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Alexus [3.1K]
3 years ago
9

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:

ok

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:

<u>We know that:</u>

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

<u>Solution:</u>

  • 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<br>y = x -7​
Dahasolnce [82]

Answer:

x=-1/3

x=7

Step-by-step explanation:

Not sure if this correct tho

5 0
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
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