Step-by-step answer:
Given:
5% annual interest (APR)
compounded daily
Principal = 500
Solution:
Since it is compounded daily, we first calculate the
daily rate = 5% / 365 = 0.05/365
After one year,
future value
= 500 ( 1 + 0.05/365)^365
= 525.634 (to the tenth of a cent)
note: sometimes a year is considered to be rounded to 360 days, or 366 days for a leap year, but there is practically no difference in the results for this problem.
Answer:
a for the first one, i pretty sure
Answer:
![\left[\begin{array}{ccc}2&-3\\1&-4\end{array}\right]=-5](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-3%5C%5C1%26-4%5Cend%7Barray%7D%5Cright%5D%3D-5)
Step-by-step explanation:
Given:
The given matrix is.
![\left[\begin{array}{ccc}2&-3\\1&-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-3%5C%5C1%26-4%5Cend%7Barray%7D%5Cright%5D)
the determinant of the above matrix is.
![\left[\begin{array}{ccc}2&-3\\1&-4\end{array}\right]=2\times (-4) - (-3)\times 1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-3%5C%5C1%26-4%5Cend%7Barray%7D%5Cright%5D%3D2%5Ctimes%20%28-4%29%20-%20%28-3%29%5Ctimes%201)
![\left[\begin{array}{ccc}2&-3\\1&-4\end{array}\right]=-8 - (-3)](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-3%5C%5C1%26-4%5Cend%7Barray%7D%5Cright%5D%3D-8%20-%20%28-3%29)
![\left[\begin{array}{ccc}2&-3\\1&-4\end{array}\right]=-8 +3](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-3%5C%5C1%26-4%5Cend%7Barray%7D%5Cright%5D%3D-8%20%2B3)
Therefore, the determinant of the matrix is -5
Length of AA' = √(5^2 + 2^2) = √29 = 5.39
Answer
5.39
