Rosa has a bag that contains 14 beads the bag is 20% fault how many beds are in a full bag

This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the ex

velikii [3]

Answer:

The maximum value= 36

Minimum value = - 36

Step-by-step explanation:

Given that

f(x, y, z) = 8 x + 8 y + 4 z

h(x,y,z)=4 x² + 4 y² + 4 z² - 36

From Lagrange multipliers

Δf = λ Δh

Δf = < 8 ,8 , 4>

Δh = < 8 x ,8 y , 8 z>

Δf = λ Δh

So

< 8 ,8 , 4> = < 8 λ x ,8 λ y , 8 λ z>

8 = 8 λ x -------------1

8 = 8 λ y ---- ------2

4 = 8 λ z ----------------3

From equation 1 ,2 and 3

Now by putting the value of x,y and z in the following equation

4 x² + 4 y² + 4 z² = 36

$4\times \dfrac{1}{\lambda^2 }+4\times \dfrac{1}{\lambda^2 }+4\times \dfrac{1}{(2\lambda)^2 }=36$

$\dfrac{4}{\lambda^2 }+ \dfrac{4}{\lambda^2 }+ \dfrac{1}{\lambda^2 }=36$

So the value of λ is

$\lambda =\pm \dfrac{1}{2}$

When λ = 1/2

x = 1 / λ , y=1 / λ , z= 1 /2 λ

x= 2 , y = 2 , z=1

So

f(x, y, z) = 8 x + 8 y + 4 z

f(2, 2, 1) = 8 x 2 + 8 x 2 + 4 x 1

f(2, 2, 1) =36

When λ = - 1/2

x = 1 / λ , y=1 / λ , z= 1 /2 λ

x= - 2 , y = - 2 , z= - 1

So

f(x, y, z) = 8 x + 8 y + 4 z

f(-2, -2, -1) = 8 x (-2) + 8 x (-2) + 4 x (-1)

f(-2, -2, -1) = - 36

The maximum value= 36

Minimum value = - 36

7 0

3 years ago

Read 2 more answers

I need help on this one aswell if anyone wants to help me.

Lelechka [254]

Answer:

y=63

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%20-%2030%20%3D%202%28x%20-%2097%29" id="TexFormula1" title=" - 30 = 2(x - 97)" alt=" - 30 = 2

Korolek [52]

Hey there!

In order to find out the answer to this question, we can distribute

$-30 = 2(x - 97) \\ \\ \\ 2(x) = 2x \\ \\ 2(97) = 197$

Flip your problem around!

$2x - 194 = -30$

Add by $194$ on each of your sides

Like: $2x - 194 + 194 \\ \\ \\ -30 + 194$

Cancel out: $-194 + 194$ because they would give you the outcome of $0$

Keep: $-30 + 194 [/tex] because that'll give you: [tex]164$

Your problem becomes: $2x = 164$

Now, we have to divide by $2$ on each of the sides

Like: $\frac{2x}{2} = \frac{164}{2}$

Cancel: $\frac{2x}{2}$ because it will give you a outcome of $1$

Keep: $\frac{164}{2}$ because this will give you your answer

$Answer: x = 82$

Good luck on your assignment and enjoy your day!

~ $LoveYourselfFirst:)$

7 0

3 years ago

Casey and her two friends made $54 selling lemonade in their neighborhood. They will share their money equally. How much money w

cluponka [151]

To find out how much money Casey and her two friends will each get, we simply need to divide the total amount of income by the amount of people receiving a part of it

54 / 3 = 18

Casey and her two friends each got $18 from their lemonade stand.
Hope that helped! =)

7 0

3 years ago

I GIVES BRAINLIEST IF U SOLVE IT

kkurt [141]

Answer:

False

Step-by-step explanation:

The following statement is false so in conclusion it will not be enough for both bird houses

Cleopatra= 12 1/2

Jesse=6-10

20ft will not be enough for both jesse and cleopatra !

Hope this helps

-<em>Tobie The dog <3</em>

5 0

3 years ago