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Katena32 [7]
2 years ago
15

Pls help me I need this now pls

Mathematics
2 answers:
Anarel [89]2 years ago
7 0

Answer: C

Step-by-step explanation:

LenaWriter [7]2 years ago
4 0

Answer:

450 cm

Step-by-step explanation:

25 on both sides 2x25

4 squares = 25x4

4 sides for 4 squares = 100x4

400+50

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. Use Lagrange multipliers to find the maximum and minimum values of the function, f, subject to the given constraint, g. (Place
zzz [600]

Answer:

Minimum value of f(x, y, z) = (1/3)

Step-by-step explanation:

f(x, y, z) = x⁴ + y⁴ + z⁴

We're to maximize and minimize this function subject to the constraint that

g(x, y, z) = x² + y² + z² = 1

The constraint can be rewritten as

x² + y² + z² - 1 = 0

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x, y and z

L(x,y,z) = x⁴ + y⁴ + z⁴ - λ(x² + y² + z² - 1)

We then take the partial derivatives of the Lagrange function with respect to x, y, z and λ. Because these are turning points, each of the partial derivatives is equal to 0.

(∂L/∂x) = 4x³ - λx = 0

λ = 4x² (eqn 1)

(∂L/∂y) = 4y³ - λy = 0

λ = 4y² (eqn 2)

(∂L/∂z) = 4z³ - λz = 0

λ = 4z² (eqn 3)

(∂L/∂λ) = x² + y² + z² - 1 = 0 (eqn 4)

We can then equate the values of λ from the first 3 partial derivatives and solve for the values of x, y and z

4x² = 4y²

4x² - 4y² = 0

(2x - 2y)(2x + 2y) = 0

x = y or x = -y

Also,

4x² = 4z²

4x² - 4z² = 0

(2x - 2z) (2x + 2z) = 0

x = z or x = -z

when x = y, x = z

when x = -y, x = -z

Hence, at the point where the box has maximum and minimal area,

x = y = z

And

x = -y = -z

Putting these into the constraint equation or the solution of the fourth partial derivative,

x² + y² + z² = 1

x = y = z

x² + x² + x² = 1

3x² = 1

x = √(1/3)

x = y = z = √(1/3)

when x = -y = -z

x² + y² + z² = 1

x² + x² + x² = 1

3x² = 1

x = √(1/3)

y = z = -√(1/3)

Inserting these into the function f(x,y,z)

f(x, y, z) = x⁴ + y⁴ + z⁴

We know that the two types of answers for x, y and z both resulting the same quantity

√(1/3)

f(x, y, z) = x⁴ + y⁴ + z⁴

f(x, y, z) = (√(1/3)⁴ + (√(1/3)⁴ + (√(1/3)⁴

f(x, y, z) = 3 × (1/9) = (1/3).

We know this point is a minimum point because when the values of x, y and z at turning points are inserted into the second derivatives, all the answers are positive! Indicating that this points obtained are

S = (1/3)

Hope this Helps!!!

6 0
2 years ago
Use the equation y=3x-8 to find y when x=8
Stels [109]

Answer:  X = 8/3

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Lamar earns 40% of his money moving furniture. If he earns $150 in total, how much money did he earn moving furniture? *
alisha [4.7K]
The answer is 60 dollars.
3 0
3 years ago
Jace gathered the data in the table. He found the approximate line of best fit to be y = –0.7x + 2.36.
finlep [7]

Answer:

the answer is:

-0.86

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
What is the equation of the given in standard form? : y=-1.7x+8.5
olga_2 [115]
Y= -1.7x + 8.5
10( Y = -1.7 x + 8.5)
10Y = -17x + 85
+17x
17x + 10Y = 85
7 0
3 years ago
Read 2 more answers
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