Find cos (A). Choose 1 answer: A.) 35/12 B.) 12/37 C.) 35/37 D.) 12/35

This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the ex

ANTONII [103]

Answer:

Maximum value: $3* \sqrt{n}$

Minimum value: $-3* \sqrt{n}$

Step-by-step explanation:

Let $g(x) = x_1^2 + x_2^2+x_3^2+ ----+ x_n^2$ , the restriction function.The Lagrange Multiplier problem states that an extreme (x1, ..., xn) of f with the constraint g(x) = 9 has to follow the following rule:

$\nabla{f}(x_1, ..., x_n) = \lambda \nabla{g} (x_1,...,x_n)$

for a constant $\lambda$ .

Note that the partial derivate of f respect to any variable is 1, and the partial derivate of g respect xi is 2xi, this means that

$1 = \lambda 2 x_1$

Thus,

$x_i = \frac{1}{2\lambda} = c$

Where c is a constant that doesnt depend on i. In other words, there exists c such that (x1, x2, ..., xn) = (c,c, ..., c). Now, since g(x1, ..., xn) = 9, we have that n * c² = 9, or

$c = \, ^+_- \, \sqrt{\frac{9}{n} } = \, ^+_- \frac{3}{\sqrt{n}}$

When c is positive, f reaches a maximum, which is $\frac{3}{\sqrt{n}} + \frac{3}{\sqrt{n}} + \frac{3}{\sqrt{n}} + ..... + \frac{3}{\sqrt{n}} = n * \frac{3}{\sqrt{n}} = 3 * \sqrt{n}$

On the other hand, when c is negative, f reaches a minimum, $-3 * \sqrt{n}$

8 0

4 years ago

PLEASE HELP ASAP WILL MARK BRAINLIEST

nikdorinn [45]

Answer: 314 mm

Step-by-step explanation:

Area of a circle is π*r^2

r is radius and π is 3.14

here the radius is 10

3.14 * 10^2 = 3.14 * 100 = 314

3 0

3 years ago

What’s the geometric mean of 3 and 75

IRINA_888 [86]

The geometric mean for 3 and 75 would be 15.

8 0

4 years ago

Sam watched television for the past five nights for 42 mins, 23 mins, 56mins,19 mins , and 67 mins what was the median amount sa

Vlad [161]

Answer:

42 minutes is the median amount of time

Step-by-step explanation:

The Median is the middle value of data set.

If there is "odd" number of numbers, and there are n numbers, the median is:

(n/2) + 1 th number

If there is "even" number of numbers, and there are n numbers, the median is:

Average of n/2th and (n/2) + 1 th number

Here, we have 5 numbers, so the median would be:

(5/2) + 1 th number

That is

3rd number

But, we need to arrange the numbers from least to greatest. Lets write it:

19, 23, 42, 56, 67

The third number is 42, this is the median

Step-by-step explanation:

All credits to (TaeKwonDoIsDead)

6 0

3 years ago

Solve for w: -4(w+1)=-24 Please explain this like you would a 2 year old and please explain it so it is the easiest way to solve

Andrews [41]

Answer:

Step-by-step explanation:

The first step in solving an equation is to look at it. Identify where the variable is that you're interested in, and see what operations are being performed on that variable.

Here, the variable w has 1 added to it, and the sum is multiplied by -4. The variable is only on the left side of the equation, and is inside parentheses. Inside parentheses, the coefficient of the variable is 1.

These observations tell you that, in some order, you will need to undo the operations of multiplication and addition, and you will have to eliminate parentheses.

You also observe that the multiplication factor of the parentheses (-4) is a factor of the constant on the right side of the equation (-24). This means you have a couple of options for solving this equation:

eliminate parentheses first, using the distributive property
divide by -4 first, to undo the multiplication

The second method is actually faster. We'll illustrate that one first.

__

Divide both sides of the equation by -4 to undo the multiplication by -4.

-4(w +1)/(-4) = -24/(-4) . . . . . we have indicated the division we want to do

w +1 = 6 . . . . . . . . . . . . . . . . here is the result of that division

Now, we can add the opposite of +1 to eliminate the constant from the left side. As with all operations on equations, we must do the same thing to both sides. This means we add -1 to both sides of the equation:

w +1 -1 = 6 -1 . . . . . . we have indicated the addition we want to do

w = 5 . . . . . . . . . . . here is the result of that addition

The solution of the equation is ...

w = 5

__

Often, when parentheses are involved, the numbers are such that the solution method is not as simple as what we just did. In those cases, you would take the approach of eliminating parentheses first. For this equation, it looks like this:

-4(w +1) = -24 . . . . . . . given

-4w -4 = -24 . . . . . . . . use the distributive property to eliminate parentheses

We want the variable term by itself, so we need to eliminate the constant -4 that is added on the left. To do that, we add its opposite. This means we add +4 to both sides of the equation.

-4w -4 +4 = -24 +4 . . . . . . indicating the addition of +4

-4w = -20 . . . . . . . . . . . . . the result of adding +4

Here, w is multiplied by -4. We want w by itself, so we want to undo that multiplication. That means we want to divide both sides of the equation by -4.

-4w/(-4) = -20/(-4) . . . . . . indicate the division

w = 5 . . . . . . . . . . . . . . . . the result of doing the division

The solution of the equation is ...

w = 5

_____

Our basic approach is to undo the operations done to the variable, in the reverse of the order in which they are done. In that process, we observe the rules of equality: whatever operation you do to one side of the equation must also be done to the other side. (My teacher called this last rule: "keep the equal sign sacred.")

You can always use the distributive property for factoring, collecting terms, or eliminating parentheses.

3 0

3 years ago