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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

Vesnalui [34]

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.

4 0

3 years ago

20 and 1/2 x 10 1/4 x 12

Andru [333]

Answer:

2521.5

Step-by-step explanation:

20.5 · 10.25 · 12

2521.5

5 0

3 years ago

VAN purchased a DVD player on sale. The original selling price was $171.50. The sale price was $146.35. What is the first step

snow_tiger [21]

The answer is 141.7
If you add 60

7 0

3 years ago

what is the rate of inflation if a savings account has a nominal interest rate of 3% and a real interest rate of 1%

IgorLugansk [536]

Answer:

the rate of inflation is 2%.

Step-by-step explanation:

given:

Nominal interest rate =3%

Real interest rate=1%

To Find:

Rate of inflation=?

Solution:

Nominal interest rate:

Nominal interest rate refers to the interest rate before taking inflation into account.

Inflation rate:

The inflation rate is the percent increase or decrease in prices during a specified period. It's usually over a month or a year.

Real interest rate:

A real interest rate is an interest rate that has been adjusted to remove the effects of inflation to reflect the real cost of funds to the borrower and the real yield to the lender or to an investor.

Real interest rate ≈ nominal interest rate − inflation rate.

This can be re written as

inflation rate= Real interest rate - nominal interest rate

Substituting the values,

inflation interest = 1+3

inflation interest=4%

i hope this helpsss<3

:)

if u didnt undersstand make sure to tell me so i can try to say it again

7 0

3 years ago

The measure of angle A is 15°, and the length of side