The first one- the rest don’t add up
Answer:
He will cover 1/3/6 distance in a day.
Answer:
![V=\frac{4}{3}(8)^{3}\pi](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%288%29%5E%7B3%7D%5Cpi)
Step-by-step explanation:
The formula for calculate the volume of a sphere is shown below:
![V=\frac{4}{3}r^{3}\pi](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7Dr%5E%7B3%7D%5Cpi)
Where V is the volume of the sphere and r is the radius of the sphere.
The problem says that the radius of the sphere is 8. Then, you only need to substitute this value into the formula shown above.
Therefore, you can calculate it as following:
![V=\frac{4}{3}(8)^{3}\pi=2144.66](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%288%29%5E%7B3%7D%5Cpi%3D2144.66)
Answer:
48
Step-by-step explanation:
6(24/4)+2
6(6)+2
6*8
48
![\huge\text{$m\angle O=\boxed{11^{\circ}}$}](https://tex.z-dn.net/?f=%5Chuge%5Ctext%7B%24m%5Cangle%20O%3D%5Cboxed%7B11%5E%7B%5Ccirc%7D%7D%24%7D)
Since we know that all angles in a triangle add up to
, we can solve for
and substitute it back into
to find
.
![\begin{aligned}m\angle N+m\angle O+m\angle P&=180\\(5x-8)+(x-5)+(6x+1)&=180\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%5Cangle%20N%2Bm%5Cangle%20O%2Bm%5Cangle%20P%26%3D180%5C%5C%285x-8%29%2B%28x-5%29%2B%286x%2B1%29%26%3D180%5Cend%7Baligned%7D)
Remove the parentheses and combine like terms.
![\begin{aligned}5x-8+x-5+6x+1&=180\\(5x+x+6x)+(-8-5+1)&=180\\12x-12&=180\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D5x-8%2Bx-5%2B6x%2B1%26%3D180%5C%5C%285x%2Bx%2B6x%29%2B%28-8-5%2B1%29%26%3D180%5C%5C12x-12%26%3D180%5Cend%7Baligned%7D)
Add
to both sides of the equation.
![\begin{aligned}12x-12&=180\\12x&=192\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D12x-12%26%3D180%5C%5C12x%26%3D192%5Cend%7Baligned%7D)
Divide both sides of the equation by
.
![\begin{aligned}x=16\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dx%3D16%5Cend%7Baligned%7D)
Now that we have the value of
, we can substitute it back into
to find
.
![\begin{aligned}m\angle O&=(x-5)\\&=16-5\\&=\boxed{11}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%5Cangle%20O%26%3D%28x-5%29%5C%5C%26%3D16-5%5C%5C%26%3D%5Cboxed%7B11%7D%5Cend%7Baligned%7D)