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3 years ago

Pls help!!!!!!!!!!!!!!!

Mathematics

2 answers:

victus00 [196]3 years ago

8 0

Answer:

Step-by-step explanation:

c i think

maria [59]3 years ago

6 0

Answer:

Step-by-step explanation:

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The equations that must be solved for maximum or minimum values of a differentiable function w=f(x,y,z) subject to two constrai

sammy [17]

The Lagrangian is

$L(x,y,z,\lambda,\mu)=x^2+y^2+z^2+\lambda(4x^2+4y^2-z^2)+\mu(2x+4z-2)$

with partial derivatives (set equal to 0)

$L_x=2x+8\lambda x+2\mu=0\implies x(1+4\lambda)+\mu=0$

$L_y=2y+8\lambda y=0\implies y(1+4\lambda)=0$

$L_z=2z-2\lambda z+4\mu=0\implies z(1-\lambda)+2\mu=0$

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

$L_\mu=2x+4z-2=0\implies x+2z=1$

Case 1: If $y=0$ , then

$4x^2-z^2=0\implies4x^2=z^2\implies2|x|=|z|$

Then

$x+2z=1\implies x=1-2z\implies2|1-2z|=|z|\implies z=\dfrac25\text{ or }z=\dfrac23$

$\implies x=\dfrac15\text{ or }x=-\dfrac13$

So we have two critical points, $\left(\dfrac15,0,\dfrac25\right)$ and $\left(-\dfrac13,0,\dfrac23\right)$

Case 2: If $\lambda=-\dfrac14$ , then in the first equation we get

$x(1+4\lambda)+\mu=\mu=0$

and from the third equation,

$z(1-\lambda)+2\mu=\dfrac54z=0\implies z=0$

Then

$x+2z=1\implies x=1$

$4x^2+4y^2-z^2=0\implies1+y^2=0$

but there are no real solutions for $y$ , so this case yields no additional critical points.

So at the two critical points we've found, we get extreme values of

$f\left(\dfrac15,0,\dfrac25\right)=\dfrac15$ (min)

and

$f\left(-\dfrac13,0,\dfrac23\right)=\dfrac59$ (max)

5 0

4 years ago

What is the sign of B + A? Choose 1 answer: Positive B Negative Neither positive nor negative-the sum is zero.

Andreas93 [3]

Ince they are equal in absolute value and merely differ in being positve or negative, result in a sum of 0

6 0

3 years ago

Samantha and Matt are each saving for new bikes. So far, Samantha has saved $15 and can earn $2 per hour for babysitting. Matt h

Sophie [7]

Answer:

6 hours

Step-by-step explanation:

We know that:

Samantha = 15 + 2x
Matt = 3 + 4x
Samantha = Matt
[x = Number of hours]

Solution:

15 + 2x = 3 + 4x
=> 15 - 3 = -2x + 4x
=> 12 = 2x
=> x = 6

Hence, after 6 hours of work, Samantha and Matt will have the same amount.

7 0

2 years ago

PLS HELP ASAP y = -3x + 1 y = x -7

Dahasolnce [82]

Answer:

x=-1/3

x=7

Step-by-step explanation:

Not sure if this correct tho

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3 years ago

Read 2 more answers

A spanish class has a total of 33 students. The number of males is 17 more than the number of females. How many males and how ma

andrezito [222]

Answer:

25 males and 8 females.

Step-by-step explanation:

If x is the number of males and y = number of females we have the system:

x + y = 33

x - y = 17 Adding:

2x = 50

x = 25

so y = 33 - 25 = 8.

3 0

4 years ago