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


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Using the table of ordered pairs, which equation shows the linear relationship between the x and y values? ---- ----

x|y

-2|2

1|5

3|7

---- ----

A. y = x + 4

B. y = -x

C. y = x - 4

D. y = 4 - x

Answers

Answer:

y = x + 4

Step-by-step explanation:

y = mx + b (m = slope; b = y-intercept)

I used 2 points (-2 , 2) and (1 , 5) to calculate the slope of the line

m= (y₂ - y₁)/(x₂ - x₁)

(5-2)/(1--2) = 3/3= 1

y = 1x + b

using point (1, 5)

5 = 1(1) + b

5 = 1 + b

b = 5-1

b=4

y= 1x + 4 or simply y= x + 4

Answer:

A y = x + 4

yeh i did the test

Step-by-step explanation:

Right triangle ABC is shown. Which of these is equal to cos(A)?A) cos(B)
B) cos(C)
C) sin(B)
D) sin(C)

Answers

Answer: C

cosA=AC/AB

sinB=AC/AB

hence cosA=sinB

Answer:

C).

Step-by-step explanation:

Since angles A and B are complementary, their cofunctions are equal. So, cos(A) = sin(B).

Amy raises $58.75 to participate in a walk-a-thon. Jeremy raises $23.25 more than Amy. Oscar raises 3 times as much as Jeremy. How much does Oscar raise? Please show work and equation and this is 5th grade math.1. 246.00
2. 245.00
3. 246.08

Answers

Answer:

246.000

Step-by-step explanation:

Well If you take it and Line it up like this,

(A)Amy; 58.75

(J)Jeremy; A+23.25

(O)Oscar; A+23.25= ?x3

This is an easy way to find out what it is you need to do, So A+23.25 is 58.75+23.2 which should give you the value of 82, which brings you to the next step of A+23.25= ?x3 which in this you only wanna focus on the ?x3, we now know ?= 82 so this brings it to 82 times 3 which gives you a value of 246. Thus giving you your answer.

  Hope this helps.

HELP ME I WILL GIVE BRAINLIEST California has a population of approximately 4 × 10^7 people and South Dakota has a population of approximately 8 × 10^5 people.

Answers

The population in California is 50 times greater than the population in South Dakota.

The number of times the population in California is higher than that in South Dakota

To find out how many times greater the population in California is than in South Dakota, you can divide the population of California by the population of South Dakota:

Population of California = 4 * 10⁷

Population of South Dakota = 8 * 10⁵

Population ratio = (Population of California) / (Population of South Dakota)

Population ratio = (4 * 10⁷) / (8 * 10⁵)

Population ratio = 50

Therefore the population in California is 50 times greater than the population in South Dakota.

Learn more on calculating ratio here brainly.com/question/2328454

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Question

California Has A Populatio Of Approximately 4*10^(7)People And South Dakota Has Populatio Of Approximately 8*10^(5) People. How Many Times Greater Is The Population In California Than In South Dakota

california has a populatio of approximately 4*10^(7)people and south dakota has populatio of approximately 8*10^(5) people. how many times greater is the population in california than in south dakota

Answer:

40000000 800000

Step-by-step explanation:

whats the question here?

The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year. P=$4000, r=5% t= 1 year

Answers

9514 1404 393

Answer:

  $200

Step-by-step explanation:

The interest is given by ...

  I = Prt

  I = ($4000)(0.05)(1) = $200

The simple interest owed is $200.

David says he has 2/3 of a pipe length​ left, while Don says he has 11/16 of a length left. Which person has the longest section​ left?

Answers

Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.

David says he has 2/3 of a line length left, while Wear says he has 11/16 of a length left.

Convert the fraction numbers 2/3 and 11/16 into the decimal number. Then we have

2/3 = 0.6667

11/16 = 0.6875

The decimal number 0.6875 is greater than 0.6667. Then the fraction number 11/16 is greater than the fraction number 2/3.

Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.

More about the Algebra link is given below.

brainly.com/question/953809

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Answer:

Don

Step-by-step explanation:

1. We make the fractions have common denominators so it is easier to compare them. We can do this buy multiplying 2/3 by a factor of 16, so it becomes 32/48. For 11/16, we multiply by a factor of 3 so it becomes 33/48. It is now apparent that Don has the longer pipe.