CHAPTER 11 / ESSENTIAL ALGEBRA 2 SKILLS 427
- D If the force varies inversely as the square of
the distance, then the product of the force and
the square of the distance is a constant. For these
particular stars, the force times the square of the
distance is (4)^2 (64) = 1024. If they were eight
light-yearsapart, then the force would satisfy the
equation (8)^2 (f) = 1024, so f= 16. - 4 Set up the variation equation:
a= kb/c
Substitute: 10 x+ 5 = k(10)/2
Simplify: 10 x+ 5 = 5k
Divide by 5: 2 x+ 1 = k
Substitute new values: a= (2x+ 1)(4)/(2x+ 1)
Simplify: a= 4
7. D If yvaries inversely as the square of x, then
their product x^2 yis a constant. To keep it simple,
pick xand yto be 1, so the product (1)^2 (1) = 1. To
find the value of xthat would doubley, simply
double yand solve for x.
If x^2 (2) = 1, then. This is the original
value of xdivided by.
8. B Since yincreases as xdecreases, any variation
must be an inversevariation. Since the product of
xandyis a constant (1 8 = 4 2 = 8), yvaries
inversely as x.
2
x= 12