Answer:
45p-9p+8 simplified is 36p+8
The answer would be D. It says the length is 10 millimeters less than TWICE the width, so it would be 10 millimeters greater than the original width.
The volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16 is 24.74 cubic units.
<h3>What is the volume of the solid?</h3>
Find the volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16
From the sphere and cylinder, the cylindrical coordinate will be

And the radius of the cylinder is |r| < 1 and the 0 ≤ θ ≤ 2π.
Then the volume will be given as
![\rm V = \int _0^{2\pi} \int _0^1 \int _{- \sqrt{16 - r^2}}^{\sqrt{16-r^2}} \left ( r \ dz \ dr \ d\theta \right ) \\\\\\V = 2\pi \int_0^1 \left ( 2r\sqrt{16-r^2} \right ) \ dr\\\\\\V = 4\pi \left [ -\dfrac{1}{3} (16 - r^2)^{3/2} \right ]\\\\\\V = \dfrac{4\pi}{3} \left ( 16^{3/2} - 15^{3/2} \right )\\\\\\V = 24.74](https://tex.z-dn.net/?f=%5Crm%20V%20%3D%20%5Cint%20_0%5E%7B2%5Cpi%7D%20%5Cint%20_0%5E1%20%5Cint%20_%7B-%20%5Csqrt%7B16%20-%20r%5E2%7D%7D%5E%7B%5Csqrt%7B16-r%5E2%7D%7D%20%5Cleft%20%28%20r%20%5C%20dz%20%5C%20dr%20%5C%20d%5Ctheta%20%20%5Cright%20%29%20%5C%5C%5C%5C%5C%5CV%20%3D%202%5Cpi%20%5Cint_0%5E1%20%5Cleft%20%28%202r%5Csqrt%7B16-r%5E2%7D%20%5Cright%20%29%20%5C%20dr%5C%5C%5C%5C%5C%5CV%20%3D%204%5Cpi%20%5Cleft%20%5B%20-%5Cdfrac%7B1%7D%7B3%7D%20%2816%20-%20r%5E2%29%5E%7B3%2F2%7D%20%5Cright%20%5D%5C%5C%5C%5C%5C%5CV%20%3D%20%5Cdfrac%7B4%5Cpi%7D%7B3%7D%20%5Cleft%20%28%2016%5E%7B3%2F2%7D%20-%2015%5E%7B3%2F2%7D%20%5Cright%20%29%5C%5C%5C%5C%5C%5CV%20%3D%2024.74)
More about the volume of the solid link is given below.
brainly.com/question/23705404
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Answer:
60
Step-by-step explanation:
perimeter (p) = 8 + 17 + 15 = 40
semi-perimeter (s) = p/2 = 20
Area = square root of s(s-a)(s-b)(s-c) where a,b,c are the sides of the triange by Herons formula.
Therefore, area = 20(20-8)(20-15)(20-17) = square root of 3600 = 60
Answer:
yes
Step-by-step explanation: