If each shelf is to contain exactly 3 new CDs and there are only 5 shelves, only 15 can be placed in the rack. So, the answer to the second question is no. The same goes for the first question as placing 3 or fewer CDs to the shelves will make the rack insufficient for the CDs.
tan A = 2/7 (option C)
Explanation:
Angle = A
opposite = side opposite the angle = BC
opposite = 2
adjacent = AC
AC = 7
hypotenuse not given
Since angle C is a right angle, we would apply trigonometry ratio SOHCAHTOA
We are looking for tan A, tan ratio (TOA):
Yes it is possible for a geometric sequence to not outgrow an arithmetic one, but only if the common ratio r is restricted by this inequality: 0 < r < 1
Consider the arithmetic sequence an = 9 + 2(n-1). We start at 9 and increment (or increase) by 2 each time. This goes on forever to generate the successive terms.
In the geometric sequence an = 4*(0.5)^(n-1), we start at 4 and multiply each term by 0.5, so the next term would be 2, then after that would be 1, etc. This sequence steadily gets closer to 0 but never actually gets there. We can say that this is a strictly decreasing sequence.
If your teacher insists that the geometric sequence must be strictly increasing, then at some point the geometric sequence will overtake the arithmetic one. This is due to the nature that exponential growth functions grow faster compared to linear functions with positive slope.
If you paid a total of 15.92 and also paid 1.99 per song, then you must divide the total by the cost per song.
As such 15.92/1.99 = 8 songs. :)
