A car that has a wheel radius of 1.5 feet travels 30 miles in 45 minutes. How fast are the wheels spinning? Give your answer in revolutions per minute.

373.43 rev/min

Step-by-step explanation:

Given data

r= 1.5ft

v=30 miles per 45 minutes

convert miles per hour to ft per minute

=30miles/45 minutes* 5280ft/1 mile

=158400/45 minutes

v=3520 feet per minute

so

v=wr

substitute

3520= w*1.5

w= 3520/1.5

w=2346.66 rad/min

Convert to rev/min

=2346.66 rad/min*1rev/2*π rad

=2346.66/2*3.142

=2346.66/6.284

=373.43 rev/min

Hence the answer is 373.43 rev/min

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240