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
Svet_ta [14]
2 years ago
5

Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=x+4y subject to the constraint x2+y2=9, if such values

exist. Round your answers to three decimal places. If there is no global maximum or global minimum, enter NA in the appropriate answer area. Maximum =
Mathematics
1 answer:
Vesnalui [34]2 years ago
4 0

The Lagrangian is

L(x,y,\lambda)=x+4y+\lambda(x^2+y^2-9)

with critical points where the partial derivatives vanish.

L_x=1+2\lambda x=0\implies x=-\dfrac1{2\lambda}

L_y=4+2\lambda y=0\implies y=-\dfrac2\lambda

L_\lambda=x^2+y^2-9=0

Substitute x,y into the last equation and solve for \lambda:

\left(-\dfrac1{2\lambda}\right)^2+\left(-\dfrac2\lambda\right)^2=9\implies\lambda=\pm\dfrac{\sqrt{17}}6

Then we get two critical points,

(x,y)=\left(-\dfrac3{\sqrt{17}},-\dfrac{12}{\sqrt{17}}\right)\text{ and }(x,y)=\left(\dfrac3{\sqrt{17}},\dfrac{12}{\sqrt{17}}\right)

We get an absolute maximum of 3\sqrt{17}\approx12.369 at the second point, and an absolute minimum of -3\sqrt{17}\approx-12.369 at the first point.

You might be interested in
Which statement is true about point F? a.F is the midpoint of AA' because bisects AA'. b.F is the midpoint of EG because AA' bis
Dimas [21]

Answer:

The correct option is;

a. F is the midpoint of \overline{AA'} because line \overline{EG} bisects \overline{AA'}

Step-by-step explanation:

Here, since we have that the triangle is reflected across EG therefore the location of the point F which is along EG bisects the line \overline{AA'} as the  dimensions of the line from A to F must be equal to the dimension of the line that extends from A' to F

Therefore the point F is the midpoint of \overline{AA'} because line \overline{EG} bisects \overline{AA'}.

7 0
3 years ago
How do you subtract fractions
olya-2409 [2.1K]

Answer:

make the denominators ( bottom number ) the same and whatever u do to that do to the top

Step-by-step explanation:

e.g ½ - ⅓

make the common denominator 6

to get from 2 to 6 u times by 3 so it wud be 3/6

and then to get from 3 to 6 u times by 2 so do the same to the numerator (top number) so u get 2/6

3/6 take away 2/6 is 1/6

:)

7 0
2 years ago
Read 2 more answers
Set of real numbers satisfying 2x=3
algol [13]
2x = 3
x = 3/2 or 1 1/2 or 1.5
5 0
3 years ago
Read 2 more answers
Fine the value of x in the triangle. Then classify the triangle as acute, right,
Trava [24]

Answer:

x = 88

Step-by-step explanation:

The sum of the angles in a triangle add to 180

47+45 +x = 180

Combine like terms

92+x = 180

Subtract 92 from each side

92+x-92= 180-92

x =88

7 0
3 years ago
Find the constant of variation for the relationship shown in the following table: x 1 2 3 4 y 3 6 9 12
stepan [7]

Answer:

y=3x ( the'=' sign is the proportionality sign)

Step-by-step explanation:

x = 1 , 2 , 3 , 4

y = 3 , 6 , 9 , 12

You are multiplying by 3 to get to y

1 x 3 = 3

2 x 3 = 6

3 x 3 = 9

4 x 3 = 12

7 0
2 years ago
Read 2 more answers
Other questions:
  • Which property is illustrated by the statement (4+6.1)+7=4+(6.1+7)
    6·2 answers
  • Chapter 9.1 the bar graph
    11·1 answer
  • Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?
    13·2 answers
  • X = 0.8× + 72<br><br>a)112<br>b)288<br>c)360<br>d)432
    15·1 answer
  • A tabletop is in the shape of a trapezoid. The lengths of the trapezoid's parallel sides are 48 inches and 40 inches. The height
    11·2 answers
  • Point R is located at (3, 2) and point S is located at (8, 15) . What are the coordinates of the point that partitions the direc
    7·1 answer
  • Evaluate the expression if a = 4, b = 7, and c = 9. what does ac + b =
    6·1 answer
  • Select the correct answer.
    11·2 answers
  • In a pack of candies, Marla found that for every 3 blue candies, there were 5 red ones. Identify the correct list of ratios that
    15·1 answer
  • The cost of 32 containers of her than this at a grocery store is $96 what is the price per container of hummus?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!