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SOVA2 [1]
3 years ago
6

An oblique hexagonal prism has a base area of 42 square cm. The prism is 4 cm tall and has an edge length of 5 cm. An oblique he

xagonal prism has a base area of 42 square centimeters. The prism is 4 centimeters tall and has an edge length of 5 centimeters. What is the volume of the prism? cubic centimeters
Mathematics
2 answers:
Anna [14]3 years ago
8 0

Answer:

78

Step-by-step explanation:

IgorLugansk [536]3 years ago
7 0

Answer:

168 Cubic centimeters: edeg2020

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
4 years ago
ILL MARK YOU BRAINLEST IF YOU AWNSER PLEASE!! look at the photo and what is the measure of BMC?help me please!!
Lesechka [4]
2x + (x+9) = 90
3x + 9= 90
3x= 81
x= 27
Now plug in 27 to (x+9)
27+9= 36
Final Answer = 36
6 0
3 years ago
Which situation can be represented by the equation x-6=11?
Nitella [24]

Answer:

D

Step-by-step explanation:

3 0
2 years ago
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Please help with this 2 part question and ignore the option I already clicked
melomori [17]

Answer:

B i think

Step-by-step explanation:

sorry I'm not explaining I'm doing a challange

7 0
3 years ago
If a movie starts at 10:40am and lasts for 1h and 59min, then what time should the movie end.
OverLord2011 [107]

Answer:

12:39

Step-by-step explanation:

First, to make it easier, round the amount of time the movie lasts to the nearest hour. In this case, the movie "lasts" for 2 hours.

Add 2 hours to 10:40am. Note that when it hits 12, the am becomes pm.

10:40 + 2:00 = 12:40

Now, subtract 1 minute from the amount (1 hr 60 min - 1 hr 59 min = 1 min)

12:40 - 0:01 = 12:39

12:39 pm should be the time the movie ends.

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7 0
3 years ago
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