30 children are going on a trip. It costs £5 including lunch. Some children take their own packed lunch. They pay only £3.the 30
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Simplifying h(x) gives
h(x) = (x² - 3x - 4) / (x + 2)
h(x) = ((x² + 4x + 4) - 4x - 4 - 3x - 4) / (x + 2)
h(x) = ((x + 2)² - 7x - 8) / (x + 2)
h(x) = ((x + 2)² - 7 (x + 2) - 14 - 8) / (x + 2)
h(x) = ((x + 2)² - 7 (x + 2) - 22) / (x + 2)
h(x) = (x + 2) - 7 - 22/(x + 2)
h(x) = x - 5 - 22/(x + 2)
An oblique asymptote of h(x) is a linear function p(x) = ax + b such that
In the simplified form of h(x), taking the limit as x gets arbitrarily large, we obviously have -22/(x + 2) converging to 0, while x - 5 approaches either +∞ or -∞. If we let p(x) = x - 5, however, we do have h(x) - p(x) approaching 0. So the oblique asymptote is the line y = x - 5.
Let n be the total number of puffs. Now we can write:
Adding the fractional value of n, we get:
Simplifying and rearranging gives us:
Therefore we can simplify to get:
and finally
The fraction of the puff that are tuna is found from:
Adding the fractional value of n, we get:
Simplifying and rearranging gives us:
Therefore we can simplify to get:
and finally
The fraction of the puff that are tuna is found from: