Answer:
![r=\sqrt[3]{\frac{3V}{4 \pi}}](https://tex.z-dn.net/?f=r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%20%5Cpi%7D%7D)
Step-by-step explanation:
we know that
The formula of volume of the sphere is given by
![V=\frac{4}{3}\pi r^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E%7B3%7D)
Solve for r
That means ----> isolate the variable r
Multiply by 3 both sides
![3V=4 \pi r^3](https://tex.z-dn.net/?f=3V%3D4%20%5Cpi%20r%5E3)
Divide by
both sides
![r^{3} =\frac{3V}{4 \pi}](https://tex.z-dn.net/?f=r%5E%7B3%7D%20%3D%5Cfrac%7B3V%7D%7B4%20%5Cpi%7D)
Elevate both sides to 1/3
![r =(\frac{3V}{4 \pi})^{\frac{1}{3}}](https://tex.z-dn.net/?f=r%20%3D%28%5Cfrac%7B3V%7D%7B4%20%5Cpi%7D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
![r=\sqrt[3]{\frac{3V}{4 \pi}}](https://tex.z-dn.net/?f=r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%20%5Cpi%7D%7D)
#1 is similar to write it out it’s triangle FHG ~ triangle KJL #2 is also but #3 and #4 aren’t
we are given
![sin(\theta)=cos(73)](https://tex.z-dn.net/?f=%20sin%28%5Ctheta%29%3Dcos%2873%29%20)
we have to find theta
so, firstly we can write sin in terms of cos
![sin(\theta)=cos(90-\theta)](https://tex.z-dn.net/?f=%20sin%28%5Ctheta%29%3Dcos%2890-%5Ctheta%29%20)
now, we can set it equal
![cos(90-\theta)=cos(73)](https://tex.z-dn.net/?f=%20cos%2890-%5Ctheta%29%3Dcos%2873%29%20)
Since, both sides are cos
so, we can set angles equal
![90-\theta=73](https://tex.z-dn.net/?f=%2090-%5Ctheta%3D73%20)
now, we can solve for theta
we get
..............Answer
Answer:
y^3 + 5y + 8
Step-by-step explanation:
Collect like terms
4y^3 - 3y^3 + 2y + 2y + y + 4 + 4
= 1y^3 + 5y + 8 OR y^3 + 5y + 8
the value is n=1/4
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