Answer:
61
Step-by-step explanation:
Let's find the points
and
.
We know that the
-coordinates of both are
.
So let's first solve:

Subtract 3 on both sides:

Simplify:

I'm going to use the quadratic formula,
, to solve.
We must first compare to the quadratic equation,
.






Since the distance between the points
and
is horizontal. We know this because they share the same
.This means we just need to find the positive difference between the
-values we found for the points of
and
.
So that is, the distance between
and
is:




If we compare this to
, we should see that:
.
So
.
Answer:
The slope is 5x and the y-intercept is -7
Step-by-step explanation:
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.
In a store, perhaps. People want it to be easy to shop, so it would be best for say, a top ramen package to be the same net weight as all the other top ramen packages. This makes it 1) easy to label and 2) easy to be confident buying, as it is exactly the same as all the others.