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s344n2d4d5 [400]
3 years ago
8

Could you find the greatest common multiple of two numbers?

Mathematics
1 answer:
lora16 [44]3 years ago
7 0
It's called the GCM what numbers do you want to know the answer to
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Use the method of lagrange multipliers to find
Yanka [14]

Answer:

a) The function is: f(x, y) = x + y.

The constraint is: x*y = 196.

Remember that we must write the constraint as:

g(x, y) = x*y - 196 = 0

Then we have:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y,  λ) = x + y +  λ*(x*y - 196)

Now, let's compute the partial derivations, those must be zero.

dL/dx =  λ*y + 1

dL/dy =  λ*x + 1

dL/dλ = (x*y - 196)

Those must be equal to zero, then we have a system of equations:

λ*y + 1 = 0

λ*x + 1 = 0

(x*y - 196) = 0

Let's solve this, in the first equation we can isolate  λ to get:

λ = -1/y

Now we can replace this in the second equation and get;

-x/y + 1 = 0

Now let's isolate x.

x = y

Now we can replace this in the last equation, and we will get:

(x*x - 196) = 0

x^2 = 196

x = √196 = 14

then the minimum will be:

x + y = x + x = 14 + 14 = 28.

b) Now we have:

f(x) = x*y

g(x) = x + y - 196

Let's do the same as before:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y, λ) = x*y +  λ*(x + y - 196)

Now let's do the derivations:

dL/dx = y + λ

dL/dy = x + λ

dL/dλ = x + y - 196

Now we have the system of equations:

y + λ = 0

x + λ = 0

x + y - 196 = 0

To solve it, we can isolate lambda in the first equation to get:

λ = -y

Now we can replace this in the second equation:

x - y = 0

Now we can isolate x:

x = y

now we can replace that in the last equation

y + y - 196 = 0

2*y - 196 = 0

2*y = 196

y = 196/2 = 98

The maximum will be:

x*y = y*y = 98*98 = 9,604

6 0
3 years ago
What’s 1 Apple plus 1 apple
Sphinxa [80]

Answer:

2apples

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Quadrilateral ABCD is dilated by a scale factor of 2 centered around (2,2).
ANEK [815]

Answer:

B’D’ will run through (2,2) and will be longer than BD

Step-by-step explanation:

B'D' will be twice as long as BD and run through (2, 2).

6 0
2 years ago
Which of the following quantities are continuous?
Oxana [17]

Answer:

A. only II

Step-by-step explanation:

Mathematics calculus differentiates things into discrete and continuous. Discrete things have indivisible units, the example will be how many dogs in a village. There is no half dog, it's either one, two, etc. But the distance covered by train can be written as half miles, it's divisible unit.  

The number of books and bracelets also discrete, thus the answer is A.

4 0
3 years ago
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Which answer choice correctly represents 0.513333… ?A.B.C.D.
Zepler [3.9K]
Abdc

I think so cuz I did this and got it right hopefully it is right good luck
7 0
2 years ago
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