Let h = height of the box,
x = side length of the base.
Volume of the box is

.
So

Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is


The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.

![4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86](https://tex.z-dn.net/?f=%204x%20%3D%20%5Cfrac%7B460%7D%7B%20x%5E%7B2%7D%20%7D%20%20%5C%5C%20%204x%5E%7B3%7D%20%3D%20460%20%20%5C%5C%20x%5E%7B3%7D%20%3D%20115%20%20%5C%5C%20x%20%3D%20%20%5Csqrt%5B3%5D%7B115%7D%20%3D%204.86%20)
Then

So the box is 4.86 in. wide and 4.87 in. high.
Answer:
half a sphere is called a hemisphere
Answer:
m = 3/5
Step-by-step explanation:
use the formula so m = -5 - -2 / 5 - 10 , so m = -5+2 / -5
m = -3/-5 so m = 3/5
For part (a), you have


If

, then

.
If

, then

.
So,

For part (b), since the degrees of the numerator and denominator are the same, you first need to find the quotient and remainder upon division.

In the remainder term, the denominator

can't be factorized into linear components with real coefficients, since the discriminant is negative

. However, you can still factorized over the complex numbers, so a partial fraction decomposition in terms of complexes does exist.



Then you have


When

, you have



When

, you have



So, you could write

but that may or may not be considered acceptable by that webpage.