It's not clear to me what the given interval is supposed to be, so I'll use a generic one, [a, b] with a < b.
The average acceleration of the particle over this interval is given by the average rate of change of v(t),
Answer:
A - Hopes this helps.
Step-by-step explanation:
Answer:
Step-by-step explanation:
<u>Eigenvalues of a Matrix</u>
Given a matrix A, the eigenvalues of A, called 
are scalars who comply with the relation:
Where I is the identity matrix
![I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=I%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
The matrix is given as
![A=\left[\begin{array}{cc}3&5\\8&0\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%265%5C%5C8%260%5Cend%7Barray%7D%5Cright%5D)
Set up the equation to solve
![det\left(\left[\begin{array}{cc}3&5\\8&0\end{array}\right]-\left[\begin{array}{cc}\lambda&0\\0&\lambda \end{array}\right]\right)=0](https://tex.z-dn.net/?f=det%5Cleft%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%265%5C%5C8%260%5Cend%7Barray%7D%5Cright%5D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Clambda%260%5C%5C0%26%5Clambda%20%5Cend%7Barray%7D%5Cright%5D%5Cright%29%3D0)
Expanding the determinant
![det\left(\left[\begin{array}{cc}3-\lambda&5\\8&-\lambda\end{array}\right]\right)=0](https://tex.z-dn.net/?f=det%5Cleft%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3-%5Clambda%265%5C%5C8%26-%5Clambda%5Cend%7Barray%7D%5Cright%5D%5Cright%29%3D0)
Operating Rearranging
Factoring
Solving, we have the eigenvalues
Answer:
See below.
Step-by-step explanation:
By definition the median of the triangle bisects the base of the isosceles triangle.
We need to prove that the 2 triangles formed by the median are congruent.
If the 2 triangles are ABD and ACD where BD is the median and < ABC is the angle from which BD is drawn.
BD = BD ( the common side)
AD = DC ( because BD is the median).
AB = AC ( because ABC is an isosceles triangle).
So Triangles ABD and ACD are congruent by SSS.
Therefore m < ABD = m < CBD, so BD is the bisector of < ABC.
To prove BD is also the altitude:
Triangles ABD and CBD are congruent as we have just proven. Therefore the
of measure of the base angle ABD = m < CBD . Also they are adjacent angles ( on the same line) so they add up to 180.
Therefore angles ABD and CBD are both right angles and BD is the altitude of triangle ABC.
