Answer:
yooooooo yankee with no brim ooooOOOoOOOO
Hi there!
a.
To find the total amount of people that have ENTERED by t = 20, we must take the integral of the appropriate function.

Evaluate using a calculator:

b.
To solve, we can find the total amount of people that have entered of the interval and subtract the total amount of people that have left from this value.
In other terms:

We can evaluate using a calculator (math-9 on T1-84):


c.
If:

Then:

Evaluate at t = 20:


This means that at t = 20, there is a <u>NET DECREASE</u> of people at the movie theater of around 20.823 (21) people per hour.
d.
To find the maximum, we must use the first-derivative test.
Set S(t) - R(t) equal to 0:

Graph the function with a graphing calculator and set the function equal to y = 0:
According to the graph, the graph of the first derivative changes from POSITIVE to NEGATIVE at t ≈ 17.78 hours, so there is a MAXIMUM at this value.
<u>Thus, at t = 17.78 hours, the amount of people at the movie theater is a MAXIMUM.</u>
The first thing you have to realize is that
tangent is the
slope of a curve on a given point. You can solve for the slope by finding the derivative of the given function. So:

Next use
product rule (I recommend watching videos if you're confused):
![= [sin(x)] + [x*cos(x)]](https://tex.z-dn.net/?f=%3D%20%5Bsin%28x%29%5D%20%2B%20%5Bx%2Acos%28x%29%5D)
Next substitute you x-value (π/2) into your derivative:
![= [sin( \frac{ \pi}{2} )] +[ \frac{\pi}{2}*cos( \frac{\pi}{2})]](https://tex.z-dn.net/?f=%3D%20%5Bsin%28%20%20%5Cfrac%7B%20%5Cpi%7D%7B2%7D%20%29%5D%20%2B%5B%20%5Cfrac%7B%5Cpi%7D%7B2%7D%2Acos%28%20%5Cfrac%7B%5Cpi%7D%7B2%7D%29%5D%20%20)


So our slope at π/2 is 1. Next we use our slope-form and substitute our given value and solve for y-intercept (algebra-stuff)


So we get our equation:

So our answer is E
Feel free to ask any questions.
Hopes this helps!
__Dry and Liquid Measurements__
Explanation:
Density is defined as a material per unit volume of the material.
The determination of the density of a liquid with an aerometer is based on the principle of Archimedes' law: "Any object that is immersed in a liquid will experience a lift which is equal to the weight of the liquid being moved".
The aerometer is in the form of a hollow cylinder, so that the aerometer can be immersed in the right position (the scale is immersed in liquid), then the aerometer is filled with Pb grains. The scale on the aerometer shows the density of the liquid, the smaller the density of the liquid, the deeper the aerometer will be. Therefore the aerometer scale shows an increasing number from top to bottom.