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


(5,4)
On a system of 2 perpendicular axis with O as origine, the pair (5,4) means:
5 is the distance from the origin O and situated on x-axis (on the right of O)
4 is the distance from the origin O and situated on y-axis (above O)
Then the pair (5,4) is situated in the 1st Quadrant
Answer:
Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value.
Step-by-step explanation:
Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.
Answer:
This can be solved by using the empirical rule for a normal distribution.
Step-by-step explanation:
A. The number of skateboards given is one standard deviation above the mean. Approximately 68% of the data points lie within the range plus and minus one standard deviation of the mean. Therefore the required percentage is:
68 + 16 = 84%.
B. The given number of skateboards is two standard deviations above the mean. Approximately 95% of the data points lie within the range plus and minus two standard deviations of the mean. Therefore the required percentage is:
5/2 = 2.5%
C.The given number of skateboards is one standard deviations below the mean. Therefore the required percentage is:
16%.
Answer:
4
Step-by-step explanation:
ok