Answer:
![V =\dfrac{25\pi}{\sqrt{2}}](https://tex.z-dn.net/?f=V%20%3D%5Cdfrac%7B25%5Cpi%7D%7B%5Csqrt%7B2%7D%7D)
Step-by-step explanation:
given,
y=5√sinx
Volume of the solid by revolving
![V = \int_a^b(\pi y^2)dx](https://tex.z-dn.net/?f=V%20%3D%20%5Cint_a%5Eb%28%5Cpi%20y%5E2%29dx)
a and b are the limits of the integrals
now,
![V = \int_a^b(\pi (5\sqrt{sinx})^2)dx](https://tex.z-dn.net/?f=V%20%3D%20%5Cint_a%5Eb%28%5Cpi%20%285%5Csqrt%7Bsinx%7D%29%5E2%29dx)
![V =25\pi \int_{\pi/4}^{\pi/2}sinxdx](https://tex.z-dn.net/?f=V%20%3D25%5Cpi%20%5Cint_%7B%5Cpi%2F4%7D%5E%7B%5Cpi%2F2%7Dsinxdx)
![\int sin x = - cos x](https://tex.z-dn.net/?f=%5Cint%20sin%20x%20%3D%20-%20cos%20x)
![V =25\pi [-cos x]_{\pi/4}^{\pi/2}](https://tex.z-dn.net/?f=V%20%3D25%5Cpi%20%5B-cos%20x%5D_%7B%5Cpi%2F4%7D%5E%7B%5Cpi%2F2%7D)
![V =25\pi [-cos (\pi/2)+cos(\pi/4)]](https://tex.z-dn.net/?f=V%20%3D25%5Cpi%20%5B-cos%20%28%5Cpi%2F2%29%2Bcos%28%5Cpi%2F4%29%5D)
![V =25\pi [0+\dfrac{1}{\sqrt{2}}]](https://tex.z-dn.net/?f=V%20%3D25%5Cpi%20%5B0%2B%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5D)
![V =\dfrac{25\pi}{\sqrt{2}}](https://tex.z-dn.net/?f=V%20%3D%5Cdfrac%7B25%5Cpi%7D%7B%5Csqrt%7B2%7D%7D)
volume of the solid generated is equal to ![V =\dfrac{25\pi}{\sqrt{2}}](https://tex.z-dn.net/?f=V%20%3D%5Cdfrac%7B25%5Cpi%7D%7B%5Csqrt%7B2%7D%7D)
Answer:
4.2 ft
Step-by-step explanation:
Given the equation for the Law of Cosines, we can rewrite the equation to solve for "c" directly:
![c^2=a^2+b^2-2ab(cosC)\\c=\sqrt{a^2+b^2-2ab(cosC)}\\c=\sqrt{7^2+8^2-2(7)(8)(cos32)}\\c=\sqrt{49+64-2(56)(cos32)}\\c=\sqrt{113-112(cos32)}\\c=\sqrt{113-94.98138677}\\c=\sqrt{18.01861323}\\c=4.244833711\\c=4.2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2-2ab%28cosC%29%5C%5Cc%3D%5Csqrt%7Ba%5E2%2Bb%5E2-2ab%28cosC%29%7D%5C%5Cc%3D%5Csqrt%7B7%5E2%2B8%5E2-2%287%29%288%29%28cos32%29%7D%5C%5Cc%3D%5Csqrt%7B49%2B64-2%2856%29%28cos32%29%7D%5C%5Cc%3D%5Csqrt%7B113-112%28cos32%29%7D%5C%5Cc%3D%5Csqrt%7B113-94.98138677%7D%5C%5Cc%3D%5Csqrt%7B18.01861323%7D%5C%5Cc%3D4.244833711%5C%5Cc%3D4.2)
So the length of c is approximately 4.2 ft
In this case, you simply count how many cubes are in the length, width, and height and multiply them together. In the example problem, the answer is 75 blocks because the dimensions are 5 x 5 x 3.
Answer:
you may recall that the term area tells us something about the number of squares inside a two-dimensional shape.
Step-by-step explanation:
The correct answer is C. For every mile the car is towed, the cost increases by $4.75.
Because for every mile the cost increases be $4.75.