Answer:
The volume of the solid is: ![\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)
Step-by-step explanation:
GIven that :
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)
Answer:
48 more minutes
Step-by-step explanation:
85 - 37 = 48
Answer:
correct option is option A.
Step-by-step explanation:
July sales forecast = 6000 units
cost of one unit which is going to be sold = $10.50 per unit
total sale in the month of July is equal to
= 6000 × $10.50
= $63,000
hence the total sale in the month of July comes out to be = $63,000
so, the correct option is option A.
Answer:
yes, true.
Step-by-step explanation:
she add 125 to her account and then takes away 125
125-125 = 0
Answer:
-4, -3.5, -2, -0.5, 1.5, 2.5
Step-by-step explanation:
you find the number with the least value which is -4 and then you go to the next one up which is -3.5 and you keep going
