Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Mathematics

1 answer:

Solnce55 [7]3 years ago

6 0

Answer:

85-4x<40

12 cars

Step-by-step explanation:

85-4x<40

Solve for x.

-4x<-45

x<11.25

If he build 11 cars, the amount of tires would be over 40, so if he builds 12 cars, it will be below 40.

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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

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

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

<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 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 $x \in [-3, 3]$ . $\blacksquare$

<h3>Remark</h3>

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?