Answer:
Step-by-step explanation:
we are asked to find the volume of solid that lies within both the cylinder
![x^2 + y^2 = 25](https://tex.z-dn.net/?f=x%5E2%20%2B%20y%5E2%20%3D%2025)
and
the sphere![x^2 + y^2 + z^2 = 49.](https://tex.z-dn.net/?f=x%5E2%20%2B%20y%5E2%20%2B%20z%5E2%20%3D%2049.)
Conversion from rectangular to cylindrical is
![x=rcost\\y = rsint\\z=z](https://tex.z-dn.net/?f=x%3Drcost%5C%5Cy%20%3D%20rsint%5C%5Cz%3Dz)
|J| =r
In cylindrical coordinates the volume is bounded by the cylinder r=5 and
![r^2+z^2 =49](https://tex.z-dn.net/?f=r%5E2%2Bz%5E2%20%3D49)
Hence we can write volume as
![\int \int \int dxdydz\\=\\\int _0^5 \int_0^{2\pi} \int_{-\sqrt{49-r^2} } ^{\sqrt{49-r^2} rdzdtdr\\= 2\pi \int _0^5 (2\sqrt{49-r^2} rdr\\=4\pi (-(49-r^2) (2/3)\\= \frac{4\pi}{3} (343-48\sqrt{6} )](https://tex.z-dn.net/?f=%5Cint%20%5Cint%20%5Cint%20dxdydz%5C%5C%3D%5C%5C%5Cint%20_0%5E5%20%5Cint_0%5E%7B2%5Cpi%7D%20%5Cint_%7B-%5Csqrt%7B49-r%5E2%7D%20%7D%20%5E%7B%5Csqrt%7B49-r%5E2%7D%20rdzdtdr%5C%5C%3D%202%5Cpi%20%5Cint%20_0%5E5%20%282%5Csqrt%7B49-r%5E2%7D%20rdr%5C%5C%3D4%5Cpi%20%28-%2849-r%5E2%29%20%282%2F3%29%5C%5C%3D%20%5Cfrac%7B4%5Cpi%7D%7B3%7D%20%28343-48%5Csqrt%7B6%7D%20%29)
Hi the answer to your question is p=r-9/5 i hope this helps.
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Joan makes $275/week.
In addition to $275, she also makes 4 percent on sales over $1000.
So, 1250 - 1000 = 250.
Then 250(0.04) = 10.
Let t = amount of her paycheck for the week.
t = $275 + $10
t = $285