Answer:
Step-by-step explanation:
We want to simplify:
Recall the Pythagorean Identity:
So:
Substitute:
Factor. We can use the difference of two squares pattern:
Cancel. Hence:
Answer:
x ≥ - 9
Step-by-step explanation:
The expression inside the radical must be greater than or equal to zero
9 + x ≥ 0 ( subtract 9 from both sides )
x ≥ - 9 ← domain
The asymptote is
Domain is
Range is
Explanation:
Given that the function is
<u>Asymptote:</u>
The function has no horizontal asymptote.
The given function is of the form, has a vertical asymptote
where
Thus, the vertical asymptote is
<u>Domain:</u>
The domain of the function is the set of all independent x - values for which the function is real and well defined.
Let us find the positive values for log
Thus, we have,
Thus, the function domain in interval notation is
<u>Range:</u>
The range of the function is the set of all dependent y - values of the function.
Hence, the range of the function is
Answer:
336 ways ;
56 ways
Step-by-step explanation:
Number of ways to have the officers :
Number of qualified candidates, n = 8
Number of officer positions to be filled = 3
A.)
Using permutation (since the ordering matters):
nPr = n! ÷(n-r)!
8P3 = 8! ÷ (8-3)!
8P3 = 8! ÷ 5!
8P3 = (8*7*6)
8P3 = 336 ways
B.) Different ways of appointing committee: (ordering doesn't count as officers can also be appointed)
Using the combination relation :
nPr = n! ÷(n-r)!r!
8C3 = 8! ÷ (8-3)! 3!
8C3 = 8! ÷ 5!3!
8C3 = (8*7*6) ÷ (3*2*1)
8C3 = 336 / 6
8C3 = 56 ways