The bar graph shows the population of the United States in millions for seven selected years. Here are two function that model the data: M ( x ) = 1.48 x + 115.1 Male U .S .pepolalias, M ( x ) , is aillises, x y e a r a f t e r 1985 F ( x ) = 1.44 x + 120.9 Female U .S .pepolalias, F ( x ) , is aillises, x y e a r a f t e r 1985 Use the functions to solve Exercises 97-98. a. Write a function that models the difference between the female U.S. population and the male U.S. population for the years shown in the bar graph. b. Use the function from par (a) to find how many more women than men there were in the U.S. population in 2010. c. Does the result in part (b) overestimate or underestimate the actual difference between the female and male population in 2010 shown by the bar graph? By how much?
The bar graph shows the population of the United States in millions for seven selected years. Here are two function that model the data: M ( x ) = 1.48 x + 115.1 Male U .S .pepolalias, M ( x ) , is aillises, x y e a r a f t e r 1985 F ( x ) = 1.44 x + 120.9 Female U .S .pepolalias, F ( x ) , is aillises, x y e a r a f t e r 1985 Use the functions to solve Exercises 97-98. a. Write a function that models the difference between the female U.S. population and the male U.S. population for the years shown in the bar graph. b. Use the function from par (a) to find how many more women than men there were in the U.S. population in 2010. c. Does the result in part (b) overestimate or underestimate the actual difference between the female and male population in 2010 shown by the bar graph? By how much?
Solution Summary: The author calculates a function that describes the difference between the female and male population when x years have passed from 1985.
The bar graph shows the population of the United States in millions for seven selected years.
Here are two function that model the data:
M
(
x
)
=
1.48
x
+
115.1
Male
U
.S
.pepolalias,
M
(
x
)
,
is aillises,
x
y
e
a
r
a
f
t
e
r
1985
F
(
x
)
=
1.44
x
+
120.9
Female
U
.S
.pepolalias,
F
(
x
)
,
is aillises,
x
y
e
a
r
a
f
t
e
r
1985
Use the functions to solve Exercises 97-98.
a. Write a function that models the difference between the female U.S. population and the male U.S. population for the years shown in the bar graph.
b. Use the function from par (a) to find how many more women than men there were in the U.S. population in 2010.
c. Does the result in part (b) overestimate or underestimate the actual difference between the female and male population in 2010 shown by the bar graph? By how much?
Rylee's car is stuck in the mud. Roman and Shanice come along in a truck to help pull her out. They attach
one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck
starts to pull. Meanwhile, Roman and Shanice get behind the car and push. The truck generates a
horizontal force of 377 lb on the car. Roman and Shanice are pushing at a slight upward angle and generate
a force of 119 lb on the car. These forces can be represented by vectors, as shown in the figure below. The
angle between these vectors is 20.2°. Find the resultant force (the vector sum), then give its magnitude
and its direction angle from the positive x-axis.
119 lb
20.2°
377 lb
An airplane flies due west at an airspeed of 428 mph. The wind blows in the direction of 41° south of west
at 50 mph. What is the ground speed of the airplane? What is the bearing of the airplane?
A vector with magnitude 5 points in a direction 190 degrees counterclockwise from the positive x axis.
Write the vector in component form, and show your answers accurate to 3 decimal places.
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