Step-by-step explanation:
2(4 – 16) – (–30) 2(–12) – (–30) 24 – (–30) 54= 2×4-2×16 -×-30×2×-12-×-30×24-×-30= 8-32+30-24+30×24+30: 732
Solve for x in first equation:
x-2y=7
Add “2y” to both sides
x=2y+7
Put this in to second equation:
3(2y+7)+2y=21
Solve for y:
Distribute the 3 into the ()
6y+21+2y=21
Combine the like y terms
8y+21=21
Subtract 21 from both sides
8y=0
Divide by 8 on both sides
y=0
Put this into the first solved equation:
x=2(0)+7
Solve for x:
Multiple 2(0)
x=0+7
Add 0 and 7
x=7
So the value of x is positive 7.
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:
3/4=63/84
66.66%=56/84
5/7=60/84
⇒66.66%; 5/7; 3/4
Step-by-step explanation:
