A = 7/3
quadratic formula
don’t know if that’s the method ur teacher wanted u to answer
Answer:
A
Step-by-step explanation:
rational numbers are numbers that can be expressed as fractions.
e.g. 1 , 1/2, 2/7
See the attached picture for explanation and steps:
Answer:
![\frac{dh}{dt}=-\frac{1}{2\pi}cm/min](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D-%5Cfrac%7B1%7D%7B2%5Cpi%7Dcm%2Fmin)
Step-by-step explanation:
From similar triangles, see diagram in attachment
![\frac{r}{4}=\frac{h}{16}](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7B4%7D%3D%5Cfrac%7Bh%7D%7B16%7D)
We solve for
to obtain,
![r=\frac{h}{4}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bh%7D%7B4%7D)
The formula for calculating the volume of a cone is
![V=\frac{1}{3}\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h)
We substitute the value of
to obtain,
![V=\frac{1}{3}\pi (\frac{h}{4})^2h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%28%5Cfrac%7Bh%7D%7B4%7D%29%5E2h)
This implies that,
![V=\frac{1}{48}\pi h^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B48%7D%5Cpi%20h%5E3)
We now differentiate both sides with respect to
to get,
![\frac{dV}{dt}=\frac{\pi}{16}h^2 \frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B%5Cpi%7D%7B16%7Dh%5E2%20%5Cfrac%7Bdh%7D%7Bdt%7D)
We were given that water is drained out of the tank at a rate of ![2cm^3/min](https://tex.z-dn.net/?f=2cm%5E3%2Fmin)
This implies that
.
Since we want to determine the rate at which the depth of the water is changing at the instance when the water in the tank is 8cm deep, it means
.
We substitute this values to obtain,
![-2=\frac{\pi}{16}(8)^2 \frac{dh}{dt}](https://tex.z-dn.net/?f=-2%3D%5Cfrac%7B%5Cpi%7D%7B16%7D%288%29%5E2%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![\Rightarrow -2=4\pi \frac{dh}{dt}](https://tex.z-dn.net/?f=%5CRightarrow%20-2%3D4%5Cpi%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![\Rightarrow -1=2\pi \frac{dh}{dt}](https://tex.z-dn.net/?f=%5CRightarrow%20-1%3D2%5Cpi%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dh}{dt}=-\frac{1}{2\pi}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D-%5Cfrac%7B1%7D%7B2%5Cpi%7D)
I believe that it is a concurrent power