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.
$ 9802.9and it said the answer had to be 20 characters long so i wrote this
Answer: f⁻¹(x)=4x-56
Step-by-step explanation:
f⁻¹(x) is the inverse of f(x). To find the inverse, we replace the y with x, and x with y. Once we do that, we solve for y.
[subtract 14 on both sides]
[multiply both sides by 4]
[distribute 4]
your answer is
b = 15 pi
length of ypx = circumfrance of circle - 1/4 of circumfrance of circle
= 2pi r - 2pi r/4 = 6 pi r / 4 = 3 pi r / 2
= 3 pi × 10/2 = 15 pi
Answer:
b
Step-by-step explanation: