Concept explainers
22. Installing Cable TV MetroMedia Cable is asked to provide service to a customer whose house is located 2 miles from the road along which the cable is buried. The nearest connection box for the cable is located 5 miles down the road. See the figure.
(a) If the installation cost is S500 per mile along the road and per mile off the road, build a model that expresses the total cost C of installation as a function of the distance x (in miles) from the connection box to the point where the cable installation turns off the road. Find the domain of .
(b) Compute the cost if mile.
(c) Compute the cost if miles.
(d) Graph the function . Use TRACE to see how the cost C varies as x changes from 0 to 5.
(e) What value of x results in the least cost?
To find:
a. To model that expresses the total cost of installation as a function of distance . To find the domain of .
Answer to Problem 22AYU
Solution:
a. .
Explanation of Solution
Given:
1. The house is 2 miles from the road.
2. The nearest connection box is 5 miles down the road.
3. Cost of installation is per mile along the road and per off the road.
Calculation:
The can be expressed as the figure below.
Let be the distance along the road.
Let be the distance off the road.
a. The total cost of installation
From the figure, .
The Cost of installation .
To find:
b. To compute the cost if mile.
Answer to Problem 22AYU
Solution:
b. .
Explanation of Solution
Given:
1. The house is 2 miles from the road.
2. The nearest connection box is 5 miles down the road.
3. Cost of installation is per mile along the road and per off the road.
Calculation:
The can be expressed as the figure below.
Let be the distance along the road.
Let be the distance off the road.
b. For
To find:
c. To compute the cost if miles.
Answer to Problem 22AYU
Solution:
c.
Explanation of Solution
Given:
1. The house is 2 miles from the road.
2. The nearest connection box is 5 miles down the road.
3. Cost of installation is per mile along the road and per off the road.
Calculation:
The can be expressed as the figure below.
Let be the distance along the road.
Let be the distance off the road.
c. For .
To find:
d. To graph the function .
Answer to Problem 22AYU
Explanation of Solution
Given:
1. The house is 2 miles from the road.
2. The nearest connection box is 5 miles down the road.
3. Cost of installation is per mile along the road and per off the road.
Calculation:
The can be expressed as the figure below.
Let be the distance along the road.
Let be the distance off the road.
d. To graph :
Sl No | In miles | In |
---|---|---|
1. | 0 | |
2 | 1 | |
3 | 2 | |
4 | 3 | |
5 | 4 | |
6 | 5 |
To find:
e. To find the value of in which the cost is least..
Answer to Problem 22AYU
Solution:
e. .
Explanation of Solution
Given:
1. The house is 2 miles from the road.
2. The nearest connection box is 5 miles down the road.
3. Cost of installation is per mile along the road and per off the road.
Calculation:
The can be expressed as the figure below.
Let be the distance along the road.
Let be the distance off the road.
e. The value of is least when miles.
Chapter 2 Solutions
Precalculus
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