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Eddi Din [679]
3 years ago
5

Find the dimensions of the rectangle with perimeter 64 inches that has maximum area, and then find the maximum area.

Mathematics
1 answer:
gregori [183]3 years ago
4 0

Answer:

  the maximum area is 256 in^2

Step-by-step explanation:

It is well-known that the rectangle of given perimeter with maximum area is a square. A square with a perimeter of 64 inches has a side length of 64/4 = 16 inches. The area of that square is the square of the side length, ...

   (16 in)^2 = 256 in^2

_____

<em>Derivation of the well-known fact</em>

Let P represent the perimeter of a rectangle with side lengths x and (P/2 -x). The area is the product of these dimensions:

  A = x(P/2 -x)

This is the equation of a downward-opening parabola with zeros at x=0 and at x=P/2. The vertex (maximum) is halfway between these zeros, at x=P/4. Hence, the dimensions of the rectangle are ...

  x = P/4 . . . . . . . . . . . length

  (P/2 -P/4) = P/4 . . . . width

The length and width are the same, and both are 1/4 of the perimeter, so the rectangle is a square. Its area in terms of perimeter is ...

   A = (P/4)^2 = P^2/16

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Yall pls help meeeee (brainliest btw)!!!!!
Korvikt [17]
<h2>Answer:</h2>

<u><em>Let m be the amount each mom can paint and d be the amount each daughter can paint.</em></u>

<u><em>On the first day, 8 mothers were painting so the mothers painted 8m square feet. 12 daughters also painted so the daughters painted 12d square feet. The total amount painted on the first day is then 8m+12d square feet. Since 220 square feet was painted on the first day, then 8m+12d=220.  Dividing both sides by 4 gives a simplified equation of 2m+3d=55.</em></u>

<u><em>On the second day, 6 mothers were painting so the mothers painted 6m square feet. 8 daughters also painted so the daughters painted 8d square feet. The total amount painted on the second day is then 6m+8d square feet. Since 152 square feet was painted on the second day, then 6m+8d=152</em></u>

<u><em /></u>

<u><em>Multiply the first equation by -3 and then add it to the second equation to eliminate m and solve for d:</em></u>

<u><em>d=13</em></u>

<u><em>2m+3d=55</em></u>

<u><em>2m+3(13)=55</em></u>

<u><em>2m+39=55</em></u>

<u><em>2m=16</em></u>

<u><em>m=8</em></u>

<u><em>Therefore each mom painted 8 square feet and each daughter painted 13 square feet.</em></u>

4 0
3 years ago
A fire engine starts pumping water at 9:20 am at the rate of 800 gallons per minute. Another fire engine, pumping at the rate of
AleksAgata [21]

Answer:

10:10 AM

Step-by-step explanation:

The first thing is to use an identical time variable for both cases, we will do it as follows:

Let t = number of minutes of pumping time of the first fire engine

Therefore, for the second fire truck it would be:

(t-10) = pumping time of the second fire engine, since it started 10 min after the first engine.

To find the value of t, we equalize the equations of the first engine and the second engine:

We know that the first one would be: 800 * t

And the second: 1000 * (t-10)

Thus

1000 * (t-10) = 800 * t

1000 * t - 10000 = 800t

1000 * t - 800 * t = 10000

200 * t = 10000

t = 10000/200

t = 50 minutes

In other words, 50 minutes after the first engine starts pumping, it equaled the second

To know the time they were matched it would be like this:

9:20 AM +: 50 = 10:10 AM

Therefore, at 10:10 AM both engines were matched.

To check the above we have to:

50 * 800 = 40000

40 * 1000 = 40000

Therefore, in that time, they were equalized.

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3 years ago
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vovangra [49]

Answer:

$1.15

Step-by-step explanation:

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Answer: No. It's not proportional

Step-by-step explanation:

The direct proportion in mathematics is expressed as:

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We then solve for k

y = kx

200 = 7.50k

k = 200/7.50

k = 26.67

Since k isn't a whole number, then the amount of money in her bank account proportional to the number of pumpkin she sells.

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