1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
n200080 [17]
2 years ago
13

A parcel delivery service will deliver a package only if the length plus the girth (distance around, i.e., perimeter, taken perp

endicular to the length) does not exceed 120 inches. Find the maximum volume of a rectangular box with square ends that satisfies the delivery company's requirements.
Mathematics
1 answer:
alex41 [277]2 years ago
6 0

Answer:

16,000 cubic inches.

Step-by-step explanation:

Let x, y, z  be the length, width and height of the parcel.  

Since the parcel is a rectangular box with square ends,

y = z and the girth is 4y.

The volume is

V=xy^2

The maximum volume must occur when the length plus the girth equals 120 inches, that is

x + 4y = 120

We want then to find the maximum of the volume.

As

x = 120 - 4y

we have

V=(120-4y)y^2=120y^2-4y^3

Let us find the critical points of V

\displaystyle\frac{\text{d}V}{\text{d}y}=240y-12y^2\\\\\displaystyle\frac{\text{d}V}{\text{d}y}=0\Rightarrow 240y=12y^2

We can assume y>0, otherwise there is no parcel.

Dividing both sides by y:

240=12y\Rightarrow y=\displaystyle\frac{240}{12}=20

Since

\displaystyle\frac{\text{d}^2V}{\text{d}y^2}=240-24y\Rightarrow \displaystyle\frac{\text{d}^2V}{\text{d}y^2}(20)=240-480

and

y=20

is a maximum. For this value of y:

x = 120 - 4(20) = 40

We conclude that the rectangular box with maximum volume that satisfies the delivery company's requirements has the following measures:

Length = 40

Width = height = 20 inches

Volume = 40*20*20 = 16,000 cubic inches.

You might be interested in
I cant understand this.
djverab [1.8K]
Multiply the top one by 3 for x, so you can eliminate x and find y

then plug in the y into one of the equations to find x
7 0
3 years ago
Pleaseeee help !!!!!!!!!!!!!!!!!!!!!!!!!!! I don’t understand
mafiozo [28]

Answer:

None

Step-by-step explanation: Where is the question?

6 0
3 years ago
Which of the following is a numerical expression<br> A. x+y<br> B. 2b -5<br> C. 6 x 4<br> D. 425
densk [106]
2b -5 is a numerical expression
4 0
3 years ago
Read 2 more answers
Karen grew a pumpkin that weighed 4.3 pounds for the competition at the
Reil [10]
Nancy grew the largest pumpkin since it weight more than Karen’s pumpkin
5 0
3 years ago
Pls help with these problems
babunello [35]

Answer

(97, 73), x = 97

(13, -81), y = -81

(-91, -26) y = -26

(74, 25), x = 74

Step-by-step explanation

if it has an undefined slope, it is a vertical line with the equation x = (x value)

if it has a 0 slope, it is a horizontal line with the equation y = (y value)

undefined slope through (97, 73)

the x value is 97

x = 97

slope of 0 through (13, -81)

the y value is -81

y = -81

slope of 0 through (-91, -26)

the y value is -26

y = -26

undefined slope through (74, 25)

the x value is 74

x = 74

4 0
3 years ago
Other questions:
  • How do you plot a linear graph​
    11·1 answer
  • There are 2 orange picks for every 5 picks if there are 21 picks in total how many picks are orange
    15·1 answer
  • Find the value of 10 to the third power
    10·1 answer
  • How many cans of paint are needed to cover an area of 2200 square units if one can of paint covers in area 400 square units
    7·1 answer
  • Mike, a Salvation Army bell ringer, has 20% as many quarters as nickels in his cup. If Mike has $6.00 in quarters and nickels, h
    9·1 answer
  • A store is having a sale in which all items are 20% off. If p is the original price of an item, then the equation p - 0.2 = 0.8
    15·2 answers
  • Fred buys a video game disk for 4$. there was a discount of 20%. what is the sales price?
    15·2 answers
  • A movie theater holds 785 people. The theater has already sold 219 tickets. How many more tickets can be sold
    6·2 answers
  • Write the mixed numbers as fractions <br> 1/1/2
    13·1 answer
  • The perimeter of the parallelogram is 62 cm.
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!