A box of fixed volume, V, has a square base with side length, a.?

Question

A box of fixed volume, V, has a square base with side length, a.

(a) Write a formula for the height, h, of the box as a function of a. Note: V will also be in your answer.

(b) is h(a) an increasing or decreasing function of a?

Answer 1

Very easy. Figure out for yourself; your mind will be better for it.

Answer 2

(a) h = square root of(v/a)

(b) Don't understand.  

Answer 3

H = V/L/W

?

Answer 4

a)

height with respect to length = Volume / length squared

h(a) =V/ a^2

because we know V=Lwh and this is a box with a square base so.....

V=LLh=L^2*h

to solve for height, rearrange --> h=V/L^2

(I used capital 'L' because lowercase makes it look like '1')

b)

it is a decreasing function.

looks very similar to function f(x) = 1/x^2  ; if you don't understand f(x) then other way of saying it is

y= 1/(x^2)

f(x) really just means : function with respect to x, this represents the y value.

-------> just check it out on free online graphing calculator. You can find it in google to see what graph looks like.

It's called a rational function because the unknown variable x is at the bottom. That is assuming 1 = the volume. Since your question is asking h(a) then a, being the side length is the variable (in other words, x), that means that the volume is fixed and known. Making it a rational function because variable is at the bottom.

Hope this clarifies this question for you.

Answer 5

I don't know the answer, but that other guy that answered is a douche bag.