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
DaniilM [7]
3 years ago
9

Find the extreme values of f(x y)=xy subject to the constraint x^2 + y^2 -4 = 0

Mathematics
1 answer:
KATRIN_1 [288]3 years ago
4 0
Via Lagrange multipliers:

L(x,y,\lambda)=xy+\lambda(x^2+y^2-4)

L_x=y+2\lambda x=0
L_y=x+2\lambda y=0
L_\lambda=x^2+y^2-4=0

yL_x=y^2+2\lambda xy=0
xL_y=x^2+2\lambda xy=0
\implies yL_x-xL_y=y^2-x^2=0\implies y^2=x^2
\implies x^2+y^2=4=2x^2\implies x^2=2\implies x=\pm\sqrt2\implies y=\pm\sqrt2

So we have four critical points to consider, (\sqrt2,\sqrt2),(-\sqrt2,\sqrt2),(\sqrt2,-\sqrt2),(-\sqrt2,-\sqrt2). If both coordinates are positive or both are negative, we get a maximum value of (\pm\sqrt2)^2=2; otherwise, we get a minimum of (-\sqrt2)(\sqrt2)=-2.
You might be interested in
Jimmy ran with a speed of m miles per hour. How far did he run in t minutes?
Juliette [100K]

Answer:

velocity = distance / time   OR

v = d / t

In the example he runs 'm' miles in 1 hour

v = 'm' / hour

distance = velocity * time

How far did he run in 't' minutes?

Since there are 60 minutes per hour then the distance is:

distance = (velocity * time) / 60

Step-by-step explanation:

6 0
3 years ago
7.Austin has no money so he borrowed $28 over eight days from Kayla. How much did Austin borrow from Kayla each day? Show your w
MAXImum [283]
#7. let x = the amount of money he borrows each day. so, the equation would be 8x (because it’s over 8 days, so 8 times x) = 28

so equation: 8x=28
then solve for x, which is 3.5 so $3.50
4 0
2 years ago
3 A Gas station A charges $3.50 per gallon of gas plus 58 for a car wash. Gas station B charges $3.25 per gallon of gas plus S10
Hoochie [10]

9514 1404 393

Answer:

  8 gallons

Step-by-step explanation:

The $2 difference in the price of a car wash is made up by the gas purchase at the rate of $0.25 per gallon. So, it takes ...

  $2/($0.25/gal) = 8 gal

to make the costs the same.

The customer must purchase 8 gallons for the total cost to be the same at both gas stations.

___

  3.50g +8 = 3.25g +10 . . . . costs at each station for g gallons of gas + wash

  0.25g = 2 . . . . . . . . . subtract 3.25g+8 from both sides

  g = 2/.25 = 8 . . . . . . the way we did it above

4 0
3 years ago
What is center: (-4,-12) Radius: 4 ?
netineya [11]

Answer:

have a great day ❤️❤️☺️

3 0
2 years ago
Read 2 more answers
Cuál es el número que no pertenece a esta sucesión 99 koma 105 koma 111 koma 117 koma 123 koma 129 koma 135 koma 141 koma 147 ko
vladimir1956 [14]

Based on the calculations, all of the numbers belong to this arithmetic sequence.

<h3>How to calculate an arithmetic sequence?</h3>

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

a_n = a_1 +(n-1)d

<u>Where:</u>

  • d is the common difference.
  • a₁ is the first term of an arithmetic sequence.
  • n is the total number of terms.

Next, we would determine the common difference as follows:

d = a₂ - a₁

d = 105 - 99 = 6.

d = a₃ - a₂

d = 111 - 105 = 6.

d = a₄ - a₃

d = 117 - 111 = 6.

Based on the calculations, all of the numbers belong to this arithmetic sequence.

Read more on arithmetic sequence here: brainly.com/question/12630565

#SPJ1

Complete Question:

What is the number that does not belong to this sequence 99, 105, 111, 117, 123, 129, 135, 141, 147, 153

6 0
2 years ago
Other questions:
  • Sharon divides a meatloaf into elevenths.how many elevenths equalt he whole meatloaf?
    8·2 answers
  • Ines waters for plants every two days she trims them every 15 days she did both today when will she do both again
    9·1 answer
  • Brooke is using shiny rocks to make necklaces. Each necklace has 5 shiny rocks. Make a table that shows the number of shiny rock
    9·1 answer
  • I need help I dont understand. please. BTW the pool is 8,000 gallons.Thanks
    13·1 answer
  • A pie eight pieces. If Tim cuts out five pieces, and gives two to Moby, what
    8·1 answer
  • we have 10 computers ,2 don't work and your friend is using one. how many computers are free t ok use?​
    13·2 answers
  • Please answer ASAP<br><br><br>y=5/8b+10 for b, ill give brainliest and show work plz
    11·1 answer
  • 5x + 2 – 2(x - 1) = 3x + 4<br> PLS HELP !
    10·1 answer
  • Find the y-intercept of y=-5x-7
    5·2 answers
  • PLEASE HELP<br> I WILL GIVE BRAINLIST
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!