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)
The law of cosines states that, if
is the angle between sides b and c,
![a^2 = b^2+c^2-2bc\cos(\alpha)](https://tex.z-dn.net/?f=a%5E2%20%3D%20b%5E2%2Bc%5E2-2bc%5Ccos%28%5Calpha%29)
So, plugging our values, we have
![a^2 = 16+16-2\cdot 4\cdot 4\cdot\cos\left(\dfrac{\pi}{4}\right)](https://tex.z-dn.net/?f=a%5E2%20%3D%2016%2B16-2%5Ccdot%204%5Ccdot%204%5Ccdot%5Ccos%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cright%29)
This is equal to
![a^2 = 32-32\cdot\dfrac{\sqrt{2}}{2} = 32-16\sqrt{2}](https://tex.z-dn.net/?f=a%5E2%20%3D%2032-32%5Ccdot%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%3D%2032-16%5Csqrt%7B2%7D)
To find the unit rate, divide the numerator and denominator of the given rate by the denominator of the given rate
Answer:
3rd Option
Step-by-step explanation:
When you find the ratio of the 2 triangles, it is 14/5, so the 2nd option and 4th option are out of the park (The triangles are indeed similar). You are left with options 1 and 3. Option 3 is the best answer as you have to match the vertices of each triangle to each other.
She has 10 liters left. Find 4/9 of 18 by multiplying 4/9 and 18. 4/9 of 18 is 8, so she served 8 of the 18, leaving 10 liters.