Question

As shown at the right, rectangle abcd has vertices c and d on the. V-axis and vertices a and b on the part of the parabola y — 9 — x that is above the. V-axis. A. Express the perimeter p of the rectangle as a function of the. V-coordinate of a. B. What is the domain of the perimeter function?.

Answer 1

a) The perimeter function of the rectangle is $p = 18\cdot x -2\cdot x^{3}$.

b) The domain of the perimeter function is $x \in [-3, 3]$.

How to analysis the perimeter formula of a rectangle inside a parabola

a) The perimeter of a rectangle ($p$) is the sum of the lengths of its four sides:

$p = AB\cdot AC$ (1)

If we know that $AB = 2\cdot x$ and $AC = 9-x^{2}$, then the perimeter of the rectangle is represented by the following formula:

$p = 2\cdot x \cdot (9-x^{2})$

$p = 18\cdot x -2\cdot x^{3}$

The perimeter function of the rectangle is $p = 18\cdot x -2\cdot x^{3}$. $\blacksquare$

b) The domain of the function is the set of values of $x$ associated to the function. After a quick inspection, we find that the domain of the perimeter function is $x \in [-3, 3]$. $\blacksquare$

Remark

The statement is incomplete and poorly formatted. The correct form is described below:

As shown at the right, rectangle ABCD has vertices C and D on the x-axis and vertices A and B on the part of the parabola $y = 9-x^{2}$ that is above the x-axis. a) Express the perimeter $p$ of the rectangle as a function of the x-coordinate of A. b) What is the domain of the perimeter function?

To learn more on rectangles, we kindly invite to check this verified question: brainly.com/question/10046743