Help me with this question

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,

tatiyna

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

7 0

3 years ago

An airline weighed the carry-on luggage of all its

nikklg [1K]

Using the graph, it is found that 976 passengers had carry-on luggage that weighed less than 20 lb.

<h3>Graph:</h3>

The graph is not given in this problem, but an internet search indicates that the information it contains is as follows:

120 passengers carry luggage of 4 lb or less.

222 passengers carry luggage between 5 lb and 9 lb.

378 passengers carry luggage between 10 lb and 14 lb.

256 passengers carry luggage between 15 lb and 19 lb.

90 passengers carry luggage between 20 lb and 24 lb.

40 passengers carry luggage between 25 lb or more.

Hence, the number of passengers with luggage below 20 lb is:

$120 + 222 + 378 + 256 = 976$

976 passengers had carry-on luggage that weighed less than 20 lb.

A similar problem, also involving the use of graph, is given at brainly.com/question/25836450

7 0

2 years ago

4. Alejandro Juarez is paid $829 every two weeks. a. What is Alejandro's yearly salary?

Natalka [10]

Answer:

1. 21,554 PER YEAR

2. 1658 PER MONTH

Step-by-step explanation:

a.

so there are approximately 52 weeks per year

and alejandro juarez gets 829$ per 2 weeks

1..............LETS FIGURE OUT HOW MUCH HE EARNS PER WEEK

SO 829/2=414.5

so he gets 414.5 $ PER WEEK

2............LETS MULTIPLY THE AMOUNT OF MONEY PER WEEK BY THE WEEKS

SO 414.5*52=21554

SO ALEJANDRO JUAREZ EARNS 21,554$ PER YEAR

B.

SO WE ALREDY KNOWS ALEJANDRO EARNS 414.5$ PER WEEK

AND THERE ARE APPROXIMATELY 4 WEEKS IN A MONTH

SO 414.5*4=1658

SO HE EARNS 1658$ PER MONTH

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

PEACE!

8 0

3 years ago

The local hospital offers an incentive for nurses to work longer shifts. After a regular 8-hour shift, they can make double time

Evgesh-ka [11]

Answer:

$26.70/hour

Step-by-step explanation:

Let's look at 1 day.

She works a 12 hour shift. For the first 8 hours, she receives her regular hourly salary. That means 8 hours of pay at her regular hourly salary.

Then she works another 4 hours at her overtime pay. Her overtime pay is twice her regular salary, so the extra 4 hours at overtime pay are paid as if they were 8 hours of regular work. In effect, she is earning 16 hours of regular pay per day.

Monday through Friday means 5 days of work per week.

5 days/week * 16 hours/day = 80 hours/week

She is earning as if she were working 80 hours of regular pay per week.

base salary = (gross weekly income)/(effective number of hours in 1 week)

base salary = $2136/80

base salary = $26.70/hour

3 0

3 years ago

Complete the point-slope equation

BigorU [14]

Answer:

y -3 = -1/2 x (x-1)

Step-by-step explanation:

4 0

2 years ago