Suppose there is a simple index of three stocks, stock ABC, stock XYZ, and stock QRS. Stock ABC opens on day 1 with 8000 shares at $4.25 per share.
Stock XYZ opens on day 1 with 5000 shares at $2.90 per share. Stock QRS
opens on day 1 with 2000 shares at $6.40 per share. The price of stock ABC
on day 8 begins at $3.90. The price of stock XYZ on day 8 begins at $2.50.
Stock QRS opens on day 8 with a price of $6.10 per share. Assume that each
stock has the same number of shares that it opened with on day 1. What is
the rate of change of this simple index over 1 week?
A. 9.7%
B. -8.8%
O C. -9.7%
D. 8.8%

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough