I'm partial to solving with generating functions. Let
Multiply both sides of the recurrence by and sum over all .
Shift the indices and factor out powers of as needed so that each series starts at the same index and power of .
Now we can write each series in terms of the generating function . Pull out the first few terms so that each series starts at the same index .
Solve for :
Splitting into partial fractions gives
which we can write as geometric series,
which tells us
# # #
Just to illustrate another method you could consider, you can write the second recurrence in matrix form as
By substitution, you can show that
or
Then solving the recurrence is a matter of diagonalizing the coefficient matrix, raising to the power of , then multiplying by the column vector containing the initial values. The solution itself would be the entry in the first row of the resulting matrix.
76! its because its a vertical to the other 76
Slope intercept form: y=mx+b
y=5x-5
y=-3/4x-1
I’m pretty sure…
Cos = adjacent over hypotenuse
cos33 = b/170
170cos33 = b
b = 142.574 inches
The zeroes to the function are x=-8 and x=-1