dang word problem
Suppose you have 80ft of fence to enclose a rectangular garden.The function A=40x-x squared gives you the area of the garden in square feet,where x is the width in feet.
a.What width gives you the maximum gardening area?
b.What is the maximum area?
A = 40x – x²
a. when you are using the fencing to bound all four sides, you will obtain maximum area by designing a square (so width is 20). This only works for fencing on all four sides.
to prove that in algebra, you would graph your function A = 40x – x², which looks like an upside down parabola, vertex (highest point) at x = 20. You could also do a table of values or use the derivative (calculus).
b. maximum area is 400 ft².
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using a 80 ft fence. the square, which can be made is
of dimension= (20 ft X20 ft),
Its perimeter would be 80 ft.
2. A=40*X – X^2 = 40*20- 20^2 = 800-400 = 400 sq.ft. Ans.
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