Solve each problem. Round answers to the nearest tenth, as necessary.
564 CHAPTER 9 Quadratic Equations, Inequalities, and Functions
32.A large machine requires a part in the
shape of a right triangle with a hy-
potenuse 9 ft less than twice the length
of the longer leg. The shorter leg must
be the length of the longer leg. Find the
lengths of the three sides of the part.
33.A square has an area of 256. If the
same amount is removed from one di-
mension and added to the other, the re-
sulting rectangle has an area 16 less.
Find the dimensions of the rectangle.
cm^2
cm^2
3
4
x^34 x
x
x
34.Allen Moser wants to buy a mat for a photograph that measures 14 in.
by 20 in. He wants to have an even border around the picture when it
is mounted on the mat. If the area of the mat he chooses is 352
how wide will the border be?
35.If a square piece of cardboard has 3-in. squares cut from its corners and then has the flaps
folded up to form an open-top box, the volume of the box is given by the formula
, where xis the length of each side of the original piece of cardboard in
inches. What original length would yield a box with volume 432?
36.Wachovia Center Tower in Raleigh, North Carolina, is 400 ft high. Suppose that a ball is
projected upward from the top of the tower, and its position in feet above the ground is
given by the quadratic function defined by
where tis the number of seconds elapsed. How long will it take for the ball to reach a
height of 200 ft above the ground? (Source: World Almanac and Book of Facts.)
37.A searchlight moves horizontally back and forth along a
wall with the distance of the light from a starting point at
tminutes given by the quadratic function defined by
How long will it take before the light returns to the starting
point?
38.Internet publishing and broadcasting revenue in
the United States (in millions of dollars) for the
years 2004 –2007 is shown in the graph and can
be modeled by the quadratic function defined by
In the model, represents 2004,
represents 2005, and so on.
(a)Use the model to approximate revenue
from Internet publishing and broadcasting
in 2007 to the nearest million dollars. How
does this result compare to the number
suggested by the graph?
(b)Based on the model, in what year did the revenue from Internet publishing and
broadcasting reach $14,000 million ($14 billion)? (Round down for the year.) How
does this result compare to the number shown in the graph?
x= 4 x= 5
ƒ 1 x 2 =230.5x^2 - 252.9x+5987.
ƒ 1 t 2 = 100 t^2 - 300 t.
ƒ 1 t 2 =- 16 t^2 + 45 t+400,
in.^3
V= 31 x- 622
in.^2 ,
14 in.
20 in.
Wall
Starting
point
Light
Internet Publishing and
Broadcasting Revenue
Source: U.S. Census Bureau.
Year
Millions of Dollars
16,000
8000
12,000
4000
0
2004 2005 2006 2007
