Find the 15th term in the arithmetic sequence An=3n-7

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

Sergio039 [100]

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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Step-by-step explanation:

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3 years ago

50 points!!!! Will give brainliest , thanks ,and 5 star rating to the good answers to this questions! please Help! Show all work

densk [106]

Answer:

1) x ≤ 2 or x ≥ 5

2) -6 < x < 2

Step-by-step explanation:

1) We have x^2 - 7x + 10, so let's factor this as if this were a regular equation:

x^2 - 7x + 10 = (x - 2)(x - 5)

So, we now have (x - 2)(x - 5) ≥ 0

Let's imagine this as a graph (see attachment). Notice that the only place that is above the number line is considered greater than 0, and that's when x ≤ 2 or x ≥ 5 (the shaded region).

2) Again, we have x^2 + 4x - 12, so factor this as if this were a regular equation:

x^2 + 4x - 12 = (x + 6)(x - 2)

So now we have (x + 6)(x - 2) < 0

Now imagine this as a graph again (see second attachment). Notice that the only place that is below 0 (< 0) is when -6 < x < 2 (the shaded region).

Hope this helps!