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3 years ago

Is (1,3) a solution of the graphed inequality?

Mathematics

1 answer:

BaLLatris [955]3 years ago

5 0

Answer:

yes.

Step-by-step explanation:

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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

2 years ago

Plz help me get this right

sladkih [1.3K]

Answer:

12 x 8 divided by 2 = 48cm

Step-by-step explanation:

6 0

3 years ago

What ratio is equivalent to 9 6

elena-s [515]

3:2

the greatest common factor amongst 9 and 6 is 3

6 0

2 years ago

It takes 9 meters of ribon to make 24 bows. How many meters of ribbom doesnit take to make 16 bows?

Ivenika [448]

Answer:

Step-by-step explanation:yes

7 0

2 years ago

What's the value of 2. X/10=2

myrzilka [38]

Answer:

x = 20

Step-by-step explanation:

x/10 = 2 multiply both sides of the equation by ten ↓

10x x/10 = 10 x 2 reduce the numbers with the greatest common factor 10 ↓

x = 10 x 2 multiply the numbers ↓

x = 20

4 0

3 years ago