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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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Answer:

width = 18.97 inches

Step-by-step explanation:

To find the smallest width of the box to fit the bat, we need to put the bat in the diagonal of the box.

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3 years ago
Delta Math: Angle Terminology with Equations
vazorg [7]

Answer:

m∠A = 139°

Step-by-step explanation:

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Thus we put that in both equation:

( 7x - 15 ) + ( 2x - 3 ) = 180

Combine like terms & use inverse operations to find the value of x:

( 7x - 15 ) + ( 2x - 3 ) = 180

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Hence,  Angle A will have a measure of 7x - 15 which means  7 ×  22 -15 = 154 - 15 = 139°

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The measure of Angle B will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°

m∠ B = 41°

Check Answer by add 139 and 31 which equal 180

<u><em>~lenvy~</em></u>

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