Answer:
The answer is <u>80</u>
Step-by-step explanation:
78.74 is closer to 80 than it is to 70.
Answer:

Step-by-step explanation:
It is a result that a matrix
is orthogonally diagonalizable if and only if
is a symmetric matrix. According with the data you provided the matrix should be

We know that its eigenvalues are
, where
has multiplicity two.
So if we calculate the corresponding eigenspaces for each eigenvalue we have
,
.
With this in mind we can form the matrices
that diagonalizes the matrix
so.

and

Observe that the rows of
are the eigenvectors corresponding to the eigen values.
Now you only need to normalize each row of
dividing by its norm, as a row vector.
The matrix you have to obtain is the matrix shown below
(x - xo)^2 + (y - yo)^2 = r^2
[x - (-3)]^2 + [y - (2)]^2 = (1.5)^2
(x+3)^2 + (y-2)^2 = 2.25
Answer: option C
Integration by parts will help here. Letting

and

, you end up with

and

. Now


For the remaining integral, setting

gives

, so

Putting everything together, you end up with