Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum F(x,y)= 33 - x² - y² x + 5y = 26 There is a __ value of __ located at (x,y)= __ (Simplify your answers.)

Answers

Answer 1

Using Lagrange multipliers, there is a maximum value of f(x,y) = 33 - x² - y²  located at (x,y)= (4,4/5).

We can use the method of Lagrange multipliers to find the extremum of f(x,y) subject to the given constraint

Let L(x,y,λ) = f(x,y) - λ(g(x,y)) where g(x,y) = x + 5y - 26 be the Lagrangian function.

Then, we have the following system of equations

∂L/∂x = -2x - λ = 0

∂L/∂y = -2y - 5λ = 0

∂L/∂λ = x + 5y - 26 = 0

Solving this system of equations, we get

x = 4, y = 4/5, and λ = -8/5

Now, we need to check whether this point corresponds to a maximum or a minimum of f(x,y).

The Hessian matrix of f(x,y) is

H(f) = [(-2) 0; 0 (-2)]

The determinant of H(f) is det(H(f)) = (-2)(-2) - 0 = 4, which is positive. Also, fx x(-8/5) = -2 < 0. Therefore, the point (4, 4/5) corresponds to a maximum of f(x,y) subject to the given constraint.

The maximum value of f(x,y) subject to the given constraint is

f(4, 4/5) = 33 - 4² - (4/5)² = 13.6

Therefore, the extremum of f(x,y) subject to the given constraint is a maximum, and the maximum value of f(x,y) is 13.6 located at (x,y) = (4, 4/5).

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Related Questions


What is the amplitude of y = 3sin4θ ? (F) 4/3 (G) 3 (H) 4 (I) 2π

Answers

Answer:

a sin(bθ−c)+d

→ Using this, find the amplitude based off of the given formula. Use the expression as a reference to help you identify a.

a = 3

b = 4

c = 0(no defined value)

d = 0(impossible to identify)

→ Find a.

→ Since a is already given, we know that a = 3, therefore, the amplitude is 3

A= 3, B= 4, C= 0, D=0

The price of a trampoline before tax is $300. The salesvtax is 4%​

Answers

Answer - $312

300 x 1.04 = 312

Answer:

The total price is $312 and the sales tax is 12

Step-by-step explanation:

300 x 0.04= 12

300 + 12 = 312

Help this bestie plz...

Help this bestie plz...

Answers

Step-by-step explanation:

THE Coordinates of C will be

» C = (4, 6)

Answer:

C=(4,6)

HAVE A BEAUTIFUL DAY

What is the final elevation of:

A fish starts at negative 9 meters and changes negative 11 meters.


Please HELP!!! I'm begging you!

Answers

Answer:

the fish has a final elevation of negative 2

Step-by-step explanation:

A work breakdown structure (wbs) shows tasks, dates, and dependencies. true false

Answers

A work breakdown structure (wbs) shows tasks, dates, and dependencies. The given statement is false.

In project management and systems engineering, a work-breakdown structure is a deliverable-focused division of a project into more manageable parts. A essential project deliverable that divides the team's work into digestible chunks is a work breakdown structure.

A project's tasks are organized hierarchically in a work breakdown structure (WBS). The WBS "breaks down" a project's structure into doable deliverables. A project's tasks are organized hierarchically in a work breakdown structure (WBS).

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On three science tests, Olivia has received scores of 89%, 98%, and 96%. What is the lowest score Olivia can get on her fourth and final science test to
achieve an average score of 95%?

Answers

Answer:

97%

Step-by-step explanation:

89%+98%+96%+?=95×4

283+?=380

?=380-283

?=97%

The lowest score Olivia can get on her fourth test is 97%.

The average score can be determined by dividing the sum of the four scores by the total number of tests taken.

The first step is to determine the sum of the three scores Olivia already has.

Sum of scores = 89 + 98 + 96 = 283%

The second step is to multiply 95 x 4. 95% x 4 = 380%

The third step is to subtract 283% by 380%. 380% - 283% = 97%

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Match the given situations with their correct probabilities. Answers should be expressed as fractions in simplest form. For questions 1-2. there are 52 cards in a deck of cards. There are 13 of each suit (spades, diamonds, hearts, clubs)What is the probability of picking a spade from standard deck of playing cards?4/131/51/42/37/525/122/13

Answers

The probability of an event happening is calculated by possible events divided by total events.

From a standard deck of 52 cards, there are 13 spades.

So the possible events are 13 and the total events are 52

This will be:

prob = 13/52 = 1/4

The answer is 1/4

help please this increases my average mark

help please this increases my average mark

Answers

Answer:

He drove 111 miles

If we were given the distance Lan drove last weekend instead off how much gas he used then we would have to find the amount of gas used by lan.

Step-by-step explanation:

Ian's car can go 185 miles on 5 gallons of gas

On 5 gallons of gas lan's car can go 185 miles

Therefore in gallon of gas lan 's car can go

185/5 = 37

So, for 3 gallons of gas lan's car can go

3 × 37 = 111

for 3 gallons of gas lan's car can go 111 miles

If we were given the distance Lan drove last weekend instead off how much gas he used then we would have to find the amount of gas used by lan.

what is the measure of one angle in a regular 24-gon?

Answers

Answer:165degrees

Step-by-step explanation

Use formula N-2 × 180 N is the number of sides

24-2=22

22x180=3960 total

for each angle divide total by 24=165 degrees

What is the value of b?

What is the value of b?

Answers

The value of b should be 59

how do you find 25 percent of 1,000

Answers

Answer:The 25 percent of 1000 is equal to 250. It can be easily calculated by dividing 25 by 100 and multiplying the answer with 1000 to get 250.

Step-by-step explanation:

PLEASE HELP SUPER URGENT




Brandon plowed snow from 84 driveways in 7 days. He plowed the same number of driveways each day. Tell whether
the statement is True or False.
If Brandon continues at the same rate, he will plow 120 driveways in 12 days.


The whole statement is true.


Some of the statement is false.

Answers

Answer:

Some of the statement is false.

Step-by-step explanation:

84 driveways / 7 days = 12 driveways per day.

12 driveways x 12 days = 144 driveways

Fill in the blank.

|3.3| = ____

Answers

Answer:

it stays the same

Step-by-step explanation:

if it was -3.3 then it would change to 3.3 but because it is already in the positives it stays a positive plz double chesk if needed tho

Answer:

\(3.3\)

Step-by-step explanation:

Absolute value expresses the distance of a number from 0.

For this reason, no matter if the number is negative or positive, the absolute value of it will always be positive.

In this case, it is simply \(|3.3|=3.3\).

Graph the solution to this inequality on the number line.

−4m+3>11

Graph the solution to this inequality on the number line.4m+3&gt;11

Answers

Move constant

Subtract numbers
-4m>11-3

Evaluate and subtract
-4m>8

Divide by -4

Solution

M<-2

Answer: The person above me is correct. Here is a picture if you still dont get it..

Step-by-step explanation:

Graph the solution to this inequality on the number line.4m+3&gt;11

∠A and ∠B form linear pair. If m∠A =(6x-19)° and m∠B=(11x-22)°, find m∠B.

Answers

Answer: 121°

Step-by-step explanation:

The measure of angle B will be \(121^0\) .

What is angle?

Angle is formed by two rays lie in the plane that contains the rays.

We have,

\(m \angle A =(6x-19)^0\)

Now,

Linear pair angles are those angles whose sum is \(180^0\) .

i.e.

\(m \angle A + m \angle B=180^0\)

So,

\((6x-19)^0 +(11x-22)^0 =180^0\)

Now,

\(17x-41=180\)

\(17x=221\)

\(x=13\)

So,

\(m\angle B=(11x-22)^0\)

Putting value of x;

\(m\angle B=(11*13-22)^0\)

\(m\angle B=(121)^0\)

So, measure of angle B is \(121^0\).

Hence, we can say that the measure of angle B will be \(121^0\) .

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Solve this equation 3/5 (x-10) = 18 - 4x - 1

Answers

Answer:

x=5

Step-by-step explanation:

Good luck

Answer:

3/5(x-10)=18-4x-1
3/5x-6=17-4x
3x-30=85-20x
3x+20x=85+30
23x=115
23x/23=115/23
x=5

The table and scatter plot show the number of ice cream stand customers along with the high temperature for a given day. The line of fit represents the predicted number of customers y, on a day with a high temperature of x°F. Which statement correctly analyzes the residuals?


High Temperature (°F) Customers

82 805

76 612

91 1218

87 1074

85 894

79 675


A)

The smallest residual is 14, and the largest residual is 51. The largest residual corresponds to an outlier in the data.



B)

The smallest residual is 14, and the largest residual is 51. The largest residual does not correspond to an outlier in the data.


C)

The smallest residual is 18, and the largest residual is 45. The largest residual corresponds to an outlier in the data.


D)

The smallest residual is 18, and the largest residual is 45. The largest residual does not correspond to an outlier in the data.

Answers

Based on the information provided, the correct statement is: The smallest residual is 14, and the largest residual is 51. The largest residual corresponds to an outlier in the data.

A residual is the difference between the actual value of the dependent variable (in this case, the number of customers) and the predicted value of the dependent variable based on the model (in this case, the line of fit). In other words, it is the error or deviation between the observed data and the model.

In this case, the smallest residual is 14, and the largest residual is 51. This means that the model is most accurate when predicting the number of customers on days with temperatures close to 82°F and least accurate when predicting the number of customers on days with temperatures close to 91°F. The large residual of 51 corresponds to an outlier in the data, which means that the model is not a good fit for this data point and may not accurately predict the number of customers on days with temperatures close to 91°F.

Option A is correct because it correctly describes the range and magnitude of the residuals and identifies the largest residual as corresponding to an outlier in the data. Options B, C, and D are all incorrect because they either do not correctly describe the range or magnitude of the residuals or do not correctly identify the largest residual as corresponding to an outlier in the data.

What do you mean by statistical?

statistics is defined as: the branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.

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Figure ABCD is a kite. Find the
value of x.
B
A 2x + 10
С
2x
D
x = [?]
Enter

Figure ABCD is a kite. Find thevalue of x.BA 2x + 102xDx = [?]Enter

Answers

Answer:

x = 20

Step-by-step explanation:

The diagonals of a kite are perpendicular to each other, so the 4 angles at the  intersection are right.

The sum of the 3 angles in a triangle sum to 180° , then

2x + 2x + 10 + 90 = 180

4x + 100 = 180 ( subtract 100 from both sides )

4x = 80 ( divide both sides by 4 )

x = 20

Answer:

20 is the answer

Step-by-step explanation:

Correct for Acellus!

Can someone help me in this please

Can someone help me in this please

Answers

Angles supplementary to ∠3 are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, and ∠7.

What are supplementary angles?Two angles are considered to be supplementary if their sums total 180 degrees. If two angles in geometry add up to 180 degrees, they are said to be supplementary angles. For instance, A and B are referred to as supplementary angles if A + B = 180°. When combined, supplementary angles always make a straight angle (180 degrees).

So, angles supplementary to ∠3:

∠1 is supplementary to ∠3 (Straight angle)∠2 is supplementary to ∠3 (Inversely opposite angle)∠4 is supplementary to ∠3 (Straight angle)∠5 is supplementary to ∠3 (Adjacent angles)∠6 is supplementary to ∠3 (Alternate angles)∠7 is supplementary to ∠3 (Corresponding angle)

(Refer to the image attached below)

Therefore, angles supplementary to ∠3 are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, and ∠7.

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Can someone help me in this please

HOMEWORK DATE 3rd May, 2023 Show how the following were exercised in the creation story of any of the three religions. a) Commitment b) Creativity a. b. c) Obligation d) Generosity d) Generosity e) Servic

Answers

The creation story in Christianity exemplifies commitment creativity, obligation, generosity and service.

These values are demonstrated through God's actions and intentions in creating the world and his instructions to humanity to care for it.

Commitment, creativity, obligation, generosity and service are exercised in the creation story of Christianity:

Commitment:

In Christianity, the creation story in Genesis 1 shows God's commitment to creating the world in six days and resting on the seventh day.

This story shows that God was committed to his creation and intended it to be good.

Creativity:

The creation story in Genesis 1 also shows God's creativity in designing and bringing forth the world.

The story describes how God created the heavens and the earth, light, the seas and all living creatures, demonstrating his power and creativity.

Obligation:

In Christianity the creation story also demonstrates God's obligation to care for and provide for his creation.

In Genesis 1:29-30, God gives humans and animals all the plants and fruits on the earth for food showing his obligation to provide for them.

Generosity:

Similarly God's generosity is displayed in the creation story of Christianity.

God creates a world filled with beauty and abundance, with all the resources necessary for life to thrive.

He also gives humans and animals the ability to reproduce and multiply showing his generosity in sustaining life.

Service:

The creation story in Christianity also highlights the importance of service.

In Genesis 2:15 God places Adam in the Garden of Eden and instructs him to work and take care of it.

This shows the value of serving and caring for God's creation.

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An electrician cuts 114 meters from a roll of wire to install one LED bulb.
He has 1034 meters of wire available to install bulbs.

Use the drop-down menus to answer each question.

An electrician cuts 114 meters from a roll of wire to install one LED bulb.He has 1034 meters of wire

Answers

Answer: the first one is 22 5/8 divided by 2 2/3

and the second one is the whole number is the number of bows and the fraction is the leftover ribbon

two distinct integers are chosen at random and without replacement from the first six positive integers. compute the expected value of the absolute value of the difference of these two numbers.

Answers

The expected value of the absolute value of the difference of two distinct integers chosen at random from the first six positive integers is 35/12.

To find the expected value, we need to consider all possible pairs of distinct integers and their corresponding absolute differences. There are a total of 15 pairs, and we can list them as (1,2), (1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6), (3,4), (3,5), (3,6), (4,5), (4,6), and (5,6).

The absolute differences of these pairs are 1, 2, 3, 4, 5, 1, 2, 3, 4, 1, 2, 3, 1, 2, and 1, respectively. The expected value is the sum of the products of each absolute difference and its corresponding probability, which is 1/15 for each pair, giving us:

(1/15) × (1+2+3+4+5+1+2+3+4+1+2+3+1+2+1) = 35/12.

Therefore, the expected value of the absolute value of the difference of these two numbers is 35/12.

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I need to find indicated measure and tell which thereom I used

I need to find indicated measure and tell which thereom I used

Answers

Line GE is the perpendicular bisector of triangle LGK. This means that Line GE divides angle LGK into two equal halves. Thus, triangle LGE is congruent to triangle KGE. Therefore,

GL = GK

From the information given,

GL = 4x - 2

GK = 2x + 8

Thus,

4x - 2 = 2x + 8

4x - 2x = 8 + 2

2x = 10

x = 10/2

x = 5

If GE = 3x + 2, if we substitute x = 5, then

GE = 3 * 5 + 2 = 15 + 2

GE = 17

Substituting x = 5 into GL = 4x - 2,

GL = 4 * 5 - 2 = 20 - 2

GL = 18

Since GC is the perpendicular bisector of triangle JGL, it means that triangle JGC is congruent to triangle LGC

Thus, JG = LG

GJ = GL

GJ = 18

A Triangle has angles which measure 65 degrees and 32 degrees, What is the measure of the 3rd angle?

Answers

Answer:

jcjc

Step-by-step explanation:

Test the series below for convergence using the Ratio Test. ∑[infinity]​ to n=1 10^n​÷n! The limit of the ratio test simplifies to limn→[infinity]​∣f(n)∣ where f(n)=∣a^n​+1∣÷∣an∣​ f(n)= The limit is: (enter oo for infinity if needed) Based on this, the series Question Help:

Answers

The limit of the ratio test for the series ∑[infinity] to n=1 10^n÷n! is infinity (∞).

The ratio test is used to determine the convergence or divergence of a series. It involves taking the limit of the absolute value of ratio of consecutive terms. If the limit is less than 1, the series converges. If the limit is greater than 1 or infinity (∞), the series diverges. If the limit is exactly 1, the test will be inconclusive.

In this case, we have f(n) = ∣(10^n+1)÷(10^n)∣ = ∣10∣ = 10. The limit of f(n) as n approaches infinity is 10.

Since the limit of f(n) is greater than 1, the series fails the ratio test. This means that the series ∑[infinity] to n=1 10^n÷n! diverges. The ratio test suggests that the series does not have a finite sum and continues indefinitely.

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Find an
explicit formula for the arithmetic sequence 37, 74, 111, 148, ....
Note: the first term should be a(1).

Answers

Answer:

Step-by-step explanation:

a₁ = 37

a₂ = 74

Common difference d = a₂ - a₁ = 37

nth term = a₁ + (n-1)d

= 37 + (n-1)37

= 37n

Answer:

Below in bold.

Step-by-step explanation:

The common difference is 74-37 = 37.

nth term a(n) = a1 + (n - 1)d

= 37 + 37(n - 1)

= 37n.

The base of a rectangular prism has a base of 15 square cm. The height of the prism is 5 cm. What is the volume of the rectangular prism?

Answers

Step-by-step explanation:

eyeyeyeyeyyeyeyeyeeyeyeueueuryryru

8 (a). Which type of scale has been used in the following cases? Give proper explanation to justify your answer.
i. In a football match, Sachin has been assigned No. 1 in his shirt, Rahul No. 2, Virat No. 3, Maradona No. 4, Sunil No. 5 and so on.
ii. In your class test, X has secured third rank while Y has secured ninth rank and Z has secured sixth rank.
iii. Average monthly temperatures of the past five months were 70°, 80°, 90°, 95° and 105° Fahrenheit.
iv. Height of Ram is 150 cms., Rahim is 180 cms. and that of Robert is 160 cms.

Answers

In the given cases, the scale used is an ordinal scale. An ordinal scale is a type of measurement scale that allows for the arrangement of items or individuals based on their relative position or rank order.

i. In the case of the football match, the players are assigned specific numbers on their shirts. These numbers represent their positions or ranks within the team. The numbers, such as No. 1, No. 2, No. 3, etc., indicate the order in which the players are assigned their positions. The scale used here is ordinal because the numbers represent a rank order, but they do not convey any information about the magnitude of the differences between the positions. For example, we know that Maradona has a higher number than Virat (No. 4 > No. 3), but we cannot infer how much higher Maradona's position is compared to Virat's.

ii. In the context of the class test ranks, X securing the third rank, Y securing the ninth rank, and Z securing the sixth rank indicates the relative positions of the students based on their performance. The scale used here is also ordinal because the ranks (third, ninth, and sixth) represent a rank order. However, the scale does not provide information about the magnitude of the differences in performance between the students. We know that X has a higher rank than Y and Z, but we do not know how much higher the third rank is compared to the sixth or ninth rank.

In both cases, the use of specific numbers or ranks allows for a relative ordering of items or individuals, but it does not provide information about the magnitude of the differences between them. Therefore, an ordinal scale is appropriate in these situations.

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The average depth of five lakes is 229m. If none of the lakes is less than 194m deep then the greatest possible depth of one of these lakes in meters is,

Answers

Answer:

The average depth of five lakes is 229m. If none of the lakes is less than 194m deep then the greatest possible depth of one of these lakes in meters is,

Answer:

369

Step-by-step explanation:

* = Multiply

5*229=1145
Lakes * Average = Total Average Depth of Five Lakes

(1145-369)/4=194 (it worked)
4 is the other lakes, 369 would be considered the largest lake.
Answer is 369.

Cheers, iYekria

What is m<3? Please help

What is m&lt;3? Please help

Answers

Angle m∠3 is 79degree

What is linear pair?

Linear pair of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.

Given;

m∠1= (x+70)

m∠2= (5x+54)

Here, m1=m2

substituting the values of m1 and m2

x+70=5x+54

70+54=5x-x

124=4x

x=31 substituting in m2

m2=101

Now, m2+m3=180 (linear pair of angles)

101+m3=180

m3=79degree

So, the measure of angle m3 will be 79degree.

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