Answer:
--- Radius
--- Height
Explanation:
Given
Object: Can (Cylinder)

Required
Maximize the volume
The surface area is:

Substitute 517.8 for S.A

Divide through by 2

Factorize:

Divide through by 

Make h the subject
--- (1)
Volume (V) is calculated as:

Substitute (1) for h

Open Bracket

Differentiate V

Set V' to 0

Collect Like Terms

Divide through by 3

Divide through by 



Take square root of both sides


Recall that:

Substitute 5.24 for r





Hence, the dimension that maximize the volume is:
--- Radius
--- Height
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>
Yuhhhhh honor is something that you cant get on brainly lol