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horrorfan [7]
3 years ago
9

What is the variable in the expression: 25 + 5z - 3?

Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
8 0

Answer:

The variable is z

Step-by-step explanation:

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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

7 0
3 years ago
Read 2 more answers
Here are 30 best lifetime baseball batting averages of all time is shown to the right. These data can be graphically displayed a
Alex

Answer:

B). Graph B

Step-by-step explanation:

A Histogram is a graphic representation of data using bars varying in height as per the range of values.

In the given question, the second option correctly represents the data provided in the table using a histogram. It portrays the class ranging from 0.320 - 0.329 with an average of 1 in the first bar, from 0.330 - 0.339 with an average of 14 runs in the second bar, and moves so on till 0.360-0.369 correctly. The other options fail to portray the numerical distribution appropriately and hence, <u>option B</u> is the correct answer.

5 0
3 years ago
What are the next three numbers in this pattern 1,2,3,5,8
stepladder [879]
13, 21, 34 are the next three numbers
7 0
3 years ago
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F(x) = 2x2 - 4x?; Find (-4)
anastassius [24]

Answer:

0 (zero)

Step-by-step explanation:

Plug in the variable for -4 and solve

y= 2(-4)2-4(-4)

y= -8(2)-4(-4)

y=-16+16

y=0

4 0
3 years ago
Which relation is displayed in the table? {(3,3), (3,  7), (5, 8), (9,0)} {(3,3), (7,  3), (8, 5), (0,9)} {(3,3), (3, 7), (5, 9)
bulgar [2K]

Answer:

{(3,3), (3,  7), (5, 8), (9,0)

Step-by-step explanation:

The first number of an ordered pair is the x value and the second number is the y value.


3 0
2 years ago
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