Answer:
The rate of change of the height is 0.021 meters per minute
Step-by-step explanation:
From the formula

Differentiate the equation with respect to time t, such that


To differentiate the product,
Let r² = u, so that

Then, using product rule
![\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%5Bu%5Cfrac%7Bdh%7D%7Bdt%7D%20%2B%20h%5Cfrac%7Bdu%7D%7Bdt%7D%5D)
Since 
Then, 
Using the Chain's rule

∴ ![\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%5Bu%5Cfrac%7Bdh%7D%7Bdt%7D%20%2B%20h%28%5Cfrac%7Bdu%7D%7Bdr%7D%20%5Ctimes%20%5Cfrac%7Bdr%7D%7Bdt%7D%29%5D)
Then,
![\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%5Br%5E%7B2%7D%20%5Cfrac%7Bdh%7D%7Bdt%7D%20%2B%20h%282r%29%20%5Cfrac%7Bdr%7D%7Bdt%7D%5D)
Now,
From the question


At the instant when 
and 
We will determine the value of h, using





Now, Putting the parameters into the equation
![\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%5Br%5E%7B2%7D%20%5Cfrac%7Bdh%7D%7Bdt%7D%20%2B%20h%282r%29%20%5Cfrac%7Bdr%7D%7Bdt%7D%5D)
![236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]](https://tex.z-dn.net/?f=236%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%5B%2899%29%5E%7B2%7D%20%5Cfrac%7Bdh%7D%7Bdt%7D%20%2B%20%28%5Cfrac%7B20%7D%7B363%5Cpi%20%7D%29%20%282%2899%29%29%20%287%29%5D)
![236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]](https://tex.z-dn.net/?f=236%20%5Ctimes%203%20%3D%20%5Cpi%20%5B9801%20%5Cfrac%7Bdh%7D%7Bdt%7D%20%2B%20%28%5Cfrac%7B20%7D%7B363%5Cpi%20%7D%29%201386%5D)






Hence, the rate of change of the height is 0.021 meters per minute.
Think of sea level as 0 on number line
-13 + 6 - 15
Answer:
y = -2x + 5
Step-by-step explanation:
Slope-intercept form: y = mx + b
The slope of the line, m, is -2 because the line shows a negative trend and moves right 1 unit every time a point moves down 2 units.
The y-intercept, b, is 5 because the line crosses that number once on the y-axis.
Use the distance formula

Input corresponding numbers

Solve



So, the distance between the points given is 5
Answer:
3 3/4
Step-by-step explanation:
4*3 = 12 and 15-12 = 3
So whole number is 3, and the numerator is 3 the denominator stays the same.