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17 Questions on Mathematical Modeling - Test 4 | MAT 1101, Exams of Mathematics

Material Type: Exam; Professor: Molik; Class: MATHEMATICAL MODELING; Subject: Mathematics; University: Augusta Technical College; Term: Winter 2009;

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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Test 4 MAT 190 Winter 2009 Name ______________________
This test is take-home, so you may use your notes, book, Excel, MathGV, etc. This test is due back to me
at the beginning of class on Tuesday, March 10, 2009. Late tests will not be accepted. Donโ€™t forget to
simplify all of your answers and attach your work!
1. Add:
x
x
2
4
8+
โˆ’
2. Subtract:
10
1
2
6
โˆ’
โˆ’
+
x
x
)4(
810
โˆ’
โˆ’
xx
x )10)(2(
625
โˆ’+
โˆ’
xx
x
3. Find the vertices of the functions: 4. Graph the following function: f(x) = x2 + 6x + 3
a) f(x) = 2x2 โ€“ 16x + 35
(4, 3)
b) f(x) = โ€“9.8(x โ€“ 1.3)2 + 12.1
(1.3, 12.1)
5. Solve for x, if possible: 4x2 = 5x + 12 6. Graph the following function: f(x) = 2(x โ€“ 2)2 โ€“ 3
2.4664, -1.2164
Given f(x) = 6x โ€“ 3 and g(x) = 2x + 5 , find the following.
7. (f โ€“ g)(x) 8. (f โ€ข g)(x) 9. (f โ—ฆ g)(x) 10. (g โ—ฆ g)(x)
4x โ€“ 8 12x2 + 24x โ€“ 15 12x + 27 4x + 15
11. The cost of producing โ€œxโ€ DVDs can be described by the function C(x) = 1.5x + 6000. The revenue can be
described by the function R(x) = 12x. Assume that the number of DVDs produced and sold is the same.
a) What is the function that represents the profit? b) How many DVDs need to be sold to break even?
P(x) = 10.5x โ€“ 6000 572 DVDs
x y
-5
-2
-4
-5
-3
-6
-2
-5
-1
-2
x y
0 5
1 -1
2 -3
3 -1
4 5
pf2

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Download 17 Questions on Mathematical Modeling - Test 4 | MAT 1101 and more Exams Mathematics in PDF only on Docsity!

Test 4 MAT 190 Winter 2009 Name ______________________

This test is take-home, so you may use your notes, book, Excel, MathGV, etc. This test is due back to me at the beginning of class on Tuesday, March 10, 2009. Late tests will not be accepted. Donโ€™t forget to simplify all of your answers and attach your work!

  1. Add: x x
  1. Subtract: 10

x + x

x x

x ( 2 )( 10 )

x x

x

  1. Find the vertices of the functions: 4. Graph the following function: f(x) = x^2 + 6x + 3 a) f(x) = 2x^2 โ€“ 16x + 35

(4, 3)

b) f(x) = โ€“9.8(x โ€“ 1.3)^2 + 12.

(1.3, 12.1)

  1. Solve for x, if possible: 4x^2 = 5x + 12 6. Graph the following function: f(x) = 2(x โ€“ 2)^2 โ€“ 3

2.4664, -1.

Given f(x) = 6x โ€“ 3 and g(x) = 2x + 5 , find the following.

  1. (f โ€“ g)(x) 8. (f โ€ข g)(x) 9. (f โ—ฆ g)(x) 10. (g โ—ฆ g)(x)

4x โ€“ 8 12x^2 + 24x โ€“ 15 12x + 27 4x + 15

  1. The cost of producing โ€œxโ€ DVDs can be described by the function C(x) = 1.5x + 6000. The revenue can be described by the function R(x) = 12x. Assume that the number of DVDs produced and sold is the same. a) What is the function that represents the profit? b) How many DVDs need to be sold to break even?

P(x) = 10.5x โ€“ 6000 572 DVDs

x y -5 - -4 - -3 - -2 - -1 -

x y 0 5 1 - 2 - 3 - 4 5

  1. The path of a hit baseball is given by the function h(x) = -0.0032x^2 + x + 3 where h(x) represents the height of the baseball above the ground in feet and x is the distance from home plate. a) What is the maximum height reached by the ball? b) How far away from home plate does the ball land?

81.125 feet 315.47 feet

  1. Find the equation of the parabola having 14. A bulletin board is 3 feet longer than it is high. The a vertex of (-1, 2) and passing through (0, 5). bulletin board has 180 ft^2 of decorating area. What are the dimensions of the bulletin board?

f(x) = 3(x + 1)^2 + 2 12 feet by 15 feet

  1. A construction worker is working 240 feet up the side of a building when he accidentally drops a wrench and immediately shouting out a warning to those on the ground. Use h(t) = -16t^2 + vot + ho to represent the equation that represents the height of the function after t seconds. a) Find h(t). b) How long will it take the c) If sound travels at 1100 ft/sec, how wrench to hit the ground? long will the people on the ground have to respond to move out of the way? h(t) = -16t^2 + 240 โ‰ˆ3.873 seconds

3.655 seconds

  1. The population of a certain city can be represented by p(x) = 6.943x^2 + 6183.3, where x represents the year after 1800. What is the expected population in the year 2009?

309,460 people

  1. Given the graph of the quadratic equation at the right, find:

a) the vertex of the equation _____(4, 6)______

b) f(3) = 4

c) the equation of the parabola __y = -2(x โ€“ 4)^2 + 6 ___