Answer:
a. 540
Step-by-step explanation:
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.
We know the amount of copper is 85%, that means the rest is tin in the Alloy, so the tin is 15% of the Alloy then.
now, say "x" lbs is the total amount of the Alloy, and we know that 1 and 13/32 which is tin, is the 15% of "x", what the dickens is "x"?
Answer:
7/10
Step-by-step explanation:
2/5 is tha same as 4/10
so 4/10 plus 3/10 is 7/10
Answer:
49
Step-by-step explanation: