.2 and 5.4.Simplify each radical. See Section 8.5.22 + 27
25 + 23
- 7
5 - 22
2
4 + 23
15 + 9 x 2 + 1 - 4 - 8 x 2 112 + 7 y 2 - 1 - 3 + 2 y 2 1 x+ 3212 x- 52PREVIEW EXERCISES
OBJECTIVES OBJECTIVE 1 Simplify numbers of the form , where The
equation has no real number solution, since any solution must be a num-
ber whose square is In the set of real numbers, all squares are nonnegative num-
bers because the product of two positive numbers or two negative numbers is positive
and To provide a solution of the equation we introduce a new
number i.
02 = 0. x^2 + 1 =0,
- 1.
x^2 + 1 = 0
2 b b>0.
Complex Numbers
8.7
1 Simplify numbers of
the form ,
where.
2 Recognize subsets
of the complex
numbers.
3 Add and subtract
complex numbers.
4 Multiply complex
numbers.
5 Divide complex
numbers.
6 Find powers of i.b 702 - bImaginary Unit i