The area of the triangle as a function of x is A = 3x^2/[2(x -5)] and the domain is x > 5
<h3>Write the area A of the triangle as a function of x</h3>
From the figure, we have the following points:
(0,y), (5,3), and (x,0)
Next, we calculate the slopes between the points.
This is calculated as follows:
- Slope between (0,y) and (5,3) = [y - 3]/[0 - 5] = [3 - y]/5
- Slope between (5,3) and (x,0) = [3 - 0]/[5 - x] = 3/[5 - x]
The slopes are equal.
So, we have:
[3 - y]/5 = 3/[5 - x]
Cross multiply
(3 - y)(5 -x) = 15
Divide by 5 - x
(3 - y) = 15/(5 -x)
This gives
y = 3 - 15/(5 -x)
This gives
y = [15- 3x - 15]/[5 - x]
Evaluate
y = 3x/(x - 5)
The area is calculated as:
Area = 1/2 * xy
So, we have:
Area = 1/2 * x * 3x/(x - 5)
Evaluate
Area = 3x^2/[2(x -5)]
Hence, the area of the triangle as a function of x is A = 3x^2/[2(x -5)]
<h3>
The domain of the function</h3>
We have:
A = 3x^2/[2(x -5)]
Set the denominator > 0
2(x - 5) > 0
Divide by 2
x - 5 > 0
Add 5 to the sides
x > 5
Hence, the domain is x > 5
Read more about domains at:
brainly.com/question/2428614
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