SOLUTION: the function below can be used to model the area of a rectangle in square inches A, if the rectangle has a perimeter of 98 inches and a width of w inches. A= 49w-w^2. What is the d

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: the function below can be used to model the area of a rectangle in square inches A, if the rectangle has a perimeter of 98 inches and a width of w inches. A= 49w-w^2. What is the d      Log On


   

Question 1083993: the function below can be used to model the area of a rectangle in square inches A, if the rectangle has a perimeter of 98 inches and a width of w inches. A= 49w-w^2. What is the domain of the function


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!



Two things to deal with:
A=+49w-w%5E2 must be positive, so
-w%5E2%2B49w%3E0 and perimeter is 2L%2B2w=98
Also knowing that w is width, you can find length information.
2%28L%2Bw%29=98
L%2Bw=98%2F2
L%2Bw=49
L=49-w
since area
A=w%2AL we have:
A=w%28-w%5E2%2B49w%29
This means, L=49-w for L and w are only positive values allowed, so this means at least, that w%3C49
if 0=+-w%5E2%2B49=-w%28w-49%29; roots are 0 and 49;
and A is a parabola which has a maximum and opens downward
domain: 0%3Cw%3C49