Download MAT170 Review Problems for Test 1

MAT117 Review Problems for Exam 2
Combining functions
1. A firm is considering a new product. The accounting department estimates that the total cost, C(x), of
producing x units will be C(x) = 65x + 3500. The sales department estimates the revenue, R(x), from
selling x units will be R(x) = 85x, but no more than 600 units can be sold at that price.
Find and interpret (R – C)(600).
2. A firm is considering a new product. The accounting department estimates that the total cost, C(x), of
producing x units will be C(x) = 85x + 2750. The sales department estimates the revenue, R(x), from
selling x units will be R(x) = 75x, but no more than 550 units can be sold at that price.
Find and interpret (R – C)(550).
Linear functions and their applications
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3. The price p and the quantity x sold of a certain product obey the demand equation: p   x  150 What is the
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revenue when 300 units are sold?
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4. The price p and the quantity x sold of a certain product obey the demand equation: p   x  300 What is the
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revenue when 250 units are sold?
5. The revenue for a firm is given by R( x)  8 x and the cost is given by C ( x)  4.5 x  17500 , where x is the
number of units produced and sold. Find the break-even point for the firm.
6. The revenue for a firm is given by R ( x)  12 x and the cost is given by C ( x)  9 x  30000 , where x is the
number of units produced and sold. Find the break-even point for the firm.
7. The data listed in the following table represents the appearance temperature vs. the relative humidity in a
room.
Relative Humidity (%) x Apparent Temperature y
10
65
30
68
50
71
70
73
a. Use your calculator to find (linear regression) the line of best fit to the data
b. Using the regression in part (a) approximate the room temperature when the relative Humidity is 80%.
8. The aver life expectancy in the United States has been rising steadily over the past few decades, as shown in
the table below.
Year (after 1900)
Life Expectancy
60
69.79
70
70.8
80
73.7
90
75.4
a. Use your calculator to find (linear regression) the line of best fit to the data
b. Using the regression in part (a) approximate the life expectancy in the year 1995.
Factoring Polynomials
9. Factor each polynomial;
a. 3x 2  10 x  8
b. 2 x 2  5 x  3
10. Factor each polynomial;
a. 6 x3  9 x 2  4 x  6
11. Factor each polynomial:
a. x 3  125
b. 3x3  6 x 2  x  2
c. x 3  x 2  16 x  16
b. x  3  64
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12. Factor each polynomial:
a. 6 x 3  48x 2  90 x
b. x 7  x 4
13. Factor each polynomial:
a. x 4  81
b. 2  7 x 2  4 x 4
14. Factor each polynomial:
a. 35 x  6  3x  5  35 x  6  5
b. 65 x  4  56 x  1  5 x  4  56 x  1  6
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Solve Equations Radical in Form
15. Solve the Radical Equations
a.
5x 2  2 x  1
16. Solve the Equations
a. 12 x 4  x 2  1  0
b.
2x  7 -
x  7 1
b. x  2  13x  2  42  0
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2
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MAT 117 Test 2 Review Answers
Note: There is a reasonable assumption that most of these answers are not incorrect.
1. $8500 means profit, income exceeds cost
2. –$8250 means loss, cost exceeds income
3. $15,000
4. $62,500
5. x = 5000
6. x = 10,000
7. a. y  0.135 x  63.85 ; b. 74.65
8. a. y  0.1973x  57.625 ; b. 76.37
9. a. (3x – 4)(x – 2) b. (x + 1)(2x + 3)
10. a. (3x 2  2)(2 x  3) b. (3x 2  1)( x  2)
c. ( x  1)( x  4)( x  4)
11. a ( x  5)( x 2  5 x  25)
b. ( x  1)( x 2  10x  37)
12. a. 6x ( x  5)( x  3)
b. ( x 4 )( x  1)( x 2  x  1)
13. a. ( x  3)( x  3)( x 2  9)
b. (1  2 x)(1  2 x)(2  x 2 )
14. a. 3(5x  6)(20x  31)
b. 30(5 x  4)(6 x  1) 4 11x  3
15. a x = 2, -16
b. x=9
16. a x 
3
3
,
3
3
b. x= -8, -9