Fall ’06 - MATH 40 - CHAPTER 4
Show your work for credit.
Write all responses on separate paper.
1. Which
one of the following graphs represents
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a. |
b.
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c.
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d. |
e.
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f.
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2. Which
one of the following equations has intercepts at ?
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b. |
c.
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d. |
e. |
f.
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3. Which
one of the following gives an equation for the parabola shown?
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a.
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b.
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c.
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d.
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4. The
parabola whose coefficients fit the system of
equations at right contains which one of the following sets of
points?
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a. |
b. |
c. |
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d. |
e. |
f.
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5. Which
one of the following equations results from combining the equations in the
system ?
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a.
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b. |
c.
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d.
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e. |
f.
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6. Which
of the following intervals gives the solution to the inequality ?
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a.
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b.
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c.
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d.
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e.
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f.
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For problems 7-8, find the coordinates of the intercepts and the vertex of the parabola whose equation is given, then carefully sketch a graph showing these features.
7.
8.
For problems 9-10, find the coordinates of intersection for
the two curves and illustrate these by graphing the two curves.
9. and
10. and
In problems 11-13, write an equation for the parabola with x-intercepts
at which also passes through the given
point. Sketch a graph for each.
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11.
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12. |
13. |
14. Solve the system of equations algebraically and verify your solutions with a graph.
15. Solve the
inequality: . Write the solution in interval notation.
16. Solve the
inequality: . Write the solution in interval notation.
17. The area of
an annulus is found by subtracting the area of the inner circle from the area
of the outer circle: . (See the diagram at right.) Show that if the radius of the outer circle
is 1 more than 2 times the radius of the inner circle, then the area of the
annulus is
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What value of r yields A = 4?
18. The difference of twice one number and three times another number is 24. Find two such numbers so to minimize their product.
19. Salt water
is entering a tank full of water at the same time that the water is draining
out of the tank. The water is draining
out of the tank at a faster rate than the water is coming in so that the total
amount of salt in the tank, S, (measured in grams) at time t (measured
in hours) is given by the quadratic equation, . After how many hours is the amount of salt in
the tank at a maximum?
20. Set up a system of three equations in three unknowns to find the equation of a parabola through the points (1,43), (2,47) and (3,53). What are the coordinates of the vertex for this parabola? What value does it predict for y when x = 4?
21. Use a
calculator to approximate the positive solution for ,
accurate to the nearest thousandth.
22. Use a
calculator to approximate the solution interval to where r is positive. Round to the nearest thousandth included in
the interval.
23. Find the x-intercepts
of the parabola described by
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Temperature data for the years 1986 - 1990 taken from the middle of the Bay mouth (degrees Celsius) |
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Month |
1986 |
1987 |
1988 |
1989 |
1990 |
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Jan. |
5.28 |
5.52 |
1.56 |
5.76 |
5.28 |
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Feb. |
3.72 |
3.60 |
4.68 |
5.28 |
7.20 |
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Mar. |
5.76 |
5.28 |
7.20 |
5.88 |
9.72 |
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April |
10.90 |
9.84 |
11.40 |
11.50 |
12.50 |
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May |
15.80 |
17.60 |
17.30 |
16.70 |
18.40 |
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June |
21.60 |
20.40 |
21.80 |
22.50 |
21.20 |
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July |
25.60 |
24.40 |
24.70 |
26.00 |
25.10 |
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Aug. |
25.10 |
25.90 |
22.80 |
25.10 |
26.30 |
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Sept. |
22.40 |
24.40 |
21.60 |
22.70 |
24.00 |
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Oct. |
20.00 |
16.90 |
18.00 |
18.20 |
21.10 |
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Nov. |
13.40 |
12.60 |
12.80 |
13.60 |
13.00 |
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Dec. |
9.36 |
6.96 |
9.72 |
7.70 |
8.64 |
For problems 24 and 25, use the Chesapeake Bay temperature data tabulated at right.
24. Fit a parabola to the Jan., April and Aug. temperature data for 1989 in terms of the number of the number of months since Jan. 1989.
25. Fit a parabola to the the temperature during May in 1986, 1988 and 1990 in terms of years since May of 1986.