Assume that you want to construct a box with a square base (closed top) and a volume of 1000 cm3 . Find the dimensions of the box to minimize the surface area of the box.

Step-by-step explanation:

The Volume of a box with a square base  

x by  x  cm and height  h  cm is  

V =x^2h

The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.

The surface area of the box described is  

A = x ^2 +4 x h

We need  

A  as a function of  x  alone, so we'll use the fact that

V= x^2h = 1000 cm^3

This imples  

This makes

Differentiating A w.r.t. x

Now, A'=0

Therefore, minimum value x =

answer: 26

step-by-step explanation:

well, michelle wanted to measure the height of her school's flagpole she placed a mirror on the ground 48 feet from the flagpole then walk backwards until she was able to see the top of the pole in the mirror her eyes were 5 feet above the ground and she was 12 ft from the mirror using similar triangles find the height of the flagpole to the nearest tenth of a foot find the geometric mean of them pair of numbers. its easy math