ADVANCED EXERCISES - Modeling Real World Problems
(1) A Norman window has the shape of a rectangle with a semicircle on top. If the perimeter of the window is 30 m, express the area A of the window as a function of the width x of the window.
(2) A box with an open top is to be constructed from a rectangular piece of cardboard by cutting out equal squares of side x at each corner and then folding up the sides. If the dimensions of the cardboard are 12 by 20, express the volume V of the box as a function of x.
(3) (a) Given a one-litre cylinder can, express its surface area as a function of its radius. (b) Given a cylinder can of volume V, express its surface area as a function of its radius.
(4) Alphonse, Olaf, and Mortimer have $51 together. Find out how much each has if Alphonse has one half what Olaf and Mortimer have combined and Morimer has $3 more than Alphonse.
