Posted by MUFFY on Saturday, October 10, 2009 at 2:45pm.
A pool, that is 12 feet wide and 18 feet long, is to have a sidewalk of uniform length constructed around its perimeter.
a. write the equation for the area A, of the pool with the sidewalk
b. determine the domain of the area of the pool with the sidewalk
c. what would the width of the sidewalk need to be in order for the area to be 364 sq. ft.
I am confused about what they want and not sure how to begin. If you could guide me, I would appreciate it.
ap calc - MUFFY, Saturday, October 10, 2009 at 2:47pm
OOPS, I meant Pre-Calc not ap Calc sorry
ap calc - jim, Saturday, October 10, 2009 at 4:42pm
Draw the pool as a rectangle.
Now draw a rectangle around that, such that each side is equally distant from the sides of the pool. This represents the sidewalk around the pool.
The area of the pool is 12 * 18 = 216 sq.ft.
If the sidewalk were 3 feet wide everywhere, the width of the whole area would be (12 + 3 + 3) and the length (18 + 2 + 3). But we don't know the width, so call it x.
Now the width is:
12 + x + x = 12 + 2x
Fill in the length yourself similarly.
Now, the equation for the area of the whole thing is:
A = (2x + 12)(length you worked out)
Multiply that out, and you'll get a quadratic equation.
I'm a little unsure about what the question means by b. myself. I'd be inclined to say R+, but maybe I'm missing the point.
Given the formula you worked out in a., just set 364 = the quadratic equation, and solve for x.
I hope this gives you enough to go on.
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