a rectangle is constructed with its base on the diameter of a semicircle with what are the dimensions of the…

a rectangle is constructed with its base on the diameter of a semicircle with what are the dimensions of the rectangle with maximum area? let a be the area of the rectangle. what is the objective function in terms of the a = x√(484 - x²/4) (type an expression.) the interval of interest of the objective function is . (simplify your answer. type your answer in interval notation.)

a rectangle is constructed with its base on the diameter of a semicircle with what are the dimensions of the rectangle with maximum area? let a be the area of the rectangle. what is the objective function in terms of the a = x√(484 - x²/4) (type an expression.) the interval of interest of the objective function is . (simplify your answer. type your answer in interval notation.)

Answer

Explanation:

Step1: Determine domain of (x)

For the square - root function (y = \sqrt{484-\frac{x^{2}}{4}}) to be well - defined, we need (484-\frac{x^{2}}{4}\geq0). [ \begin{align*} 484-\frac{x^{2}}{4}&\geq0\ \frac{x^{2}}{4}&\leq484\ x^{2}&\leq1936\

  • 44\leq x&\leq44 \end{align*} ] Since (x) represents half of the base of the rectangle (a length), (x\geq0). So the interval of interest is ([0,44]).

Answer:

([0,44])