Answer:
V ≈3769.91
explanation:
V = π r 2h = π·10^2·12 ≈3769.91118 in³
Answer:
1.1m
Step-by-step explanation:
Let L denote longer pipe and S denote shorter part
given:
L:S = 9:2
or L/S = 9/2
2L = 9S
S = (2/9)L-----(eq 1)
Also given:
L - 1.65 = 3S
L - 3S = 1.65 ----- (eq 2)
By substitution, sub eq 1 into eq 2
L - 3(2/9)L = 1.65
L - (2/3)L = 1.65
L [ 1 - (2/3) ] = 1.65
L/3 = 1.65
L = 1.65 (3) = 4.95 (substitute into equation 1)
S = (2/9)(4.95) = 1.1m
The pile of plywood is 11.4 centimeters thick.
Work:
1.27 x 9 = 11.43
Round 11.43 to the nearest tenth
11.4
Hope this helps!
If you mean (6x^2)/(2x^2), this problem is easy.
(6x^2)/(2x^2) = (6/2) x (XX/XX) (XX is an easy way of writing X^2)
6/2 = 3
XX/XX = 1
3 x 1 = 3
so your answer is 3.
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.