Answer:
![\huge\boxed{\sqrt[3]{c^4}=c^\frac{4}{3}}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%5Csqrt%5B3%5D%7Bc%5E4%7D%3Dc%5E%5Cfrac%7B4%7D%7B3%7D%7D)
Step-by-step explanation:
![\sqrt[n]{a^m}=a^\frac{m}{n}\\\\\text{therefore}\\\\\sqrt[3]{c^4}=c^\frac{4}{3}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%5Em%7D%3Da%5E%5Cfrac%7Bm%7D%7Bn%7D%5C%5C%5C%5C%5Ctext%7Btherefore%7D%5C%5C%5C%5C%5Csqrt%5B3%5D%7Bc%5E4%7D%3Dc%5E%5Cfrac%7B4%7D%7B3%7D)
Answer:



Step-by-step explanation:
<u>Optimizing With Derivatives
</u>
The procedure to optimize a function (find its maximum or minimum) consists in
:
- Produce a function which depends on only one variable
- Compute the first derivative and set it equal to 0
- Find the values for the variable, called critical points
- Compute the second derivative
- Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum
We know a cylinder has a volume of 4
. The volume of a cylinder is given by

Equating it to 4

Let's solve for h

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

Replacing the formula of h

Simplifying

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

Rearranging

Solving for r

![\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%7D%7B%5Cpi%20%7D%7D%5Capprox%201.084%5C%20feet)
Computing h

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.
The minimum area is


Answer:
What are some other numbers of magazine subscriptions Andre could have sold and still reached his goal?
Write an inequality expressing that Andre wants to make at least $68.
Write an inequality to describe the number of subscriptions Andre must sell to reach his goal.
Answer:
B
Step-by-step explanation:
B is in Quadrant III.
B is the answer.