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2 years ago

Equation equal to z^-1 divided by 3

Mathematics

1 answer:

Luba_88 [7]2 years ago

6 0

Answer:

(z^1-2)/3

Step-by-step explanation:

z^1-2 = z^-1 meaning its different

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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

A sphere has a volume of Vequals=3600 in cubedin3. Find its surface area.

Mice21 [21]

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4}{3}\pi r^3\qquad 
\begin{cases}
r=radius\\
------\\
V=3600
\end{cases}\implies 3600=\cfrac{4}{3}\pi r^3
\\\\\\
3600=\cfrac{4\pi r^3}{3}\implies \sqrt[3]{\cfrac{3\cdot 3600}{4\pi }}=\boxed{r}\\\\
-----------------------------\\\\
\textit{surface area of a sphere}\\\\
S=4\pi r^2\implies S=4\pi \left(\boxed{\sqrt[3]{\cfrac{3\cdot 3600}{4\pi }}} \right)^2$

simplify away

8 0

3 years ago

Please help. 20 points and brainliest.

julia-pushkina [17]

Answer:

minimum -45, maximum 32

Step-by-step explanation:

C=4x-3y

x≥0, y≥4, x+y≤15

Maximum value of C can be achieved at max x and min y

min y=4 => max x=15-4=11

C=4*11-3*4= 32

Minimum value of C can be achieved at min x and max y

min x=0, max y =15

C=4*0-3*15= -45

So answer is minimum -45, maximum 32

7 0

3 years ago

What are the discontinuities of the function y= 1500/x

Ratling [72]

The discontinuity occurs at x = 0, since that is the only "problem" place in the graph that makes the function undefined. A vertical asymptote exists there. It is nonremoveable.

4 0

3 years ago

This is hard for me can anyone help me? 9

Kazeer [188]

Answer: -12.8x-20y+8.4

Step-by-step explanation: I multiplied the numbers in parentheses by 4.

5 0

2 years ago