SOLUTION: A rectangle is bounded by the x-axis and the semicircle y=[36-x^2]square root. Write the area of the rectangle as a function of x, and determine the domain of the function
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Question 162453: A rectangle is bounded by the x-axis and the semicircle y=[36-x^2]square root. Write the area of the rectangle as a function of x, and determine the domain of the function.
This is the picture of the graph: http://hmco.tdlc.com/pre3e/common/ch30/ch30c/30c_images/2901087.gif Answer by Edwin McCravy(20056) (Show Source):
You can put this solution on YOUR website! A rectangle is bounded by the x-axis and the semicircle . Write the area of the rectangle as a function of x, and determine the domain of the function.
This is the picture of the graph: http://hmco.tdlc.com/pre3e/common/ch30/ch30c/30c_images/2901087.gif
Label the upper right hand corner of the
rectangle (x,y):
Now if we just look at the right half of that
rectangle, we have:
The area of the right half of the rectangle
is .
Therefore the area of the entire rectangle:
is twice that or
.
However, that is the area in terms of both
x and y.
We must get the area A in terms of just x.
So we replace in by
Your teacher may want you to write instead of
If so the answer in functional notation is:
Edwin
