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Alinara [238K]
3 years ago
14

MATH ANYONE PLEASE HELP

Mathematics
2 answers:
BartSMP [9]3 years ago
8 0
3/8 is the answer to this question

Rom4ik [11]3 years ago
7 0
I am not sure but it looks like 2 1/8 mi.
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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

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Answer:

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Step-by-step explanation:

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It would be 21070

In standard form, 20000+1000+70

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