The volume of a cylinder is pi*r^2*h
The radius is half the diameter, so 40/2=20, and the radius is 20 ft.
Plugging in: pi*20^2*32=pi*400*32=12800pi=40212.38597
So the volume is about 40212.4 ft^3 and the expression we used is pi*20^2*32
Hope this helped!
Answer:
the proportion is false
Step-by-step explanation:
5.5/7.5 = 11/15
3.5/7= 1/2
Answer:
![(\frac{1}{2},\frac{-1}{2},\frac{1}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%2C%5Cfrac%7B-1%7D%7B2%7D%2C%5Cfrac%7B1%7D%7B2%7D%29)
Step-by-step explanation:
We have been given the intersection coordinates:
(7,1,-6) and perpendicular to the line x=-1+t ,y=-2+t and z=-1+t
From the condition of perpendicularity we know:
![(7,1,-6)(x,y,z)](https://tex.z-dn.net/?f=%287%2C1%2C-6%29%28x%2Cy%2Cz%29)
![\Rightarrow 7x+y-6z=0](https://tex.z-dn.net/?f=%5CRightarrow%207x%2By-6z%3D0)
Now, we have given x=-1+t , y=-2+t and z= -1+t
![7(-1+t)+(-2+t)-6(-1+t)=0](https://tex.z-dn.net/?f=7%28-1%2Bt%29%2B%28-2%2Bt%29-6%28-1%2Bt%29%3D0)
![-7+7t-2+t+6-6t=0](https://tex.z-dn.net/?f=-7%2B7t-2%2Bt%2B6-6t%3D0)
![\Rightarrow -3+2t=0](https://tex.z-dn.net/?f=%5CRightarrow%20-3%2B2t%3D0)
![2t=3](https://tex.z-dn.net/?f=2t%3D3)
![t=\frac{3}{2}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B3%7D%7B2%7D)
Now, substituting t in the given coordinates x,y and z we get:
![x=-1+\frac{3}{2}=\frac{1}{2}](https://tex.z-dn.net/?f=x%3D-1%2B%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D)
![y=-2+\frac{3}{2}=\frac{-1}{2}](https://tex.z-dn.net/?f=y%3D-2%2B%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B-1%7D%7B2%7D)
And ![z=-1+\frac{3}{2}=\frac{1}{2}](https://tex.z-dn.net/?f=z%3D-1%2B%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D)
Answer:
Step-by-step explanation:
x^2 + 44^2 = 55^2
x^2 + 1936 = 3025
3025-1936 = 1089
sqrt(1089) = 33
x = 33
Answer:
![\frac{1}{4x}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4x%7D)
Step-by-step explanation:
The negative exponential can be represented with the help of fractions. By this way, we also make the negative exponential disappear. For example, we can write:
![a^{-1} = \frac{1}{a}](https://tex.z-dn.net/?f=a%5E%7B-1%7D%20%3D%20%5Cfrac%7B1%7D%7Ba%7D)
The explanation is this:
Since ![a^{0}=1, \frac{1}{a}=\frac{a^{0} }{a^{1} } = a^{0-1} =a^{-1}](https://tex.z-dn.net/?f=a%5E%7B0%7D%3D1%2C%20%5Cfrac%7B1%7D%7Ba%7D%3D%5Cfrac%7Ba%5E%7B0%7D%20%7D%7Ba%5E%7B1%7D%20%7D%20%3D%20a%5E%7B0-1%7D%20%3Da%5E%7B-1%7D)
According to this definition, we can simplify our problem in the following way:
![(4x)^{-1} = \frac{1}{(4x)^{1} } = \frac{1}{4x}](https://tex.z-dn.net/?f=%284x%29%5E%7B-1%7D%20%3D%20%5Cfrac%7B1%7D%7B%284x%29%5E%7B1%7D%20%7D%20%3D%20%5Cfrac%7B1%7D%7B4x%7D)