Answer:
see explanation
Step-by-step explanation:
These are the terms of an arithmetic sequence with n th term
= a + (n - 1)d
where a is the first term and d the common difference
d = 25 - 20 = 30 - 25 = 5 and a = 20, hence
= 20 + 5(n - 1) = 20 + 5n - 5 = 5n + 15 ← n th term formula
x - 25 = (√x)^2 - 5^2 = (√x - 5)(√x + 5)
Then
(x - 25)/(√x - 5) = √x + 5
and as x approaches 25, we get a limit of √25 + 5 = 5 + 5 = 10.
Answer:
2184 different schedules
Step-by-step explanation:
Sam can make different schedules of the same three cities, so order of cities does matter, but no repetition is allowed. This makes this a permutation without repetition.
When we choose from n items, and we choose r of them, our formula is
n! / (n-r)!. We have 14 things to choose from, and 3 to choose, so our formula becomes
14! / (14-3)! = 14!/11! = 14*13*12 = 2184 different schedules