the cost in millions of dollars to manufacture x hundred thousand units of a product per month is...
TRANSCRIPT
1
The cost in millions of dollars to manufacture x hundred thousand units of a product per month is given in the table.
a. Create a scatterplot of the data in the table.
8.1-1
x (100,000 units) 0 1 2 3 4 5 6 7 8 9 10
Cost (million $) 5.4 7.7 8.65 9.38 10 10.54 11.03 11.49 11.91 12.3 12.67
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The cost in millions of dollars to manufacture x hundred thousand units of a product per month is given in the table.
b. An estimated model for this data is given by the following. Let be the cost in millions of dollars to produce x 100,000 units per month.
Graph this model with the data.
8.1-1
x (100,000 units) 0 1 2 3 4 5 6 7 8 9 10
Cost (million $) 5.4 7.7 8.65 9.38 10 10.54 11.03 11.49 11.91 12.3 12.67
( ) 2.3 5.4C x x
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c. Estimate the cost to produce 1.5 million units per month.
8.1-1
( ) 2.3 5.4C x x
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d. If this company produces up to 2 million units per month, find the domain and range of this function.
8.1-1
( ) 2.3 5.4C x x
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e. Use the graph to estimate the number of units the company can produce with a budget of $15 million.
8.1-1
( ) 2.3 5.4C x x
6
The average weight of a boy at different ages is given in the table.
Source: “The Wellness Site” aarogya.com
a. Create a scatterplot of the data in the table.
8.1-2
Age (months) 3 6 9 12 24 36
Weight (lb) 13.2 17.19 20.24 22.44 27.06 32.12
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The average weight of a boy at different ages is given in the table.
Source: “The Wellness Site” aarogya.com
b. Let be the average weight of a boy in pounds at age a months old.
Graph the function with the data.
8.1-2
( )W a3( ) 9.57W a a
Age (months) 3 6 9 12 24 36
Weight (lb) 13.2 17.19 20.24 22.44 27.06 32.12
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The average weight of a boy at different ages.
c. Estimate the average weight of boys who are 20 months old.
8.1-2
3( ) 9.57W a a
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The average weight of a boy at different ages.
d. Estimate numerically at what age the average weight of a boy will be 30lb.
8.1-2
3( ) 9.57W a a
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a. Given the function find the following.
i.
ii. Estimate numerically x such that
8.1-3
6( ) 3.2f x x(45)f
( ) 16f x
11
a. Given the graph of the function find the following.
i. Estimate
ii. Estimate x such that
8.1-3
2g
( ) 9g x
12
Give the domain and range of the following radical functions.a.
b.
c.
8.1-4
( ) 10h x x
7( ) 5g x x
( ) 8f x x
13
Give the domain and range of the following radical functions.a.
8.1-5
14
Give the domain and range of the following radical functions.b.
8.1-5
15
Give the domain and range of the following radical functions.c.
8.1-5
16
Sketch the graph of the following radical functions. a.
8.1-6
( ) 14f x x
17
Sketch the graph of the following radical functions. b.
8.1-6
( ) 7g x x
18
Sketch the graph of the following radical functions. c.
8.1-6
3( ) 3h x x
19
Sketch the graph of the following radical functions. d.
8.1-6
( ) 9f x x
20
Evaluate the following radicals without a calculator.
a.
b.
c.
d.
8.2-1
4
3 343
3 64
5 32
21
Simplify the following radicals. Assume all variables are nonnegative.a.
b.
c.
8.2-2
236m
5 860a b
4 113 54g h
22
Add or subtract the following expressions. Assume all variables are nonnegative.
a. b.
8.2-3
5 6 4 6 2 57 7 4 63ab ab a ab
23
Add or subtract the following expressions. Assume all variables are nonnegative.
c.
8.2-3
8 3 2 7 3 3 11 7a a a a
24
Add or subtract the following expressions. Assume all variables are nonnegative.a.
b.
8.2-4
5 58 3 4 3 2 3 17 3a a a a
54 45 6 2 232 3 2 5 2m n mn mn mn
25
Multiply the following and simplify the result.
a.
b.
8.3-1
3 5a b
6 10m m
26
Multiply the following and simplify the result.
c.
8.3-1
3 23 6 12a a
27
Multiply the following and simplify the result.
a.
b.
8.3-2
7 5 4 3a
2 3 74 10 15 18x y xy x x y
28
Multiply the following and simplify the result.
c.
8.3-2
3 34 5 2 7 2 2 55 12 11 6a b a b ab a b
29
Multiply the following and simplify the result.
a. b.
8.3-3
(2 11)(8 5) 2(3 5)
30
Simplify the following radicals.
a. b.
8.3-4
16
25
5 3
7
50
8
a b
ab
31
Simplify the following radicals.
c.
8.3-4
23
8 4
m n
m n
32
Rationalize the denominator and simplify the following radical expressions. a. b.
8.3-5
7
6
3
5
a
b
33
Rationalize the denominator and simplify the following radical expressions. c.
8.3-5
7 10
3 2
x
y
34
Simplify the following radical expressions.
a. b.
8.3-6
23
2
7
4
a c
ab c3 2 5
7
18
m
m n
35
Rationalize the denominator of the following fractions.
a. b.
8.3-7
6
5 24 7 2
5 6
36
Rationalize the denominator of the following fractions.
c.
8.3-7
7
4
a
a
37
Solve the following equations.
a. b.
8.4-1
12a 3 8 12m
38
The period of a simple pendulum for a small amplitude is given by the function
Where is the period in seconds and L is the length of the pendulum in feet.a. Find the period of a pendulum if its length is 1ft.
b. How long does a pendulum need to be if we want the period to be 2.5 seconds?
8.4-2
( )T L( ) 2
32
LT L
39
At sea level, the speed of sound through air can be calculated by using the following formula.
where c is the speed of sound in meter per second and T is the temperature in degrees Celsius.a. Find the speed of sound when the temperature is .
8.4-3
273.15340.3
288.15
Tc
40
At sea level, the speed of sound through air can be calculated by using the following formula.
where c is the speed of sound in meter per second and T is the temperature in degrees Celsius.b. Find the temperature if the speed of sound is 350m/s.
8.4-3
273.15340.3
288.15
Tc
41
Solve the following equations.
a. b.
8.4-4
7 3 1a a 4 3 7 4 5x x
42
Solve the following equations.
a. b.
8.4-5
2 7 3 5x x 5 4 4 3 2x x
43
Solve the following equations.
a.
8.4-6
7 10 6x
44
Solve the following equations.
a. b.
8.4-7
3 4 5 4x 52 3 8 6x
45
Simplify the following, using the imaginary number i.
a. b. c.
8.5.1
4 50 25
46
For each complex number, name the real part and the imaginary part.
a. b.
8.5-2
7 2i 8i
47
Add or subtract the following complex numbers.
a. b.
8.5-3
(7 4 ) (6 5 )i i (2 8 ) (6 3 )i i
48
Multiply the following complex numbers.
a. b. c.
8.5-4
5(2 6 )i 3 (6 4 )i i (4 7 )(2 9 )i i
49
Write the complex conjugate of the following.
a. b. c.
8.5-5
3 7i 5 8i 2i
50
Multiply the following complex numbers by their conjugates.
a. b. c.
8.5-6
3 5i 4 6i 2i
51
Divide the following. Put all answers in the standard form of a complex number.
a. b. c.
8.5-7
9 21
3
i 2 5
3 2
i
i
8 5
3
i
i
52
Solve the following equations. Give answers in the standard form of a complex number.
a. b.
8.5-8
2 16m 2 3 20x x
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Solve the following equations. Give answers in the standard form of a complex number.
c.
8.5-8
3 26 10 0t t t