Percent change = [(45 - 60) / 60] x 100 = -25 % (decrease)
2n + 8 ≤ 25 |subtract 8 from both sides
2n ≤ 17 |divide both sides by 2
<u>n ≤ 8.5</u>
Answer:
Height of cylinder (h) = (4/3)R
Step-by-step explanation:
Given:
Radius of cylinder (r1) = R
Height of cylinder (h) = H
Radius of sphere (r2) = R
Volume of cylinder = volume of sphere
Find:
Height of cylinder (h) = H = ?
Computation:

Height of cylinder (h) = (4/3)R
You would use unit rate for this. If Austin makes $209 in 11 hours, then he makes 209/11 = 19 dollars in 1 hour.
Then, we can make a proportion:
$19/1 hour = $152/ x hours
Cross multiply:
152 = 19x
Solve for x to get:
x = 8 hours.
The general form of a quadratic (second degree) equation is

, where

is called the Discriminant.
The Discriminant determines how many roots the equation will have as follows:
i) if D>0, the equation has 2 roots.
ii) if D=0, the equation has 1 double root.
iii) if D<0, the equation has no roots.
In our equation,

, a=1, b=-5, c=7
so the discriminant is D=(-5)^2-4*1*7=25-28<0
Thus the equation has no roots.
Remark: the equation has no roots in the Real numbers, but it has 2 roots in a larger set of numbers to be discussed in the future, the Complex numbers.