A rectangular box without a lid is to be made from 48 m2 of cardboard. Find the maximum volume of such a box. SOLUTION We let x, y, and z to be the length, width, and height, respectively, of the box in meters. Then we wish to maximize V

Answers

Answer 1
Answer:

Answer:

The maximum volume of such box is 32m^3

V = x×y×z = 32 m^3

Step-by-step explanation:

Given;

Total surface area S = 48m^2

Volume of a rectangular box V = length×width×height

V = xyz ......1

Total surface area of a rectangular box without a lid is

S = xy + 2xz + 2yz = 48 .....2

To be able to maximize the volume, we need to reduce the number of variables.

Let assume the rectangular box has a square base,that means; length = width

x = y

Substituting y with x in equation 1 and 2;

V = x^2(z) ....3

x^2 + 4xz = 48 .....4

Making z the subject of formula in equation 4

4xz = 48 - x^2

z = (48 - x^2)/4x .......5

To be able to maximize V, we need to reduce the number of variables to 1, by substituting equation 5 into equation 3

V = x^2 × (48 - x^2)/4x

V = (48x - x^3)/4

differentiating V with respect to x;

V' = (48 - 3x^2)/4

At the maximum point V' = 0

V' = (48 - 3x^2)/4 = 0

Solving for x;

3x^2 = 48

x = √(48/3)

x = √(16)

x = 4

Since x = y

y = 4

From equation 5;

z = (48 - x^2)/4x

z = (48 - 4^2)/4(4)

z = 32/16

z = 2

The maximum volume can be derived by substituting x,y,z into equation 1;

V = xyz = 4×4×2 = 32 m^3


Related Questions

A restaurant mixes homemade barbecue sauce with their smoked pulled pork using a ratio of two cups of sauce for every four pounds of shredded pulled pork. Write two rates to represent this relationship.
1. Angle AOC has what measurement according to the protractor?
In order to buy the microscope, we plan to walk dogs after school, charging $3 per dog. To reward the dogs, we will buy a box of treats for $5 as we start the business. The price of the microscope is $254. How many dogs do the friends need to walk in order to have enough money to buy the microscope?
What expression represents 16 more than 5 times a number, n?
Lines v and w are parallel. Which statement can you NOT deduce from this information?m∠2+m∠5=180m∠3+m∠8=180∠4-∠7∠1=∠8

Can someone please help me with this question the first one

Answers

The statement B is true the corresponding lines are proportional and the angles are congruent. The question with graph is A. AB with MN; BC with NL; AC with NL

Please Help! I'm lost, in a maze and I can't find my way out.

Answers

Show us the maze and we will help

Three teams, A, B and C, play in a competition.games won by A: games won by B = 3:1
games won by B: games won by C = 4:3
Team B has won 8 games.
In total, how many games have the three teams won?

Answers

Answer:

A = 24

B = 8

C = 6

Step-by-step explanation:

4:3 from B:C

8:6

8 games won by B and 6 games won by C.

3:1 from A:B

24:8

24 by A and 8 by B

Final answer:

Team A won 24 games, Team B won 8 games and Team C won 6 games. So, the total games won by all three teams is 38.

Explanation:

From the problem, we know that the ratio of games won by Team A to Team B is 3:1, and the ratio of games won by Team B to Team C is 4:3. We also know that Team B has won 8 games.

Since the ratio of Team B to Team A is 1:3, Team A must have won 3 times as many games as Team B. Therefore, Team A has won 3 * 8 = 24 games.

The ratio of games won by Team B to Team C is 4:3. This means Team B won 4 games for every 3 games Team C won. Since Team B won 8 games, Team C must have won 3/4 as many games as Team B. Therefore, Team C won 3/4 * 8 = 6 games.

So, in total, the three teams won 24 + 8 + 6 = 38 games.

Learn more about Ratio here:

brainly.com/question/32531170

#SPJ3

Mr. Gordon has 13 girls and 14 boys in his fourth period algebra class. One person is chosen at random.What is the probability that the person chosen is a boy?
A. 1/14
B. 1/27
C. 13/14
D. 13/27
E. 14/27

Answers

The probability that the person chosen is a boy is 14/27.

Number of girls = 13

Number of boys = 14

Total students = 27

What is probability?

Probability is a measure of the likelihood of occurrence of an event.

P(event) = Favorable outcomes / total outcomes

Favourable outcomes = 14 because there are 14 boys

Total outcomes =27

So, the probability that the person chosen is a boy will be given by:

P(boy)=14/27

So, the probability that the person chosen is a boy is 14/27.

Hence, the probability that the person chosen is a boy is 14/27.

To get more about probability visit:

brainly.com/question/24756209

Answer:

E

Step-by-step explanation:

It's E because you have to add 13 and 14 and as you can see there's 14 boys so it's E.

HELP MEE ILL MARK BRAINLEIST

Answers

Answer:

3x-3 I think that's it.

Step-by-step explanation:

Answer:

The vertex is (1, -4)

Step-by-step explanation:

Simplify the expression 7(1 +5v) =​

Answers

the answer is 7 + 35v

Answer:

7 + 35v

Step-by-step explanation:

7 × 1 + 5v × 7

7 + 35v

Hope this helps and have a nice life d: