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3 years ago

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Christine backed a pumpkin pie.she ate 1/6 of the pie.her brother ate 1/3 of it and gave the leftovers to his friends.what fract

ion of the pie did he give to his friends?

1 answer:

algol133 years ago

3 0

Answer:

33

Step-by-step explanation:

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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

Drag and drop the statement into the correct box.

a_sh-v [17]

Answer:

true on all but the last one

Step-by-step explanation:

the last one is false because a trapezoid is considered a quadrilateral that has exactly one pair of parallel sides.

8 0

2 years ago

One canned juice is 15% orange juice another 10% orange juice. How many liters of each should be mixed together in order to get

Delicious77 [7]

<span>Equation:
0.15x + 0.10(5-x) = 0.11*5
---
Multiply thru by 100:
15x + 10*5 - 10x = 11*5

---
5x = 5
x = 1 liter (amt. 15% oj needed)
----
5-x = 4 liters (amt of 10% oj needed)
======</span>

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2 years ago

What is the solution to 2x^2-3x-1=0

Tems11 [23]

<span>x=<span><span>4</span><span><span>3+<span>√<span><span><span>17</span></span><span></span></span></span></span></span><span></span></span>,<span><span>4</span><span><span>3−<span>√<span><span><span>17</span></span><span></span></span></span></span></span><span> Is the answer.
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I hope this helps. :)

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3 years ago

Graph y > 1 -3x<br> A<br> B<br> C<br> Or D

bazaltina [42]

Answer:

D (You got it right.)

Step-by-step explanation:

Whenever the sign is facing them we will always shade the top. Then we have to find the slope which in this case would be 3(the number that is being multiplied by x. Lastly is the sign does not have a line under it or an equal sign. it won't be a straight line it will have little gaps.

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2 years ago