Which description best fits the distribution of

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 is the common ratio of the geometric sequence below? –96, 48, –24, 12, –6, ... a, -2 b,-1/2 c, 2 d, 1/2

marysya [2.9K]

Answer:

Option b is correct.

The common ratio for the given geometric sequence is; $\frac{-1}{2}$

Step-by-step explanation:

The given sequence is; -96, 48 , -24, 12 , -6, .....

Since, given sequence is Geometric

Geometric Sequence in which each term is found by multiplying the previous term by a constant(i.e common ratio)

In general we write geometric sequence as;

$a , ar, ar^2, ar^3 , .....$

where a be the first term and r is the common ratio.

On comparing the given sequence with general geometric sequence;

we get

a = -96 ......[1]

ar = 48 ......[2]

ar^2 = -24 .....[3]

and so on....

To find the common ratio i.e, r;

Divide equation [2] by [1];

$\frac{ar}{a} =\frac{48}{-96}$

Simplify:

$r = \frac{-1}{2}$

Similarly,

by dividing the equation [3] by [2] we get;

$\frac{ar^2}{ar} = \frac{-24}{48}$

Simplify:

$r = \frac{-1}{2}$

As, you can see that the value of r is constant i.e, $r= \frac{-1}{2}$ in the given sequence.

Therefore, the common ratio for the given geometric sequence is; $r= \frac{-1}{2}$

8 0

3 years ago

Read 2 more answers

2 divided by 3 + 2 divedes by 3 +3 divided by 3 =?

kotegsom [21]

Answer:

1/5

Step-by-step explanation:

1/5

2/3+3/3+4/3

=2/5*3/6

= 1/5

I'm not sure.

4 0

3 years ago

Read 2 more answers

Explain how you can use place-value patterns to describe how 50 and 5000 compare

Masteriza [31]

If you have 50. and want to make it 5000 you can move the decimals point over 2 which would also be ×100

6 0

3 years ago

11 5/8 +9 1/2 is my problem

Leto [7]

Answer:21 1/8 is the answer

Step-by-step explanation:

6 0

2 years ago