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saveliy_v [14]
3 years ago
6

The product of , and the sum of a number and - 4 is less than or equal to 64.

Mathematics
1 answer:
lozanna [386]3 years ago
3 0

Answer:

6

Step-by-step explanation:

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A rectangle has its base on the x axis and its upper two vertices on the parabola y = 9 − x2. (a) Draw a graph of this problem.
gtnhenbr [62]

Answer:

  • (a) see attached
  • (b) width: 2x; height: y = 9-x²
  • (c) A=2x(9-x²) . . . 0 ≤ x ≤ 3
  • (d) dA/dx = -6x² +18; x=±√3
  • (e) 12√3 units²

Step-by-step explanation:

(a) The attachment shows the graph of the parabola in blue. It also shows an inscribed rectangle in black.

(b) The upper right point of the rectangle is shown in the attachment as (x, y). The dimension y is the height of the rectangle. The x-dimension is half the width of the rectangle, which is symmetrical about the y-axis. Hence the width is 2x.

(c) As with any rectangle, the area is the product of length and width:

... A = (2x)(9 -x²) . . . . . the attachment shows a graph of this

... A = -2x³ +18x . . . . . expanded form suitable for differentiation

A suitable domain for A is where both x and A are non-negative: 0 ≤ x ≤ 3.

(d) The derivative of A with respect to x is ...

... A' = -6x² +18

This is defined everywhere, so the critical values will be where A' = 0.

... 0 = -6x² +18

... 3 = x² . . . . . . . divide by -6, add 3

... √3 = x . . . . . . . -√3 is also a solution, but is not in the domain of A

(e) The rectangle will have its largest area where x=√3. That area is ...

... A = 2x(9 -x²) = 2√3(9 -(√3)²) = 2√3(6)

... A = 12√3 . . . . square units . . . . ≈ 20.785 units²

7 0
3 years ago
A house purchased for $230,000 has lost 6% of its value each year for the last four years. What is the house worth now?
lutik1710 [3]
You can use the compound growth to work this out,

Firstly you need to make a multiplier for -6%;
1-(6/100) = 0.94

The you times the amount of money by 0.94 to the power of 4 because you are working out 4 years:
230000*0.94^4 = 179527.26

The answer is $179527.26,
Hope this helps! :)
3 0
3 years ago
The equation g(x) = f(x + 2) is graphed on a coordinate plane. Which equation, h(x), results from moving g(x) to the right 2 uni
Archy [21]

Answer: D

Step-by-step explanation:

5 0
2 years ago
Mrs.Jacinto asked carpenter to construct a rectangular bulletin board for her classroom. She told the Carpenter that the board's
Misha Larkins [42]

Answer:

6 ft by 3 ft

Step-by-step explanation:

3 0
3 years ago
An hour a jogger brings about 8 calories 2 lb of body weight how many calories will a jooger
Nezavi [6.7K]

Answer:

640 calories

Step-by-step explanation:

I attachedmy handwritten work and this is what I got

I'm only like 97.48% sure I understand the question. If I'm wrong someone tell me and I will try to fix it

and if it's too difficult to read, just tell me that too and I will fix it.

3 0
3 years ago
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