Use definition 7.1.1. definition 7.1.1 laplace transform let f be a function defined for t ≥ 0. then the integral ℒ{f(t)} = ∞ e−stf(t) dt 0 is said to be the laplace transform of f, provided that the integral converges. find ℒ{f(t)}. (write your answer as a function of s.)

Step-by-step explanation:

Let be defined for .

The Laplace transform of is an integral transform given by the Laplace integral:

, provided that this improper integral exists.

If we let , then

Recall that:

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.

16 would be your answer