If he gets paid 60 for 5 hours that's 12 per hour so 12 times 8 is 96
166 hope this helps u with ur homwork
Answer:
The volume of the solid = 1444
Step-by-step explanation:
Given that:
The region of the solid is bounded by the curves
and the axis on ![[-\dfrac{\pi}{2}, \dfrac{\pi}{2}]](https://tex.z-dn.net/?f=%5B-%5Cdfrac%7B%5Cpi%7D%7B2%7D%2C%20%5Cdfrac%7B%5Cpi%7D%7B2%7D%5D)
using the slicing method
Let say the solid object extends from a to b and the cross-section of the solid perpendicular to the x-axis has an area expressed by function A.
Then, the volume of the solid is ;
![V = \int ^b_a \ A(x) \ dx](https://tex.z-dn.net/?f=V%20%3D%20%5Cint%20%5Eb_a%20%20%5C%20A%28x%29%20%5C%20%20dx)
However, each perpendicular slice is an isosceles leg on the xy-plane and vertical leg above the x-axis
Then, the area of the perpendicular slice at a point
is:
![A(x) =\dfrac{1}{2} \times b \times h](https://tex.z-dn.net/?f=A%28x%29%20%3D%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20b%20%5Ctimes%20h)
![A(x) =\dfrac{1}{2} \times(38 \sqrt{cos \ x})^2](https://tex.z-dn.net/?f=A%28x%29%20%3D%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%2838%20%5Csqrt%7Bcos%20%5C%20x%7D%29%5E2)
![A(x) =\dfrac{1444}{2} \ cos \ x](https://tex.z-dn.net/?f=A%28x%29%20%3D%5Cdfrac%7B1444%7D%7B2%7D%20%5C%20cos%20%5C%20x)
![A(x) =722 \ cos \ x](https://tex.z-dn.net/?f=A%28x%29%20%3D722%20%5C%20cos%20%5C%20x)
Applying the general slicing method ;
![V = \int ^b_a \ A(x) \ dx \\ \\ V = \int ^{\dfrac{\pi}{2} }_{-\dfrac{\pi}{2}} (722 \ cos x) \ dx \\ \\ V = 722 \int ^{\dfrac{\pi}{2}}_{-\dfrac{\pi}{2}} cosx \dx](https://tex.z-dn.net/?f=V%20%3D%20%5Cint%20%5Eb_a%20%5C%20A%28x%29%20%5C%20dx%20%5C%5C%20%5C%5C%20V%20%3D%20%5Cint%20%5E%7B%5Cdfrac%7B%5Cpi%7D%7B2%7D%20%7D_%7B-%5Cdfrac%7B%5Cpi%7D%7B2%7D%7D%20%28722%20%5C%20cos%20x%29%20%5C%20dx%20%5C%5C%20%5C%5C%20V%20%3D%20722%20%5Cint%20%5E%7B%5Cdfrac%7B%5Cpi%7D%7B2%7D%7D_%7B-%5Cdfrac%7B%5Cpi%7D%7B2%7D%7D%20cosx%20%20%5Cdx)
![V = 722 [ sin \ x ] ^{\dfrac{\pi}{2}}_{-\dfrac{\pi}{2}}](https://tex.z-dn.net/?f=V%20%3D%20722%20%5B%20sin%20%5C%20x%20%5D%20%5E%7B%5Cdfrac%7B%5Cpi%7D%7B2%7D%7D_%7B-%5Cdfrac%7B%5Cpi%7D%7B2%7D%7D)
![V = 722 [sin \dfrac{\pi}{2} - sin (-\dfrac{\pi}{2})]](https://tex.z-dn.net/?f=V%20%3D%20722%20%5Bsin%20%5Cdfrac%7B%5Cpi%7D%7B2%7D%20-%20sin%20%28-%5Cdfrac%7B%5Cpi%7D%7B2%7D%29%5D)
![V = 722 [sin \dfrac{\pi}{2} + sin \dfrac{\pi}{2})]](https://tex.z-dn.net/?f=V%20%3D%20722%20%5Bsin%20%5Cdfrac%7B%5Cpi%7D%7B2%7D%20%2B%20sin%20%5Cdfrac%7B%5Cpi%7D%7B2%7D%29%5D)
![V = 722 [1+1]](https://tex.z-dn.net/?f=V%20%3D%20722%20%5B1%2B1%5D)
![V = 722 [2]](https://tex.z-dn.net/?f=V%20%3D%20722%20%5B2%5D)
V = 1444
∴ The volume of the solid = 1444
The whole story begins at 9:00 AM, so let's make up a quantity called ' T ',
and that'll be the number of hours after 9:00 AM. When we find out what ' T ' is,
we'll just count off that many hours after 9:00 AM and we'll have the answer.
-- The first car started out at 9:00 AM, and drove until the other one caught up
with him. So the first car drove for ' T ' hours.
The first car drove at 55 mph, so he covered ' 55T ' miles.
-- The second car started out 1 hour later, so he only drove for (T - 1) hours.
The second car drove at 75 mph, so he covered ' 75(T - 1) ' miles.
But they both left from the same shop, and they both met at the same place.
So they both traveled the same distance.
(Miles of Car-#1) = (miles of Car-#2)
55 T = 75 (T - 1)
Eliminate the parentheses on the right side"
55 T = 75 T - 75
Add 75 to each side:
55 T + 75 = 75 T
Subtract 55 T from each side:
75 = 20 T
Divide each side by 20 :
75/20 = T
3.75 = T
There you have it. They met 3.75 hours after 9:00 AM.
9:00 AM + 3.75 hours = <u>12:45 PM</u> . . . just in time to stop for lunch together.
Also by the way ...
when the 2nd car caught up, they were 206.25 miles from the shop.