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just olya [345]

3 years ago

12

Which of the following represents the distance

1 answer:

Lunna [17]3 years ago

3 0

Answer:

D. d = sqrt( ( x2-x1)^2 + (y2-y1)^2)

C. d = sqrt( ( x1-x2)^2 + (y1-y2)^2)

B. d = sqrt( (|x2-x1|^2 + |y2-y1|^2)

Step-by-step explanation:

Given two points (x1, y1) and (x2,y2) we can find the distance using

d = sqrt( ( x2-x1)^2 + (y2-y1)^2)

The order of the terms inside the square doesn't matter

d = sqrt( ( x1-x2)^2 + (y1-y2)^2)

When we are squaring are term, we can take the absolute value before we square and it does not change the value

d = sqrt( (|x2-x1|^2 + |y2-y1|^2)

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Estimate the sum of 4.27 and 9.91 by first rounding each number to the nearest whole number.

mart [117]

4.27 + 9.91

Round them to the nearest whole number.

4.27 ⇒ 4
9.91 ⇒ 10

Now you can add them up.

4 + 10 = 14

4 0

3 years ago

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are

alexgriva [62]

Answer:

$P=\left(\begin{array}{ccc}-\frac{2}{3}&-\frac{2}{3}&\frac{1}{3}\\\frac{1}{\sqrt{5}}&0&\frac{2}{\sqrt{5}}\\-\frac{4}{3\sqrt{5}}&\frac{\sqrt{5}}{3}&\frac{2}{3\sqrt{5}}\end{array}\right)$

Step-by-step explanation:

It is a result that a matrix $A$ is orthogonally diagonalizable if and only if $A$ is a symmetric matrix. According with the data you provided the matrix should be

$A=\left(\begin{array}{ccc}-9&-4&2\\ -4&-9&2\\2&2&-6\\\end{array}\right)$

We know that its eigenvalues are $\lambda_{1}=-14, \lambda_{2}=-5$ , where $\lambda_{2}=-5$ has multiplicity two.

So if we calculate the corresponding eigenspaces for each eigenvalue we have

$E_{\lambda_{1}=-14}=\langle(-2,-2,1)\rangle$ , $E_{\lambda_{2}=-5}=\langle(1,0,2),(-1,1,0)\rangle.$ .

With this in mind we can form the matrices $P, D$ that diagonalizes the matrix $A$ so.

$P=\left(\begin{array}{ccc}-2&-2&1\\1&0&2\\-1&1&0\\\end{array}\right)$

and

$D=\left(\begin{array}{ccc}-14&0&0\\0&-5&0\\0&0&-5\\\end{array}\right)$

Observe that the rows of $P$ are the eigenvectors corresponding to the eigen values.

Now you only need to normalize each row of $P$ dividing by its norm, as a row vector.

The matrix you have to obtain is the matrix shown below

3 0

3 years ago

Select all radical expressions that are equivalent to 3 4/7

enot [183]

The second and the third one because first is the same as 3 4/7 and 81=3^4

5 0

3 years ago

Read 2 more answers

Given f(x) = x² - 10x + 22, what is the range of f?

adoni [48]

Answer:

[-3, ∞)

Step-by-step explanation:

There are many ways to find the range but I will use the method I find the easiest.

First, find the derivative of the function.

f(x) = x² - 10x + 22

f'(x) = 2x - 10

Once you find the derivative, set the derivative equal to 0.

2x - 10 = 0

Solve for x.

2x = 10

x = 5

Great, you have the x value but we need the y value. To find it, plug the x value of 5 back into the original equation.

f(x) = x² - 10x + 22

f(5) = 5² - 10(5) + 22

= 25 - 50 +22

= -3

Since the function is that of a parabola, the value of x is the vertex and the y values continue going up to ∞.

This means the range is : [-3, ∞)

Another easy way is just graphing the function and then looking at the range. (I attached a graph of the function below).

Hope this helped!

6 0

3 years ago

5p + 9c = p for c <br><br> Help out with this problem

Rom4ik [11]

Answer:

Step-by-step explanation:

5p + 9c = p

9c = p - 5p

9c = -4p

c = -4p/9

c= $\frac{-4p}{9}$

5 0

1 year ago

Read 2 more answers