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3 years ago

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Mathematics

1 answer:

Mashcka [7]3 years ago

6 0

Angle 3 is 96 degrees - angles on a straight line add up to 180 degrees

Hope this helps!

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Please help will mark BRAINLIEST

Murrr4er [49]

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3 0

3 years ago

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of th

Aliun [14]

Answer:

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

$A=\left[\begin{array}{ccc}-3&0&1\\2&-4&2\\-3&-2&1\end{array}\right]$

to find the eigenvalues of the matrix you use the following:

$det(A-\lambda I)=0$

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

$A-\lambda I=\left[\begin{array}{ccc}-3-\lambda&0&1\\2&-4-\lambda&2\\-3&-2&1-\lambda\end{array}\right]$

and by taking the determinant:

$[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-\lambda)+(2)(-2)(-3-\lambda)]=0\\\\-\lambda^3-6\lambda^2-12\lambda-16=0$

and the roots of this polynomial is:

$\lambda_1=-4\\\\\lambda_2=-1+i\sqrt{3}\\\\\lambda_3=-1-i\sqrt{3}$

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

3 0

3 years ago

What is 7/9 times 21/28 as a simplified fraction

Serga [27]

Answer: 7/12!

Step-by-step explanation: 7/9 times 21/28 = 147/252. But you have to reduce it (simplify it) by dividing both the numerator and denominator by the greatest common factor and you get 7/12! Hope this helped.

7 0

3 years ago

Find all solutions of given equation<br> 2cosx-1=0

skad [1K]

There are an infinite number of solutions, so I don't plan to list them all.
I'll list two of them, and then describe how to get all of the rest.

You said that <u>2cos(x) - 1 = 0</u>

Add 1 to each side: 2cos(x) = 1

Divide each side by 2: cos(x) = 1/2

The angles whose cosine is 1/2 are 60 degrees, 300 degrees,
and any multiple of 360 degrees added to either of those.

5 0

3 years ago

Read 2 more answers

Match the formula to the correct figure.

forsale [732]

Given:

The figures cylinder, cube, cone, and pyramid.

To find:

The formula of volume for the given figures.

Solution:

Volume of a cylinder is:

$V_1=\pi r^2h$