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kherson [118]
2 years ago
14

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?.
Mathematics
1 answer:
Sergio039 [100]2 years ago
4 0

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

b) The domain of the <em>perimeter </em>function is x \in [-3, 3].

<h3>How to analysis the perimeter formula of a rectangle inside a parabola</h3>

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 <em>perimeter</em> 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 <em>perimeter </em>function is x \in [-3, 3]. \blacksquare

<h3>Remark</h3>

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

<em>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 </em>y = 9-x^{2}<em> that is above the x-axis. a) Express the perimeter </em>p<em> of the rectangle as a function of the x-coordinate of A. b) What is the domain of the perimeter function?</em>

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

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