<h3>Straightforward Solution</h3>
The long way around is to compute the return from each investment and relate the sum of those returns to the toal investment.
You have invested $33×100 = $3300 in clooney. You expect a return of 20%×$3300 = $660 on that investment.
You have invested $42×100 = $4200 in marx. You expect a return of 12%×$4200 = $504 on that investment.
Your total expected return is $660 + 504 = $1164. Your total investment is $3300 + 4200 = $7500. Thus, the return on your investment is expected to be
... $1164/$7500 = 0.1552 ≈ 15.5% . . . . matches choice a.
<h3>Alternative Solution</h3>
Since the same number of shares is involved in both investments, you can weight the expected return percentages by the ratio of share price to total of share prices:
expected return = (33/75)×20% + (42/75)×12%
... = 8.80% + 6.72% = 15.52%
√200 = √2·100 = √2 · √100 = 10√2
From the given triangle, midpoint of AB = ((-2 + 3)/2, (0 + 6)/2) = (1/2, 3) and the midpoint of BC = ((3 + 8)/2, (6 + 0)/2) = (11/2, 3)
Length of the line segment joining points (1/2, 3) and (11/2, 3) is given by
l = sqrt[(11/2 - 1/2)^2 + (3 - 3)^2] = sqrt(5^2) = 5.
Therefore, option A is the correct answer.
The solution to the problem is as follows:
<span>cos2A - cos4A = -2 sin(6A/2).sin(-2A/2) = +2 sin(3A).sinA
and
sin4A - sin2A = 2 cos(6A/2).sin(2A/2) = 2 cos(3A).sinA
Hence RHS = (cos(2A)-cos(4A))/ (sin(4A)- Sin(2A)) = sin 3A / cos 3A = tan 3A = LHS
</span>
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