Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

A postal service says that a rectangular
package can have a maximum combined length
and girth of 108 inches. The girth of a package is the
distance around the perimeter of a face that does not
include the length.
a. Write an inequality that represents the allowable
dimensions for the package.
b. Find three different sets of allowable dimensions that are
reasonable for the package. Find the volume of each package.
girth

Sagot :

MrRoyal

The volume of the rectangular package is the amount of space in the package

  • The inequality that represents allowable dimensions is 4x + y ≤ P
  • Three possible dimensions are: 2 by 100,1 by 104 and 1.5 by 102

The inequality that represents allowable dimensions

Let the dimension of the package be x and y.

So, the perimeter (P) and the volume (V) are

P = 4x + y

V = x²y

The maximum perimeter of the box is P.

So, the inequality is:

4x + y ≤ P

The three different dimensions

Recall that:

P = 4x + y

The perimeter becomes

4x + y = 108

Make y the subject

y = 108 - 4x

Substitute y = 108 - 4x in V = x²y

V = x²(108 - 4x)

Expand

V = 108x² - 432x

Differentiate

V' = 216x - 432

Set to 0

216x - 432 = 0

Add 432 to both sides

216x = 432

Divide by 216

x = 2

Substitute x = 2 in y = 108 - 4x

y = 108 - 4 * 2

Evaluate

y = 100

So, the inequalities are:

x ≤ 2 and y ≤ 100

Using the above inequality, three possible dimensions are: 2 by 100,1 by 104 and 1.5 by 102

Read more about maximum volumes at:

https://brainly.com/question/10373132

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.