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.
Well you multiply the -4 to the 9 using and you will get -36 then you divide by -6 and you will get 6 simple as that
D = sqrt((0-18)^2 + (-5--10)^2)
D= sqrt ((-18)^2 + (5)^2)
D= sqrt( 324 + 25)
D= sqrt ( 349)
D = 18.7
Answer:
34%
Step-by-step explanation:
Step 1:
34/100 = 0.34
Step 2:
0.34 = 34%
Answer:
34%
Hope This Helps :)