1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nookie1986 [14]
3 years ago
7

The function ​f(x,y)=2x + 2y has an absolute maximum value and absolute minimum value subject to the constraint 9x^2 - 9xy + 9y^

2 =25. Use Lagrange multipliers to find these values.
Mathematics
1 answer:
deff fn [24]3 years ago
4 0

Answer:

the minimum is located in x = -5/3 , y= -5/3

Step-by-step explanation:

for the function

f(x,y)=2x + 2y

we define the function g(x)=9x² - 9xy + 9y² - 25  ( for g(x)=0 we get the constrain)

then using Lagrange multipliers f(x) is maximum when

fx-λgx(x)=0 → 2 - λ (9*2x - 9*y)=0 →

fy-λgy(x)=0 → 2 - λ (9*2y - 9*x)=0

g(x) =0 → 9x² - 9xy + 9y² - 25 = 0

subtracting the second equation to the first we get:

2 - λ (9*2y - 9*x) - (2 - λ (9*2x - 9*y))=0

- 18*y + 9*x + 18*x - 9*y = 0

27*y = 27 x  → x=y

thus

9x² - 9xy + 9y² - 25 = 0

9x² - 9x² + 9x² - 25 = 0

9x² = 25

x = ±5/3

thus

y = ±5/3

for x=5/3 and y=5/3 →  f(x)= 20/3 (maximum) , while for x = -5/3 , y= -5/3 →  f(x)= -20/3  (minimum)

finally evaluating the function in the boundary , we know because of the symmetry of f and g with respect to x and y that the maximum and minimum are located in x=y

thus the minimum is located in x = -5/3 , y= -5/3

You might be interested in
WILL GIVE BRAINIEST TO THE PERSON THAT ANSWERS ALL THREE QUESTIONS ASAP!
Radda [10]

Answer:

1. Your answer would be C) 2√3-5√2.

2. Your answer would be -39.7i.

3. Your answer would be -1.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
After once again losing a football game to the college'ss arch rival, the alumni association conducted a survey to see if alumni
antoniya [11.8K]

Answer:

a) The 90% confidence interval would be given (0.561;0.719).

b) p_v =P(z>2.8)=1-P(z

c) Using the significance level assumed \alpha=0.01 we see that p_v so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion is higher than 0.5 or 50%.    

Step-by-step explanation:

1) Data given and notation  

n=100 represent the random sample taken    

X=64 represent were in favor of firing the coach

\hat p=\frac{64}{100}=0.64 estimated proportion for were in favor of firing the coach

p_o=0.5 is the value that we want to test since the problem says majority    

\alpha represent the significance level (no given, but is assumed)    

z would represent the statistic (variable of interest)    

p_v represent the p value (variable of interest)    

p= population proportion of Americans for were in favor of firing the coach

Part a

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 90% confidence interval the value of \alpha=1-0.9=0.1 and \alpha/2=0.05, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=1.64

And replacing into the confidence interval formula we got:

0.64 - 1.64 \sqrt{\frac{0.64(1-0.64)}{100}}=0.561

0.64 + 1.64 \sqrt{\frac{0.64(1-0.64)}{100}}=0.719

And the 90% confidence interval would be given (0.561;0.719).

Part b

We need to conduct a hypothesis in order to test the claim that the proportion exceeds 50%(Majority). :    

Null Hypothesis: p \leq 0.5  

Alternative Hypothesis: p >0.5  

We assume that the proportion follows a normal distribution.    

This is a one tail upper test for the proportion of  union membership.  

The One-Sample Proportion Test is "used to assess whether a population proportion \hat p is significantly (different,higher or less) from a hypothesized value p_o".  

Check for the assumptions that he sample must satisfy in order to apply the test  

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.  

b) The sample needs to be large enough  

np_o =100*0.64=64>10  

n(1-p_o)=100*(1-0.64)=36>10  

Calculate the statistic    

The statistic is calculated with the following formula:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o(1-p_o)}{n}}}  

On this case the value of p_o=0.5 is the value that we are testing and n = 100.  

z=\frac{0.64 -0.5}{\sqrt{\frac{0.5(1-0.5)}{100}}}=2.8

The p value for the test would be:  

p_v =P(z>2.8)=1-P(z

Part c

Using the significance level assumed \alpha=0.01 we see that p_v so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion is higher than 0.5 or 50%.    

6 0
3 years ago
Plz help this is from Khan academy ty!!
Trava [24]

Answer:

The answer is A

7 0
3 years ago
4st^2-s^2 were s=5 and t=7
barxatty [35]

       ➣ Assignment: \bold{Solve \ Equation: \ \left(4\left(5\cdot \:7^2\right)\right)-5^2}

↔↔↔↔↔↔↔↔

       ➣ Answer: \boxed{\bold{955}}

↔↔↔↔↔↔↔↔

Explanation: ↓↓↓↓↓

↔↔↔↔↔↔↔↔

       ➤ [ Step One ] Follow PEMDAS Order Of Operations

\bold{4\left(5\cdot \:7^2\right): \ 980}

       ➤ [ Step Two ] Rewrite Equation

\bold{4\left(5\cdot \:7^2\right)}

       ➤ [ Step Three ] Calculate Within Parenthesis

\bold{4\left(5\cdot \:7^2\right): \ 245}

       ➤ [ Step Four ] Rewrite Equation

\bold{4\cdot \:245}

       ➤ [ Step Five ] Multiply

\bold{4\cdot \:245: \ 980}

       ➤ [ Step Six ] Rewrite Equation

\bold{980-5^2}

       ➤ [ Step Seven ] Calculate Exponents

\bold{5^2: \ 25}

       ➤  [ Step Eight ] Rewrite Equation

\bold{980-25}

       ➤  [ Step Nine ] Solve

\bold{955}

↔↔↔↔↔↔↔↔

\bold{\rightarrow Mordancy \leftarrow}

4 0
3 years ago
Help please please help​
GREYUIT [131]

Answer:

24/35

Step-by-step explanation:

Hope this helps!:)

5 0
2 years ago
Read 2 more answers
Other questions:
  • Pls help i'll mark as brainliest pls help
    12·1 answer
  • Jeff drove 249 laps around the racetrack is 9 miles long. how many miles did jeff drive
    8·1 answer
  • Nandini makes 'halwa' one evening and divides it into four equal portions for her family of four. However, just as they are abou
    11·1 answer
  • jayden and carson are selling t-shirts and sweatshirts for a fundraiser. jayden sells 9 t-shirts and 3 sweatshirts for $288. car
    14·1 answer
  • Solve for y: y/3=-4+y<br><br> What is y?
    14·1 answer
  • I NEED HELP W THIS QUESTION!!
    9·1 answer
  • Factor (x^2-26x+169-y^2)
    5·1 answer
  • Another easy question need fast please
    15·1 answer
  • 20 points math there are 2 queshtons awnser both
    13·1 answer
  • There are 5 red balls, 4 blue balls, 6 yellow balls and 10 green balls in a box,
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!