Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p is a square. Let the sides of the rectangle be x and y and let f and g represent the area (A) and perimeter (p), respectively. Find the following. A = f(x, y) = p = g(x, y) = ∇f(x, y) = ????∇g = Then ???? = 1 2 y = implies that x = . Therefore, the rectangle with maximum area is a square with side length .

Answers

Answer 1

Answer:

a) Rectangle of maximum area ( given perimeter p ) is

A= x²     That means the rectangle of maximum area,  is a square

Step-by-step explanation:

The equation:   A (x,y) = x*y   is the area of a rectangle  ( to maximize)

Subject to:   p  = 2*x + 2*y    or  g(x,y) =  2*x + 2*y -p

Now

A(x,y) = x*y         δA/δx  = y          δA/δy  = x

And

g(x,y) =  2*x + 2*y -p

δg(x,y)/δx = 2       and    δg(x,y)/δy  = 2

Matching respective partial derivatives we get a system of equation

δA/δx  = y  = λ *  = δg(x,y)/δx = 2  

y = 2*λ

δA/δy  = x  = 2*λ

The system of equations is:

y = 2*λ

x  = 2*λ

And 2*x + 2*y -p = 0

p = 2*x +2*y

So   x = y      p is equal either  4*x  or  4*y

Solving for λ


Related Questions

Find the interquartile range (IQR) of the data in the box plot below.
cm
Amount of rain in Vietnam cities
(centimeters)
+
++
0 1 2
3
4
5
6
7
8
9
10
Stuck? Watch a video or use a hint.

Answers

Answer:

1.5 cm

Step-by-step explanation:

Interquartile range (IQR) = Q3 - Q1

From the box plot given, the third quartile (Q3) is the data value that falls exactly at the end of the edge of the rectangular box = 7 cm

The first quartile (Q1) is the data value exactly at the beginning of the edge of the box = 5.5 cm

Interquartile range (IQR) = 7 - 5.5 = 1.5 cm

PLS HELP ITS DUE TODAY

Which has the greatest effect on the amount of salt in a salt marsh?

A) the number of animals living in the marsh
B) the closeness of the marsh to the ocean
C) the depth of the water in the marsh
D) the temperature of the water in the marsh

Answers

Answer:

the answer is B because ocean water has salt in it

A textbook store sold a combined total of 354 history and sociology test books in a week. The number of history textbooks sold was two times the number of sociology textbooks sold. How many textbooks of each those were sold?

Answers

Answer: History textbooks sold = 236, Sociology textbooks sold = 118

Step-by-step explanation:

Given

- There are in total 354 books

- Let x be the number of sociology textbooks sold

- Let 2x be the number of history textbooks sold

Solve

Given

x + 2x = 354

Combine like terms

3x = 354

Divide 3 on both sides

3x / 3 = 354 / 3

x = 118

2x = 118 × 2 = 236

Hope this helps!! :)

Please let me know if you have any questions

Answer:

sociology textbooks = 118history textbooks = 236

Explanation:

sociology textbooks = 2 × history textbooks

354/3 = 118

sociology textbooks = 118

history textbooks = 118×2 = 236

Ben has a box of marbles. 30 of the marbles are red, 14 are green and 16 are blue. Ben randomly selects a marble from the box, records the color and then replaces the marble in the box. If he selects a marble 30 times, how many times do you predict he will select a blue marble?

Answers

Answer:

he will select about 5 blue marbles

Step-by-step explanation:

( BONUS POINTS PLEASE HELP ) the bases of a trapezoid are 24 ft and 6ft the height of the trapezoid is 12 ft what is the area of the trapezoid​

Answers

Answer:

1728

Step-by-step explanation:

I cant understand the question that well but i think this is the right one

Answer:

180

Step-by-step explanation:

The formula to find the area of a trapezoid is base1 + base2. Multiply that by the height of the trapezoid, then divide your answer until that point by 2. When we do the same thing here we get:

(24+6)12/2

=30(12)/2

=360/2

=180

*Brainliest would be appreciated*

Write an equation that can be used to find the degree measure of angle b

Don’t put links !

Answers

Answer:

Because they are supplementary angles, their sum is 180°.

∠b = 180° - 81°

∠b = 99°

Answer:

[tex]180-81=b[/tex]

Step-by-step explanation:

Supplementary angles are angles that add up to 180. Normally, they are supplementary because they lie adjacent to one another on a line.

In this base, b is supplementary to 81! Meaning, to find b we can simply subtract 81 from 180.

~~~~~~~~~~~~~~~~~~~

Have a nice day, fam. Spread The Love <3

A researcher posts a radio advertisement offering $35 in exchange for participation in a short study. The researcher accepts the first eight people who respond to the advertisement. Which of the following statements is true about the sample? (5 points)
A. It is a valid sample because the first eight people were selected to participate.
B. It is not a valid sample because it is not a random sample of the population.
C. It is a valid sample because money was offered to participants.
D. It is not a valid sample because it is only a short study.

Answers

Answer:

B.

Step-by-step explanation:

Its meh best guess

Answer:

B.

Step-by-step explanation:

I think it is B

What is the sum of 1 - 0.5 + 899

Answers

Answer:

899.5

Step-by-step explanation:

Write the property that matches the equation.
3+(4+7)=(3+4)+7

Answers

Answer:

associative property

Step-by-step explanation:

Answer:

Associative property of addition

Step-by-step explanation:

The associative property states that numbers can be added or multiplied regardless of their paratheses. This means that how the numbers are grouped can change and still be equal. Another example of this would be [tex]2+(6+5)=(2+6)+5[/tex]. In both equations the sides are balanced.

6. What equation would you use to solve for x?*

Answers

tan70=x/6
Opposite over adjacent

Tomas drew a rectangle with an area of 6 square centimeters.what is the greatest possible perimeter of this rectangle?Explain please. i want 20 answers please

Answers

The answer is 14. Hope it helps!

1. Gracie and her son Landon are celebrating spring with an egg hunt! Gracie has hidden eggs filled with candy
for Landon to find.

(a) Landon finds a total of 27 eggs. One third of the eggs have 4 pieces of candy, the rest have 2 pieces of
candy. How many pieces of candy did Landon get?

(b) Gracie offers him a deal: he can either have three pieces of candy now, or if he waits until after lunch he
can have one-seventh of his candy. Which way gets Landon the most candy?

Answers

Answer:

a is 72 total pieces of candy

b is more candy if he waits and gets one-seventh

Step-by-step explanation:

a. 9 eggs have 4 so 9x4=36

leaving 18 eggs with 2 so 18x2=36

36+36=72 total

b. 3 now or...

1/7 x 72 = 10.28

Answer:

b.72×1/7=10.28

I think he can wait untul after lunch time

Step-by-step explanation:

Hope this right.But if it's not,im so sorry...Have a nice day

Select the correct answer.
Which is the apparent solution set of the system of equations graphed on the grid?



A.
{(-0.25,0), (4.25,0)}
B.
{(1,-4), (4,-1)}
C.
{(0,-5), (5,0)}
D.
{(0,-1), (2,-5)}

Answers

B, because the lines connect at (1,-4) and (4,-1)

The solution set of the system of equations graphed on the grid is

{(1, -4), (4, -1)}. Hence, option B is the right choice.

What do we mean by the solution set to a system of equations?

The solution set to a system of equations is the set of all points that satisfies every equation in the given system.

How do we solve the given question?

We are asked to find the apparent solution set of the system of equations graphed on the grid.

The solution set will be the set of common points on the graph as they satisfy both the equations in the given system.

The common points are (1, -4) and (4, -1), as the equations pass through these points simultaneously.

∴ The solution set of the system of equations graphed on the grid is

{(1, -4), (4, -1)}. Hence, option B is the right choice.

Learn more about the system of equations at

https://brainly.com/question/2226590

#SPJ2

Rabbit populations can double every 30
days. If there are 20 rabbits on a farm,
how many rabbits will be on the farm
after 210 days?
First, complete the equation:
Future Amount = [?](1+[]0

Answers

I think the answer is 140.
My equation: 210 divided by 30 equals 7. Then, 7 times 20 rabbits equals 140 rabbits. Tell me if I'm right I'm not really sure.

Pls help i will mark brainliest
:D Stay cooool

Answers

Answer:

B) -40

C)22

D)-11

Step-by-step explanation:

a) 60

b) -40

c) 22

d) -11

hope it helps :D

hi I really need help with my math questions because I am on the edge of failing math class please help me out thank you!

The owner of an art supply store wants to know which arts are popular among her customers.
Select the methods that will likely create a representative sample.

1 - Group of answer choices

2 - Survey every employee who works in the store.

3 - Survey every customer whose name is picked randomly from a list of all customers.

4 - Survey every fifth person at a painting exhibition.

5 - Survey every fifth customer who purchases sketching supplies.

6 - Survey every customer who spends more than $200.

Answers

survey every employee who works in the store

Step-by-step explanation:

u(3u+4)-u(u+2)

HELP PLEASE I NEED IT RN

Answers

the answer is 2u x (u+1)

please help i can't figure this problem out​

Answers

Answer:

The initial fee is $2

Step-by-step explanation:

If each stop is $1.50, then the initial fee for each of the trips is $2.

4*1.5=6, 6+2=8

8*1.5=12, 12+2=14

12*1.5=18, 18+2=20

Why Earth Day is important?

Answers

Answer:

Earth Day is important because it raises mass awareness for climate change and global warming. Earth day inspires the act to fight and do something to help our environment.

Answer:

earth day is important because ur saving the earth from polution,global warming and ice caps melting

Step-by-step explanation:

hav a gud day fam ^_^

Un grupo de estudiantes alquila un piso por el que tienen que pagar 420 € al mes. Uno de ellos hace cuentas
y observa que si fueran dos estudiantes más, cada uno tendría que pagar 24 € menos. ¿Cuántos estudiantes
han alquilado el piso? ¿Cuánto paga cada uno?

Answers

Answer:

I dont know but i just need these points

On the first two downs, a football team lost 15 yards and then lost 19 yards. Write an expression with addition that shows the changes in yards on the first two downs.​

Answers

Answer:

The expression with addition that shows the changes in yards on the first two downs is -(15 + 19) = -34

Step-by-step explanation:

At the first down, the net yardage of the football team was of 0.

After the first play:

Lost 15 yards, so the change in yards is:

0 - 15 = -15

After the second play:

Lost 19 yards, so the change in yards is:

-15 - 19 = -(15 + 19) = -34

The expression with addition that shows the changes in yards on the first two downs is -(15 + 19) = -34

could someone possibly help me ??

Answers

Answer:

b

Step-by-step explanation:

The answer is A. Remember reflections by thinking of them as mirrors, you are looking into the mirror and your reflection looks back at you.

Can someone please help me am stuck on this, thanks.

Answers

Answer:

First box: -5, 0, 6, 9

Second box: 10, 12.5

Step-by-step explanation:

4x-12≤24

4x≤24+12

4x≤36

x≤36÷4

x≤9

So the first box would have all the solutions less than or equal to 9:

-5, 0, 6, 9

And the second box would have the solutions greater than 9:

10, 12.5

a tringle with sides of lengths 16, 30, and 35 is a right triangle

Answers

Answer: no

Step-by-step explanation:

when using the pythagorean theorm, the math doens't add up

16^2+30^2 does not equal 35^2

hope this helps!

Solve the systems of equations by using the substitution method,show your work.
3x - 8y = -50
6y = x
Please.Help

Answers

3•(6y)-8y=-50
18y-8y=-50
10y=-50
y=-5

Four members of a relay team evenly split the distance of a race. Each person ran more than 100 meters. Which inequality can be used to represent d, the total distance the group ran?
4 d greater-than 100
4 d less-than 100
StartFraction d Over 4 EndFraction greater-than 100
StartFraction d Over 4 less-than 100

Answers

Answer:

The answer would be C.

Step-by-step explanation:

Since each person ran more than 100 meters, the answer would be greater than 100.

d is the total distance the group ran, not the individual distance, so it couldn't be 4d because that would mean it would be 4 times d.

The answer would be d divided by 4. d/4. That is because the total distance divided by 4 would be the individual distance.

Answer:

it is c

Step-by-step explanation:

A point is chosen at random on AK what is the probability that the point will be on FI don't reduce

Answers

Answer: 3/10

Step-by-step explanation:

The probability that the point will be on FI is 3/10 if a point is chosen at random on AK the answer is 3/10.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have a number line shown in the picture:

Total Number partition or gaps between each letter(between A and K):

= 10

Total number of outcomes = 10

Total number of favorable outcomes(between F and I) = 3

The probability that the point will be on FI:

By using the definition of the probability:

= favorable outcomes/total outcomes

= 3/10

Thus, the probability that the point will be on FI is 3/10 if a point is chosen at random on AK the answer is 3/10.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ2

Complete the set of data with value so that the mean of the data is 24

26, 35, 10, 18, 15, 37, 25, 20, 15, ?

Answers

26+35+10+18+15+37+25+20+15/9= 22.33

Given a standardized normal distribution (with a mean of O and a standard deviation of 1), determine the following probabilities.
a. P(Z > 1.09) b. P(Z < -0.22) c. P(-1.96 d. What is the value of Z if only 8.08% of all possible Z-values are larger?

Answers

Answer:

a) P(Z > 1.09) = 0.1379

b) P(Z < -0.22) = 0.4129.

c) P(Z < -1.96) = 0.025, P(Z > -1.96) = 0.025

d) Z = 1.4

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

a. P(Z > 1.09)

This is 1 subtracted by the pvalue of Z = 1.09.

Z = 1.09 has a pvalue of 0.8621

1 - 0.8621 = 0.1379, so

P(Z > 1.09) = 0.1379

b. P(Z < -0.22)

This is the pvalue of Z = -0.22.

Z = -0.22 has a pvalue of 0.4129. So

P(Z < -0.22) = 0.4129.

c) P(Z < -1.96) or P(Z > -1.96)

Z = -1.96 has a pvalue of 0.025. So

1 - 0.025 = 0.975

P(Z < -1.96) = 0.025

P(Z > -1.96) = 0.025

d. What is the value of Z if only 8.08% of all possible Z-values are larger?

Z with a pvalue of 100 - 8.08 = 91.92 = 0.9192, so Z = 1.4

Determine the intercepts of the line I need help quick!!!!!

Answers

Answer:

x-inter = (-40,0), y-inter= (0,15)

Step-by-step explanation:

the fitnessgram pacer test is an automated aerobic capacity test that progressively gets more difficult as it continues.

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