Hello from MrBillDoesMath!
Answer:
csc (90° – x) = sec (x
)
sin (90° – x) = cos (x
)
tan (90° – x) = cot (x)
cos (90° – x) = sin (x
)
cot (90° – x) = tan (x
)
sec (90° – x) = csc (x)
Thank you,
MrB
Answer:
x=8
Step-by-step explanation:
set up a proportion:
simplify:
now solve this equation for x:
7,500 x 2 = 15,000
you know you can just use a calculator...
There are a total of 16 coins, so out of the ratio, that 16 goes on the bottom. Now you have to add up the coins that are NOT quarters and that number goes on the top. So your ratio is 8/16 or 1/2
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.)
