Find the general solution of yʹ − 3y = 8e3t + 4sin t .

Step-by-step explanation:

Given differential equation,

Since, the above equation is of the type of linear differential equation

,

In which P = -3, Q = ,

Thus, the integrating factor,

Hence, the solution of the given differential equation would be,

Let,

Integrating by parts,  ( First term = sin t, second term = )

( from equation (2))

( where, C' = 9C/10 )

From equation (1),

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

two data sets with the same median will not have the same varaibility

step-by-step explanation: