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Tems11 [23]
3 years ago
7

According to u.s. postal regulations, the girth plus the length of a parcel sent by mail may not exceed 108 inches, where by "gi

rth" we mean the perimeter of the smallest end. what is the largest possible volume of a rectangular parcel with a square end that can be sent by mail? such a package is shown below. assume y>x. what are the dimensions of the package of largest volume?

Mathematics
1 answer:
Pepsi [2]3 years ago
8 0
Let x represent the side length of the square end, and let d represent the dimension that is the sum of length and girth. Then the volume V is given by
  V = x²(d -4x)
Volume will be maximized when the derivative of V is zero.
  dV/dx = 0 = -12x² +2dx
  0 = -2x(6x -d)
This has solutions
  x = 0, x = d/6

a) The largest possible volume is
  (d/6)²(d -4d/6) = 2(d/6)³
  = 2(108 in/6)³ = 11,664 in³

b) The dimensions of the package with largest volume are
  d/6 = 18 inches square by
  d -4d/6 = d/3 = 36 inches long

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Geometry/////
Montano1993 [528]

Answer:

A = 388.58 cm^2

Step-by-step explanation:

For a cone whose base has a radius R, and a hypotenuse S, the area is:

A = pi*R^2 + pi*R*S

Where pi = 3.14

In this case, we can see that the diameter is: 15cm

Then the radius, half of the diameter, is:

R = 15cm/2 = 7.5cm

The hypotenuse is 9cm, then S = 9cm

A = 3.14*(7.5cm)^2 + 3.14*(9cm)*(7.5cm) = 388.575 cm^2

Rounding to two decimal places, we need to look at the third one, which is a five, so we need to round up:

A = 388.58 cm^2

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3 years ago
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78 . Hope this was helpful
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3 years ago
Which of the following se solutions to the inequality -7x+14&gt;3x-6? Select all that apply. A. -10 B. 10 C. -5 D. 5 E. -3 F. 3
sweet-ann [11.9K]
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8 0
3 years ago
Find the length of the legs of a right triangle if the legs are the same length and
xenn [34]

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6 0
2 years ago
Mr. Nolan has a bank account that compounds interest
german

Answer: At the end of the day on December 8, he has a total balance of $2841.02

Step-by-step explanation:

The rate at which the compound interest adds up is a 3.7%.

His principal is $2644.08, on the 7th of December, he withdraws $550. Thus, his balance is = $2644.08 - $550 = $2094.08.

He later deposits $934, after being paid by his employer.

That is $2094.08 + $934 = $3028.08

Which is his balance at the end of the day on December 7.

Remember that the rate is daily, at a 3.7%.

A 3.7% of the balance of December 7, $3028.08 is $112.039.

In total, interest +amount = real balance,

$112.039+$3028.08 = $3140.119

He later withdraws $300 for holiday shopping = $3140.119 - 300 = $2840.119

But 1 dollar = 100 cents and vice versa.

Therefore, $2840.119 = $2841.019

In two decimal places, that is approximately $2841.02

Therefore, Mr Nolan's balance at the end of December 8 is $2841.02.

4 0
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