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.
Answer:
122.5 cm²
Step-by-step explanation:
a = 21cm
b = 14cm
h = 7cm
Area of given figure(trapezium) =
= 21 + 14/ 2 * 7
= 35/2 * 7
= 17.5 * 7
= 122.5 cm²
Answer:
3i √3
Step-by-step explanation:
you can't have the square root of a negative number
so we use "i"
<span>f(x) = 3x - 7. you replace Y with f(x) because f(x) is the inverse of y</span>
3/45 because it is simplified 15/5=3 and 225/5=45