Chapter 9 - XYZ Custom Plus

9.6 Problem Set
567
Applying the Concepts
73. Digital Video The most popular video download of all
time was a Star Wars movie trailer. The video was
compressed so it would be small enough for people to
download over the Internet. A formula for estimating
the size, in kilobytes, of a compressed video is
S 5
height ? width ? fps ? time
}}}
35,000
where height and width are in pixels, fps is the number
of frames per second the video is to play (television
plays at 30 fps), and time is given in seconds.
a. Estimate the size in kilobytes of the Star Wars trailer
that has a height of 480
pixels, has a width of
216 pixels, plays at 30
fps, and runs for 150
seconds.
b. Estimate the size in
kilobytes of the Star
Wars trailer that has
a height of 320 pixels,
has a width of 144 pixels,
plays at 15 fps, and
runs for 150 seconds.
74. Vehicle Weight If you can measure the area that the tires
on your car contact the ground, and you know the air
pressure in the tires, then you can estimate the weight
of your car, in pounds, with the following formula:
W 5 APN
where W is the vehicle’s weight in pounds, A is the average
tire contact area with a hard surface in square
inches, P is the air pressure in the tires in pounds per
square inch (psi, or lb/in 2 ), and N is the number of
tires.
Tire Pressure P
Contact Area A
a. What is the approximate weight of a car if the average
tire contact area is a rectangle 6 inches by 5
inches and if the air pressure in the tires is 30 psi?
b. What is the approximate weight of a car if the average
tire contact area is a rectangle 5 inches by 4
inches, and the tire pressure is 30 psi?
75. Temperature The chart shows the temperatures for some
of the world’s hottest places.
Heating Up
160
140
76. Fermat’s Last Theorem The postage stamp shows Fermat’s
last theorem, which states that if n is an integer greater
than 2, then there are no positive integers x, y, and z
that will make the formula x n 1 y n 5 z n true.
137˚F Al’Aziziyah, Libya
134˚F Greenland Ranch, Death Valley, United States
131˚F Ghudamis, Libya
131˚F Kebili, Tunisia
130˚F Tombouctou, Mali
120
100
80
60
Source: Aneki.com
40
a. Use the formula C 5 } 5 }(F 2 32) to find the temperature
in Celsius for
9
Al’Aziziyah.
b. Use the formula K 5 } 5 }(F 2 32) 1 273 to find the temperature
in Ghudamis, Libya, in
9
Kelvin.
Use the formula x n 1 y n 5 z n to
a. Find x if n 5 1, y 5 7, and z 5 15.
b. Find y if n 5 1, x 5 23, and z 5 37.