Precalculus
Name:
HW#9
Word problem practice. Only #1 and #2 require a graphing calculator.
1) An open box with a square base is required to have a volume of 25 cubic inches. Write a function that
expresses the amount A of material used to make the box in terms of the length x of a side of the square base.
What are the dimensions of the box that requires the least amount of material?
2) Let P = (x,y) be a point of the graph of y  x  1. Draw this function.
a) Express the distance from P to the origin as a function of x.
2
b) What is the distance if x  0.
c) What is the distance if x  4
d) Use the graphing calculator to find the x value that will be the shortest distance.
3) A rectangular playground is to be fenced off and divided in two by another fence parallel to the width of the
playground. 600 feet of fencing is to be used. Let x be the width of the rectangle.
a) What is the domain?
b) Find the area when the width is 75 feet.
c) Find the dimensions that maximize the total enclosed area.
x
d) What is the max area?
3
4) A right triangle has one vertex on the graph of y  x  1 at (x,y) another at (1,0) and a third on the x-axis at
(x,0) for x>1.
a) Sketch the function and a triangle on the graph.
b) Express the area of the triangle as a function of x.
Bonus* Express the perimeter of the triangle as a function of x.