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valentina_108 [34]
3 years ago
12

The sum of two numbers is 62 . The smaller number is 16 less than the larger number. What are the numbers?

Mathematics
2 answers:
GenaCL600 [577]3 years ago
6 0
39 and 23!

If we broke down the problem to 62=x+y (y being the smaller number) we can solve from there. 
If y is the smaller number, then y= x-16
Therefore if we plug that back in we get 62=x+x-16 which simplifies to     62=2x-16.
Now we just solve for x which is the bigger number and we get 39. But we still have y which is 16 less so we subtract 16 from 39 to get 23.
Artyom0805 [142]3 years ago
5 0
23 and 39

23 + 39 = 62 
39 - 23 = 16 
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Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=4x2 2y2; 3x
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For given f(x, y) the extremum: (12, 24) which is the minimum.

For given question,

We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108

We use the constraint to build the constraint function,

g(x, y) = 3x + 3y

We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:

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Setting up the Lagrange multiplier equations:

f_x=\lambda g_x

⇒ 8x = 3λ                                        .....................(1)

f_y=\lambda g_y

⇒ 4y = 3λ                                         ......................(2)

constraint: 3x + 3y = 108                .......................(3)

Taking (1) / (2), (assuming λ ≠ 0)

⇒ 8x/4y = 1

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Substitute this value of y in equation (3),

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So, the saddle point (critical point) is (12, 24)

Now we find the value of f(12, 24)

⇒ f(12, 24) = 4(12)² + 2(24)²

⇒ f(12, 24) = 576 + 1152

⇒ f(12, 24) = 1728                             ................(1)

Consider point (18,18)

At this point the value of function f(x, y) is,

⇒ f(18, 18) = 4(18)² + 2(18)²

⇒ f(18, 18) = 1296 + 648

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From (1) and (2),

1728 < 1944

This means, given extremum (12, 24) is minimum.

Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.

Learn more about the extremum here:

brainly.com/question/17227640

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1 year ago
How to solve (-7)+10?
slavikrds [6]
-7 + 10 = 3
=
10 + (-7)
Is the same as
10 - 8
…
Not sure if this was that helpful.. I hope it did.
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Alex

Answer:

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Step-by-step explanation:

hope this can help you

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