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To find:
a. To express the total area enclosed by the pieces of wire as a function of the length of a side of the equilateral triangle.
![Check Mark](/static/check-mark.png)
Answer to Problem 12AYU
Solution:
a.
Explanation of Solution
Given:
A 10m long wire is cut into two pieces. One piece is shaped as an equilateral triangle and other piece is shaped as a circle.
Calculation:
a. To express the total area enclosed by the pieces of wire as a function of the length of a side of the equilateral triangle.
The side of the equilateral triangle .
Therefore, Area of the equilateral triangle .
Total length of the wire which made equilateral triangle is .
The perimeter of the circle .
Area of the circle .
Therefore, the total area enclosed by the wire .
To find:
b. To the domain of .
![Check Mark](/static/check-mark.png)
Answer to Problem 12AYU
Solution:
b.
Explanation of Solution
Given:
A 10m long wire is cut into two pieces. One piece is shaped as an equilateral triangle and other piece is shaped as a circle.
Calculation:
b. To the domain of :
Since, perimeter has to be positive, the domain of
To find:
c. To graph and to find the value of is smallest.
![Check Mark](/static/check-mark.png)
Answer to Problem 12AYU
Solution:
c.
Explanation of Solution
Given:
A 10m long wire is cut into two pieces. One piece is shaped as an equilateral triangle and other piece is shaped as a circle.
Calculation:
c. To graph and to find the value of is smallest.
From the graph it can be seen that when attains its minimum value .
Therefore, is smallest when .
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
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