Download Homework section 2.2 In problems 1

Homework section 2.2
In problems 1-10, translate each sentence into a mathematical equation. Be sure to
define the meaning of all symbols.
1) The area of a circle is the product of the number
radius.
and the square of the
2) The circumference of a circle is the product of the number
radius.
and twice the
3) The area of a square is the square of the length of a side.
4) The perimeter of a square is four times the length of a side.
5) Force equals the product of mass and acceleration.
6) Pressure is force per unit area.
7) Work equals force times distance.
8) Kinetic energy is one-half the product of the mass and the square of the
velocity.
9) The total variable cost of manufacturing x dishwashers is $150 per
dishwasher times the number of dishwashers manufactured.
10)The total revenue derived from selling x dishwashers is $250 per dishwasher
times the number of dishwashers sold.
11)A total of $10,000 is to be divided between Sean and George with George to
receive $3000 less than Sean. How much will each receive?
12)Going into the final exam, which will count as two- thirds of the final grade,
Mike has test scores of 86, 80, 84, and 90. What score does Mike need on the
final exam in order to earn a B, which requires a score of 80? What does he
need to earn an A, which requires an average of 90?
13)The suggested list price of a new car is $12,000. The dealer’s cost is 85% of
the list. How much will you pay if the dealer is willing to accept $100 over the
cost for the car?
14)A wool suit, discounted by 30% for a clearance sale, has a price tag of $399.
What was the suits original price?
15)Wendy, a loan officer at a bank, has $1,000,000 to lend and is required to
obtain an average return of 18% per year. If she can lend at the rate of 19%
or at the rate of 16%, how much can she lend at the 16% rate and still meet
her requirement?
Principal
Rate %
Time
Interest
Lend at 18%
interest
Lend at 16%
interest
Total
16)A motorboat heads upstream on a river that has a current of 3 miles per
hour. The trip upstream takes 5 hours, and the return trip takes 2.5 hours.
What is the speed of the motorboat? (Assume that the motorboat maintains a
constant speed relative to the water.
V mph
Upstream
Downstream
t hrs
s
17)A Metra commuter train leaves union station in Chicago at 12 noon. Two
hours later, an Amtrak train leaves on the same track, traveling at an average
speed that is 50 miles per hour faster than the Metra train. At 3 pm, the
Amtrak train is 10 miles behind the commuter train. How fast is each going?
V mph
t hrs
s
Metra
Amtrack
18)Two cars enter the Florida Turnpike at Commercial Boulevard at 8:00 AM,
each heading for Wildwood. One car’s average speed is 10 miles per hour
more than the others. The faster car arrives at wildwood at 11:00AM, ½ hour
before the other car. What is the average speed of each car? How far did each
travel?
V mph
Slower Car
Faster Car
t hrs
s
19)How much water should be added to 1 gallon of pure anti freeze to obtain a
solution that is 60% antifreeze?
gallon solution
% antifreeze
gallon antifreeze
Antifreeze
Water
Mixture
20)The cooling system of a certain foreign made car has a capacity of 15 liters. If
the system is filled with a mixture that is 40 % antifreeze, how much of the
mixture should be drained and replaced by pure antifreeze so that the
system is filled with a solution that is 60% antifreeze?
liter solution
40% antifreeze sol.
Pure antifreeze
Mixture
% antifreeze
liter antifreeze
21)How much water must be evaporated from 32 ounces of a 4% salt solution to
make a 6% salt solution?
Oz. solution
% Salt
Oz Salt
4% salt solution
Water
Mixture
22)How much water must be evaporated from 240 gallons of a 3% salt solution
to produce a 5% salt solution?
Oz. solution
3% salt solution
Water
Mixture
% Salt
Oz Salt
23)The monthly payment p on a mortgage varied directly with the amount
borrowed B. if the monthly payment on a 15-year mortgage is $8.99 for every
$1000 borrowed, find a linear function that relates the monthly payment p to
the amount borrowed B for a mortgage with the same terms. Then, find the
monthly payment p when the amount borrowed B is $175,000.
In problems 24 – 29, examine the scatter diagram and determine whether the type
of relation, if any, that may exist is linear or nonlinear.
24)
25)
26)
27)
28)
29)
In problems 30, 31,
a) Draw a scatter diagram.
b) Select two points from the scatter diagram and find the equation of the line
containing the points selected.
c) Graph the line found in part (b) on the scatter diagram.
d) Use a graphing utility to find the line of best fit.
e) Use a graphing utility to graph the line of best fit on the scatter diagram.
30)
x
3
4
5
6
7
8
9
y
4
6
7
10
12
14
16
31)
x
-30
-27
-25
-20
-14
y
10
12
13
13
18
32) An economist wishes to estimate a linear function that relates per capita
consumption expenditures C and disposable income I. Both C and I are measured in
dollars. The following lowing data represent the per capita disposable income
(income after taxes) and per capita consumption in the United States for 1990 to
1998.
Year
Per Capita Disposable
income (I)
Per capita consumption
(C)
1990
15,695
14,547
1991
16,700
15,400
1992
17,346
16,035
1993
18,153
16,951
1994
19,711
18,419
1995
20,316
19,061
1996
21,127
19,938
1997
21,871
20,807
1998
22,212
21,385
Let I represent the independent variable and C the dependent variable.
a) Using a graphing utility to draw a scatter diagram.
b) Use a graphing utility to find the line of best fit to the data. Express the
solution using function notation.
c) Interpret the slope. The slope of this line is called the margin propensity to
consume.
d) Predict the per capita consumption in a year where disposable income is
$21,500.
e) What is the income in a year where consumption is $17,200?
33) The amount of money that a lending institution will allow you to borrow mainly
depends on the interest rate and your annual income. The following data represent
the annual income, I, required by a bank in order to lend L dollars at an interest rate
of 7.5% for 35 years.
Annual Income (I)
Loan Amount (L)
15,000
44,600
20,000
59,500
25,000
74,500
30,000
89,400
35,000
104,300
40,000
119,200
45,000
134,100
50,000
149,000
55,000
163,900
60,000
178,800
65,000
193,700
70,000
208,600
Let I represent the independent variable and L the dependent variable.
a) Use a graphing utility to draw a scatter diagram.
b) Use a graphing utility to find the line of best fit to the data.
c) Graph the line of best fit on the scatter diagram drawn in part (a).
d) Interpret the slope of the line of best fit.
e) Determine the loan amount that an individual would qualify for if her income
was $42,000.