Answer: The required matrix is
![T=\left[\begin{array}{ccc}-1&3\\2&4\end{array}\right] .](https://tex.z-dn.net/?f=T%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%263%5C%5C2%264%5Cend%7Barray%7D%5Cright%5D%20.)
Step-by-step explanation: We are given to find the transition matrix from the bases B to B' as given below :
B = {(-1,2), (3, 4)) and B' = {(1, 0), (0, 1)}.
Let us consider two real numbers a, b such that
Again, let us consider reals c and d such that
Therefore, the transition matrix is given by
Thus, the required matrix is
Answer: $15385 should be deposited.
Step-by-step explanation:
The principal was compounded monthly. This means that it was compounded 12 times in a year. So
n = 12
The rate at which the principal was compounded is 7.8%. So
r = 7.8/100 = 0.078
It was compounded for 4 years. Therefore,
t = 4
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. The total amount is given as $21000. Therefore
21000 = P (1+0.078/12)^12×4
21000 = P (1+0.078/12)^48
21000 = P (1+0.0065)^48
21000 = P (1.0065)^48
P = 21000/1.365
P = $15385
Lots of red herrings in this question! The beacon is circular, so you need to find the area of a circle with a diameter of 36 inches.
Area of a circle = pi x radius^2
remember radius is half the diameter!
