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kodGreya [7K]
3 years ago
13

Find the length of a picture frame whose width is 3 inches and whose proportions are the same as a 9-inch wide by 12-inch long p

icture frame.
Mathematics
1 answer:
barxatty [35]3 years ago
7 0

Answer:

4 inches

Step-by-step explanation:

We can set up a proportion to find out the length value (assuming x is the length of the frame)

\frac{3}{x} = \frac{9}{12}

We multiply 12 and 3...

12\cdot3=36

And divide by 9...

36\div9=4

So, the length of the frame is 4 inches.

Hope this helped!

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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
Express decimal as a fraction 8.25
aksik [14]

Answer:

33/4

Step-by-step explanation:

3 0
2 years ago
before Christmas a story steals fake Christmas trees for $289 after Christmas they sell the same trees for $150 what is the appr
Katarina [22]
48% decrease :)

hope this helps
6 0
3 years ago
-Ready Understand On Earth Day, 40 people volunteert are high-school students. The coordi in high school. ). Write a fraction to
Elden [556K]

Answer:

1/40

Step-by-step explanation:

4 0
3 years ago
Write the fraction 7/8 as an equivalent fraction with the given denominator 40
Mekhanik [1.2K]

Answer:

35/40

Step-by-step explanation:

7/8, with the given denominator 40

So how do we get 8, to turn into 40?

Simple multiplication.

8x5 = 40, and whatever we multiply times the denominator, we multiply for the numerator.

So

7x5 = 35

The answer should be 35/40

8 0
3 years ago
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