Posted by **Amie** on Monday, September 13, 2010 at 7:28pm.

1) A box with a square base has a total surface area of 12m^2. Express the volume of the box as a function of the base edge.

2) A 10 foot tall lamppost causes a child 4 feet tall to cast a shadow of x feet on the ground. If the distance along the ground from the child to the lamppost is d meters, express x as a function.

- Math - function problems -
**Reiny**, Monday, September 13, 2010 at 7:38pm
let the side of the square base be x m

let the height be y m

I will assume the box has a lid so the surface area is made up of 2x^ + 4xy

then 2x^2 + 4xy = 12

4xy = 12-2x^2

y = (6-x^2)/(2x)

volume = x^2y

= x^2(6-x^2)/(2x)

= x(6-x^2)/2

for the second, you have similar triangles, so set up a ratio

4/x = 10/(x+d)

10x = 4x + 4d

take it from there

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