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raketka [301]
2 years ago
14

What's the missing number

Mathematics
1 answer:
Pepsi [2]2 years ago
5 0
G because 30 + 5 =35 so 4x35
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 50, 60,72,... Find the 8th term.
Vadim26 [7]

Answer:

179.159

Step-by-step explanation:

Given the sequence :

50, 60, 72,..

The sequence given is a geometric sequence :

For a geometric sequence ;

ar^(n - 1)

a = first term

r = a2 / a1 = 60 / 50 = 1.2

The 8th term ; n =8

a8 = ar^(n - 1)

a8 = 50*1.2^(8 - 1)

a8 = 50*1.2^7

a8 = 50*3.5831808

a8 = 179.15904

a8 = 179.159 (nearest thousandth )

8 0
2 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
Multiply.<br> (5v+6w-7)(-3)<br> Simplify your answer.
Zielflug [23.3K]

Answer:

if my calculator is not wrong Is 21

3 0
2 years ago
How do I write this in word form???
alisha [4.7K]
The way you say this is one hundred nineteen ten thousandths if this helps mark brainiest
5 0
3 years ago
Pls help, I don’t understand how to do this
MAVERICK [17]

Answer:

5 parts are shaded and 4 parts are white so:

There are 9 parts all together.

We can then form ratio's of the white areas and the shaded areas:

White Area Ratio =

\frac{4}{9}

Shaded Area Ratio =

\frac{5}{9}

Let the area of sqaure be equated to x, which means let the entire area of the square equal to x:

x = Area of whole square

Now we can form an equation :

\frac{5}{9} x = 165

So now we just need to solve for x:

x = \frac{165}{ \frac{5}{9} }

x = 297

The area of the square is:

297 {cm}^{2}

4 0
3 years ago
Read 2 more answers
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