You have 40 inches of wire and you want to use two sections of it to form the outlines of a square and a circle. how much of it should be used for the square, and how much for the circle, so that there is a minimum amount of area for the combined shapes?

22.404 inches of the wire should be used for square

17.596 inches of the wire should be used for the circle.

Step-by-step explanation:

We're forming one square and one circle from a 40 inch long wire.

Hence we know that the sum of the perimeters(P) of the two shapes will be 40.

let,

It is also stated that the combined area of both shapes should be minimum.

Hence, we can formulate the sum of the areas(A) similarly to how we did for perimeters.

is the combined area

this is a function y(x,r). In order to find the minimum combined area, we need to differentiate the function. But first we need to replace one of the variables 'x' or 'r' so that the function 'y' only has one variable.

we can substitute this in y

now substitute

we can use this to find 'r'.

these are the dimensions of the two shapes for which the combined areas will be minimum.

we can find how much of the wire segments will be used for each of the shapes.

22.404 inches of the wire should be used for square

17.596 inches of the wire should be used for the circle.

step-by-step explanation:

what are the statements? and what do you mean by "216 2 1 6"?

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.