45.90*0.05=2.295.
The answer is $2.30 when you round it off.
Rewrite equation so that it is homogeneous .

Solve characteristic equation:
The solutions to the homogeneous equation are:

Finally you need the constant term in "cy" to equal 'd' to satisfy the particular solution.
Answer:
The required position of the particle at time t is: 
Step-by-step explanation:
Consider the provided matrix.



The general solution of the equation 

Substitute the respective values we get:


Substitute initial condition 

Reduce matrix to reduced row echelon form.

Therefore, 
Thus, the general solution of the equation 


The required position of the particle at time t is: 
Given:
second term = 18
fifth term = 144
The nth term of a geometric sequence is:

Hence, we have:

Divide the expression for the fifth term by the expression for the second term:

Substituting the value of r into any of the expression:

Hence, the explicit rule for the sequence is: