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
yarga [219]
3 years ago
9

A cylindrical package with half a hemisphere to be sent by a postal service can have a maximum combined length (height of the cy

linder) and girth (perimeter of a cross section of the cylinder) of 108 inches. Find the dimensions of the package of maximum volume that can be sent. Assume the cross section is a circle. (Make sure you verify that the value you found is the maximum).
Mathematics
2 answers:
artcher [175]3 years ago
5 0

Answer:

36 x 18 x 18

Step-by-step explanation:

By Lagrange multiplier's method,

∇f(x,y,z)= λ∇g(x,y,z) & g(x,y,z)=k

considering x,y,z as three unequal sides of the box

f(x,y,z)=xyz

If x represents the length, then constraint condition is g(x,y,z)= x + 2(y+z) =108

We have the following three equations:

yz= λ -->eq(1)               fx= λgx

xz=2λ -->eq(2)              fy=λgy

xy= 2λ -->eq(3)             fz=λgz

x+2y+2z=108-->eq(4)

Dividing eq(2) by eq(1), we'll have

x / y =2

=> x= 2y

Also, by using eq(2)and eq(3), we can represent y=z

By substituting 'x= 2y' and 'y=z' in eq(4), we have

eq(4)=>

2y+ 2(y+y)= 108

y=108/6

y=18

<u>For x: </u> x=2y=> 2(18)=>36

<u>For z: </u>z= y = 18

Therefore, the dimensions are 36 x 18 x 18

yKpoI14uk [10]3 years ago
4 0

Answer:

Radius of package is 36/π inches

Height of package is 36 inches

Step-by-step explanation:

Here we have

Sum of height plus perimeter of package = 108 inches that is

2πr + h = 108 inches

Where:

Height of package = h

Radius of package = r

Volume of package = πr²h

However, h = 108 - 2πr

Therefore, the equation for the volume of the package is;

Volume of package, V = πr²(108 - 2πr) = πr²×108 - 2π²r³

Differentiating the above equation and equating to zero to find a maximum value, we have;

2πr×108 - 6r²π² = 0

2πr×108 = 6r²π²

36 = r·π

r = 36/π inches

h = 108 - 2πr = 108 - 72 = 36 inches

Radius of package, r = 36/π inches

Height of package, h = 36 inches.

You might be interested in
Multiply 1/8 x 3/4 =
Novay_Z [31]

Answer:

3/32

Step-by-step explanation:

1 times 3= 3 and 8 times 4=32

8 0
3 years ago
Read 2 more answers
If 4 pound of sugar cost of 1 pound of sugar is and the cost of ten pounds of sugar is
fenix001 [56]

Answer:

Ten pounds of sugar costs 2.5 pounds

Step-by-step explanation:

5 0
3 years ago
Factor the following polynomial completely 6x^5-30x^4-84x^3
Andrei [34K]

Answer:

6x^3(x+2)(x-7)

Step-by-step explanation:

1st step: factor out common term, 6x^3(x^2 - 5x - 14)

2nd step: Factor x^2 - 5x - 14, (x + 2)(x - 7)

3rd step: simplify, 6x^3(x+2)(x-7)

I am joyus to assist :)

8 0
3 years ago
Find the​ mean, median, and mode of the​ data, if possible. If any of these measures cannot be found or a measure does not repre
Ber [7]

Answer:

The mean cholesterol levels

= 173873.7

Step-by-step explanation:

For The mean

The mean is going to be sum of the numbers divide by the number

Mean = (130130 +145145+ 215215 +170170+ 165165 +225225+ 240240 +185185+ 130130 +132132 )/10

Mean =1738737/10

= 173873.7

For Median

Wee arrange ascending order

130130, 130130, 132132, 145145, 165165, 170170, 185185, 215215, 225225, 240240

Median = (165165+170170)/2

Median = 335335/2

Median = 167667.5

Mode = 130130

4 0
3 years ago
Matt's Mechanics charges $45.95 per hour to do a car repairs plus $30.50 for waste disposal. Write an equation to represent this
katrin2010 [14]

Answer:

45.95x + 30.50

Step-by-step explanation:

<u>Step 1:  Convert words into an expression</u>

Matt's Mechanics charges $45.95 per hour to do a car repairs plus $30.50 for waste disposal.

<em>45.95x + 30.50</em>

<em />

Answer:  45.95x + 30.50

6 0
3 years ago
Read 2 more answers
Other questions:
  • Hello ya'll. I have a quick question to ask ya'll.
    12·1 answer
  • Match each polynomial with its degree
    8·1 answer
  • Find sum 3.24 +.07 =
    14·2 answers
  • NEED ANSWERS FAST!!!! If there are 100 students in a room and 40 of them are boys, how many are girls?
    11·2 answers
  • Simplify square root at end. pythagoreoms theorm
    13·2 answers
  • Please I will give brainliest
    12·2 answers
  • What is the determinant of the coefficient matrix of the system 9x+ Oy + 5z -
    5·1 answer
  • Hey i hope ur having a good day can you answer these?<br> thank you
    9·2 answers
  • Which of these is a non-real complex number?
    12·2 answers
  • I need help on 3 the explanation is above on how to do it. NOT A TEST
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!