a.
To show: that the equation of the line segment is given by
a.
Answer to Problem 82E
Explanation of Solution
Given information: A right triangle is formed in the first quadrant by the x -axis, the y -
axis, and a line segment through the point (3,2).
Formula used:
The equation of the line passing through two points
Calculation:
The equation of the line passing through (3,2) and ( a ,0):
b.
To show: that the area of the triangle is given by
b.
Answer to Problem 82E
A =
Explanation of Solution
Given information: A right triangle is formed in the first quadrant by the x -axis, the y -
axis, and a line segment through the point (3,2).
Formula used:
Area of the triangle=
Calculation:
The base of the triangle would be length a.
The height can be get using the equation from part (a) ,where x =0:
Therefore,
c.
To sketch: a graph of the area function using graphing utilityand estimate the value of a that yields a minimum area.Estimate the minimum area. Verify answer numerically using the table feature of the graphing utility.
c.
Answer to Problem 82E
a =6 appears to give the minimum area 12.
Explanation of Solution
Given information: A right triangle is formed in the first quadrant by the x -axis, the y -
axis, and a line segment through the point (3,2).
Calculation:
Below table shows values of a andA.
a | Area |
4.00 | 16.00 |
4.50 | 13.50 |
5.00 | 12.50 |
5.50 | 12.10 |
6.00 | 12.00 |
6.50 | 12.07 |
7.00 | 12.25 |
7.50 | 12.50 |
8.00 | 12.80 |
The graph of the function
Wherex -axis shows value of a and y -axis shows value of area A.
a =6 appears to give the minimum area 12.
Chapter 2 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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