So you know that 3^4 is your numerator and that is (4)(4)(4)(4)=81
3^2 is your denominator and that is (3)(3)=9
81/9
=9
I'm assuming the limit is supposed to be
Multiply the numerator by its conjugate, and do the same with the denominator:
so that in the limit, we have
Factorize the first term in the denominator as
The 
terms cancel, leaving you with
and the limand is continuous at 
, so we can substitute it to find the limit has a value of -1/18.
Answer:
17. 6
18. 18 (as shown)
19. 10/3 = 3 1/3
20. 20/3 = 6 2/3
Step-by-step explanation:
17. For this, you can subtract the given length GB=12 from the length you found for problem 18, BF=18. Doing that tells you FG = 18-12 = 6, as you have marked on the diagram.
19. As with median BF, the point G divides it into two parts that have the ratio 1:2. The distance from G to D is the shorter of the distances, so you have ...
... GD = (1/3) CD = (1/3)·10 = 10/3
... GD = 3 1/3
20. You can subtract GD from CD to get CG, or you can multiply CD by 2/3. The result is the same either way.
... CG = CD -GD = 10 -3 1/3
... CG = 6 2/3
_____
<em>Comment on centroid and median</em>
The centroid (G) divides each median into parts in the ratio 1:2. Hence the shorter of those parts is half the length of the longer one, or 1/3 the total length of the median.
The longer of the parts is double the length of the shorter one, or 2/3 the total length of the median.
Your marking of median BF seems to show an understanding of these relationships. (Total length: 18; length of parts: 6 and 12.)
Answer:
8 miles per hour
Step-by-step explanation:
<span>Initial number of the people that belong to a certain social website is 412. It is growing at a rate of 5% every month. It means that every month the number of people is growing 1.05 times. We can calculate how many of them will there be in 9 months: 412 * 1.05^9 = 412 * 1.55 = 638.6. When we round to the nearest whole number: there will be 369 members.</span>
