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Kazeer [188]
3 years ago
14

3. Simplify the following 32*37

Mathematics
1 answer:
Elanso [62]3 years ago
6 0

Answer:

1,184

Step-by-step explanation:

32 times 37 is equal to 1,184

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Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting fl
Vikki [24]

Answer:

Height: 3/2 inches

Length:  12 inches

Width: 4 inches

Step-by-step explanation:

Let x is the side length of the square

The height of the box by cutting squares off :x

  • The new length of the cardboard = 15 -2x (because we cut from 4 corners)
  • The new width of the cardboard = 7 -2x (because we cut from 4 corners)

The new volume of it is:

V = (15 -2x) (7 -2x) x

<=> V = 4x^3 -44x^2 +105x

To maximum volume, we use the first derivative of the volume

\dfrac{dV}{dx} = 0

<=> 12x^2-88x+105=0

<=> \left(2x-3\right)\left(6x-35\right) = 0

<=> 2x -3 = 0 or 6x -35 = 0

<=> x = 3/2 or x = 35/6

To determine which value of x gives a maximum, we evaluate

\dfrac{d^2V}{dx^2} = 24x -88

  • If  x = 3/2, we have:

\dfrac{d^2V}{dx^2}= 24(3/2) -88  = -52

  • If x = 35/6, we have:

\dfrac{d^2V}{dx^2} = 24(35/6) -88 = 52

We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.

So the dimensions (in inches) of the box is:

Height: 3/2 inches

Length: 15-2(3/2) = 12 inches

Width: 7 - 2(3/2) = 4 inches

5 0
3 years ago
A driver drove for 3 hours at a certain speed. If he drove 12 more miles at the same speed, the distance would be 132 miles. At
Zinaida [17]
Distance traveled in 3 hrs was (speed in mph)(3 hrs)

Then s(3 hrs) + 12 mi = 132 mi.

Therefore, 3s = 120, and s = 120 miles   /   3 hrs   = 40 mph (answer)
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3 years ago
Can u help me the s solve this problem <br> If 5x-8=37,the x=9
SVEN [57.7K]

Answer:x=9

Step-by-step explanation:

X=9-8=37

(5x9)-8=37

45-8=37

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3 years ago
How do you express your terms in pi
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Answer:

To express your answer in terms of pi, simply refrain from substituting pi's numerical value for its symbol in the equation. That way, your answer will look like xπ where x is whatever number you come up with, and π is simply a placeholder.

4 0
3 years ago
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A baker sells cookies for 1.5 each. If a minimum of two dozen cookies is ordered
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36.00 that is the answer
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