Arcsin x + arcsin 2x = π/3
arcsin 2x = π/3 - arcsin x
sin[arcsin 2x] = sin[π/3 - arcsin x] (remember the left side is like sin(a-b)
2x = sinπ/3 cos(arcsin x)-cosπ/3 sin(arc sinx)
2x = √3/2 . cos(arcsin x) - (1/2)x)
but cos(arcsin x) = √(1-x²)===>2x = √3/2 .√(1-x²) - (1/2)x)
Reduce to same denominator:
(4x) = √3 .√(1-x²) - (x)===>5x = √3 .√(1-x²)
Square both sides==> 25x²=3(1-x²)
28 x² = 3 & x² = 3/28 & x =√(3/28)
2x-7y=18 _(1)
-2x+4y=5
11y=23 , Y=23/11 sub in 1
2x-7×23/11=18
2x = 18×11 + 7×23
x = ( 198 + 161 )/2 = 359/2
68 is the answer of the question you ask the committee
1. x - 6; Mark has 6 less dollars than Kim. Let x be the number of dollars Kim has.
2. 2(x/2); Robert lost half his money in the stock market last week, and then doubled that amount this week.
3. 4(x - 8); 4 people spent $8 on a movie. How much money (x) did each person have before seeing the movie?
The surface area of the triangle is 1/2 * 6*8 so it is 24 sq units
The whole thing is 24* 7.5 so it is 180 sq units
