Find constants A and B such that the function y = A sin(x) + B cos(x) satisfies the differential equation y'' + y' − 2y = sin(x).

A = - 0.3 and B = - 0.1.

Step-by-step explanation:

y(x) = A sinx + B cosx

y'(x) = A cosx - B sinx

y"(x) = -A sinx - B cos x

So, substituting we have:

y" + y' - 2y = -A sinx - B cos x + A cosx - B sinx - 2(A  sinx + B cosx)

=    -3A sin x - B sinx + A cosx  - 3B cos x = sinx

sin x (-3A - B) + cos x(A - 3B) = sin x

Since this is an identity then we equate coefficients:

-3A - B =  1

A - 3B = 0

Solving these we get A = - 0.3 and B = - 0.1.

idk man good luck man

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~