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Blizzard [7]
3 years ago
12

Determine the minimum value of f(x, y, z) = 2x 2 + y 2 + 2z 2 + 5 subject to the constraint 3x + 2y + 3z = 4. +

Mathematics
1 answer:
vlada-n [284]3 years ago
8 0
<span>We want to optimize f(x,y,z)=x^2 y^2 z^2, subject to g(x,y,z) = x^2 + y^2 + z^2 = 289. 

Then, ∇f = λ∇g ==> <2xy^2 z^2, 2x^2 yz^2, 2x^2 y^2 z> = λ<2x, 2y, 2z>. 

Equating like entries: 
xy^2 z^2 = λx 
x^2 yz^2 = λy 
x^2 y^2 z = λz. 

Hence, x^2 y^2 z^2 = λx^2 = λy^2 = λz^2. 

(i) If λ = 0, then at least one of x, y, z is 0, and thus f(x,y,z) = 0 <---Minimum 
(Note that there are infinitely many such points.) 
(f being a perfect square implies that this has to be the minimum.) 

(ii) Otherwise, we have x^2 = y^2 = z^2. 
Substituting this into g yields 3x^2 = 289 ==> x = ±17/√3. 

This yields eight critical points (all signage possibilities) 
(x, y, z) = (±17/√3, ±17/√3, ±17/√3), and  
f(±17/√3, ±17/√3, ±17/√3) = (289/3)^3 <----Maximum 

I hope this helps! </span><span>
</span>
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Fred has 230 animals at his zoo. Grace at 349 more animals in her zoo than Fred has. how many animals do they have altogether? T
WARRIOR [948]

Step-by-step explanation:

okay so im in 8th grade and i just worked the problem out and i got , 809 ,

first you add 230 + 349 to see how much she has in her farm

she has 579, then you add 579 because she has that many , and he has 230 so you add 579 +230 and tou get 809

work:

230

+349

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579

+230

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809

hope i helped!!

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3 years ago
A soup can has a diameter of 8 cm and a height of 12 cm. What is the volume of the soup can? Use 3.14 for Pi. A cylinder has a h
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Step-by-step explanation:

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Any help please? For extra credit
Law Incorporation [45]

Answer:

see explanation

Step-by-step explanation:

(a)

A recursive formula allows any term in the sequence to be found by adding the common difference d to the previous term.

Here d = - 4 , then recursive formula is

a_{n} = a_{n-1} - 4 with a₁ = 2

(b)

The explicit formula for an arithmetic sequence is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = - 4, thus

a_{n} = 2 - 4(n - 1) = 2 - 4n + 4 = 6 - 4n ← explicit formula

(c)

Using the recursive formula

a₁ = 2

a₂ = 2 - 4 = - 2

a₃ = - 2 - 4 = - 6

Using the explicit formula

a₅ = 6 - 4(5) = 6 - 20 = - 14

a₁₀ = 6 - 4(10) = 6 - 40 = - 34

a₁₀₀ = 6 - 4(100) = 6 - 400 = - 394

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inysia [295]

divide both sides by a negative one to get ride of the -y then on your graph it be a horizontal line at the point (0,-34)

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Select the best answer for the question.
LiRa [457]

Answer: the answer is B

Step-by-step explanation:

8 0
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