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BlackZzzverrR [31]

3 years ago

12

Harry goes to hogwarts a School of witchcraft. He decides to choose his methods of transportation to and from hogwarts at this r

andom this year.

1 answer:

REY [17]3 years ago

3 0

Answer:

it is both A and B !!

Step-by-step explanation:

:)

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Use Lagrange multipliers to find the maximum and minimum values of (i) f(x,y)-81x^2+y^2 subject to the constraint 4x^2+y^2=9. (i

sp2606 [1]

i. The Lagrangian is

$L(x,y,\lambda)=81x^2+y^2+\lambda(4x^2+y^2-9)$

with critical points whenever

$L_x=162x+8\lambda x=0\implies2x(81+4\lambda)=0\implies x=0\text{ or }\lambda=-\dfrac{81}4$

$L_y=2y+2\lambda y=0\implies2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1$

$L_\lambda=4x^2+y^2-9=0$

If $x=0$ , then $L_\lambda=0\implies y=\pm3$ .
If $y=0$ , then $L_\lambda=0\implies x=\pm\dfrac32$ .
Either value of $\lambda$ found above requires that either $x=0$ or $y=0$ , so we get the same critical points as in the previous two cases.

We have $f(0,-3)=9$ , $f(0,3)=9$ , $f\left(-\dfrac32,0\right)=\dfrac{729}4=182.25$ , and $f\left(\dfrac32,0\right)=\dfrac{729}4$ , so $f$ has a minimum value of 9 and a maximum value of 182.25.

ii. The Lagrangian is

$L(x,y,z,\lambda)=y^2-10z+\lambda(x^2+y^2+z^2-36)$

with critical points whenever

$L_x=2\lambda x=0\implies x=0$ (because we assume $\lambda\neq0$ )

$L_y=2y+2\lambda y=0\implies 2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1$

$L_z=-10+2\lambda z=0\implies z=\dfrac5\lambda$

$L_\lambda=x^2+y^2+z^2-36=0$

If $x=y=0$ , then $L_\lambda=0\implies z=\pm6$ .
If $\lambda=-1$ , then $z=-5$ , and with $x=0$ we have $L_\lambda=0\implies y=\pm\sqrt{11}$ .

We have $f(0,0,-6)=60$ , $f(0,0,6)=-60$ , $f(0,-\sqrt{11},-5)=61$ , and $f(0,\sqrt{11},-5)=61$ . So $f$ has a maximum value of 61 and a minimum value of -60.

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3 years ago

Multiply (2x+5) (x+3) <br> please do it step by step and please hurry

Harrizon [31]

Answer:

Step-by-step explanation:

(2x+5)(x+3)

2x^2+6x+5x+15

2x^2+11x+15

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1. Which statement about this triangular prism is NOT true?

Arte-miy333 [17]

I believe it’s d) if not please comment the answer

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3 years ago

Find the value of x.<br> A. 80°<br> B. 70°<br> C. 60°<br> D. 50°

borishaifa [10]

Answer:

A

Step-by-step explanation:

80 degree becaue a triangle = 180 degress

180 - 100 = 80

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2 years ago

Please help me simplify complex fractions <br><br> 1/5/3/4

Inga [223]

The answer is 4/15 decimal form is .26 and six repeates

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