Acardboard box without a top is to have volume 62500 cubic cm. find the dimensions which minimize the amount of material used.

A cardboard box without a lid is to have a volume of 32,000 cubic cm. Find the dimensions that minimize the amount of cardboard used

. ans: base 40 x 40, height = 20  

Solution:  

The typical box might look like the one below  

where . In addition we have xyz = 32000 ,so we need to minimize .  

We have,  

From the geometry of the problem  so y = x. So  or x = 40.  

Finally, y = x = 40 and z = 32000/(xy)=20.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

e

step-by-step explanation:

an equation by definition has to have two or more variables (x and 2 in this case)