Answer:
LCD = 4 x^2
Step-by-step explanation:
The least common denominator : LCD
(x + 1) / 4x and (3(x + 1)) / 2x^2
factor 4x : 2, 2, x
factor 2x^2 : 2, x, x^2
take highest powers 2^2 and x^2
LCD is 4*x^2
Answer:
the correct answer is ( C )
Answer:
4
Step-by-step explanation:
Answer:
136
Step-by-step explanation:
4 times 32 = 128
32/4=8
128+8=136
Answer:
meters per minute
Step-by-step explanation:
<u>Given:</u>
![V=\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2h)
![r=5](https://tex.z-dn.net/?f=r%3D5)
![\frac{dV}{dt}=3](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D3)
![\frac{dh}{dt}=?](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%3F)
<u>Substitute r=5:</u>
![V=\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2h)
![V=\pi(5)^2h](https://tex.z-dn.net/?f=V%3D%5Cpi%285%29%5E2h)
![V=25\pi h](https://tex.z-dn.net/?f=V%3D25%5Cpi%20h)
<u>Differentiate both sides:</u>
![\frac{d}{dt}V=\frac{d}{dt}(25\pi h)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7DV%3D%5Cfrac%7Bd%7D%7Bdt%7D%2825%5Cpi%20h%29)
![\frac{dV}{dt}=25\pi\frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D25%5Cpi%5Cfrac%7Bdh%7D%7Bdt%7D)
<u>Solve for dh/dt:</u>
![3=25\pi\frac{dh}{dt}](https://tex.z-dn.net/?f=3%3D25%5Cpi%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{3}{25\pi}=\frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B25%5Cpi%7D%3D%5Cfrac%7Bdh%7D%7Bdt%7D)
Therefore, the height of the water is increasing at a rate of
meters per minute.