Let x = number of miles, cost per mile = 93 cents = $0.93
Cost = 20.95 + 0.93*x
200.44 = 20.95 + 0.93x
0.93x + 20.95 = 200.44
0.93x = 200.44 - 20.95
0.93x = 179.49
x = 179.49/0.93
x = 193
He drove 193 miles.
Volume of A= πR².H ==> V(A)=4π m³
Volume of V =πR².H ==>V(B)=8π m³
.Ratio of A to B =(4π) /(4π) = 1/2
The answer is The equation 3.5|6x – 2| = 3.5 has one solution
Answer:
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Step-by-step explanation:
Answer:
The volume of the solid is:
Step-by-step explanation:
GIven that :
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This implies that the distance between the x-axis and the axis of the rotation = 2 units
The distance between the x-axis and the inner ring is r = (2+sec x) -2
Let R be the outer radius and r be the inner radius
By integration; the volume of the of the solid can be calculated as follows:
![V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5Cint%5Climits%5E%7B%5Cdfrac%7B%5Cpi%7D%7B3%7D%7D_%7B%5Cdfrac%7B-%5Cpi%7D%7B3%7D%7D%20%5B%284-2%29%5E2%20-%20%282%2B%20sec%20%5C%20x%20-2%29%5E2%5Ddx%20%5C%5C%20%5C%5C%20%5C%5C%20V%20%3D%20%5Cpi%20%5Cint%5Climits%5E%7B%5Cdfrac%7B%5Cpi%7D%7B3%7D%7D_%7B%5Cdfrac%7B-%5Cpi%7D%7B3%7D%7D%20%5B%282%29%5E2%20-%20%28sec%20%5C%20x%20%29%5E2%5Ddx%20%5C%5C%20%5C%5C%20%5C%5C%20V%20%3D%20%5Cpi%20%5Cint%5Climits%5E%7B%5Cdfrac%7B%5Cpi%7D%7B3%7D%7D_%7B%5Cdfrac%7B-%5Cpi%7D%7B3%7D%7D%20%5B4%20-%20sec%5E2%20%5C%20x%20%5Ddx)
![V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ]](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5B4x%20-%20tan%20%5C%20%20x%5D%5E%7B%5Cdfrac%7B%5Cpi%7D%7B3%7D%7D_%7B%5Cdfrac%7B-%5Cpi%7D%7B3%7D%7D%20%20%5C%5C%20%5C%5C%20%5C%5C%20V%20%3D%20%5Cpi%20%5B4%28%5Cdfrac%7B%5Cpi%7D%7B3%7D%29%20-%20tan%20%28%5Cdfrac%7B%5Cpi%7D%7B3%7D%29%20-%204%28-%5Cdfrac%7B%5Cpi%7D%7B3%7D%29%2B%20tan%20%28-%5Cdfrac%7B%5Cpi%7D%7B3%7D%29%5D%20%5C%5C%20%5C%5C%20%5C%5C%20V%20%3D%20%5Cpi%20%5B4%28%5Cdfrac%7B%5Cpi%7D%7B3%7D%29%20-%20tan%20%28%5Cdfrac%7B%5Cpi%7D%7B3%7D%29%20%2B%204%28%5Cdfrac%7B%5Cpi%7D%7B3%7D%29-%20tan%20%28%5Cdfrac%7B%5Cpi%7D%7B3%7D%29%5D%20%20%5C%5C%20%5C%5C%20%5C%5C%20V%20%3D%20%5Cpi%20%5B8%28%5Cdfrac%7B%5Cpi%7D%7B3%7D%29%20%20-%202%20%5C%20%20tan%20%28%5Cdfrac%7B%5Cpi%7D%7B3%7D%29%20%5D)
![\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}](https://tex.z-dn.net/?f=%5Cmathbf%7BV%20%3D%20%5Cpi%20%5B%20%5Cdfrac%7B8%20%5Cpi%7D%7B3%7D%20-%202%5Csqrt%7B3%7D%5D%7D)