I think we can use the identity sin x/2 = sqrt [(1 - cos x) /2]
cos x - sqrt3 sqrt ( 1 - cos x) /sqrt2 = 1
cos x - sqrt(3/2) sqrt(1 - cos x) = 1
sqrt(3/2)(sqrt(1 - cos x) = cos x - 1 Squaring both sides:-
1.5 ( 1 - cos x) = cos^2 x - 2 cos x + 1
cos^2 x - 0.5 cos x - 0.5 = 0
cos x = 1 , -0.5
giving x = 0 , 2pi, 2pi/3, 4pi/3 ( for 0 =< x <= 2pi)
because of thw square roots some of these solutions may be extraneous so we should plug these into the original equations to see if they fit.
The last 2 results dont fit so the answer is x = 0 , 2pi Answer
What are the answer options?
A rotation of 270 would be equal to 630, 990, etc. Adding 360 degrees would result in the same rotation.
A rotation of 90 degrees counter-clockwise would also result in the same rotation, as would 90 plus any multiple of 360 if rotated counter-clockwise.
Answer:
The midpoint is;
(-1,-0.5)
Step-by-step explanation:
To do this, we shall use the midpoint formula
That would be;
(x,y) = (x1 + x2)/2 , (y1 + y2)/2
(x1,y1) = (-9,-1)
(x2,y2) = (7,0)
(x,y)
= (7-9)/2 , (0-1)/2
= -2/2 , -1/2
= (-1, -0.5)
4 ft x 6 ft = 24 sq ft = 2160 sq in.
6 in. x 12 in. = 72 sq in.
(2160 sq in. / 72 sq in. = 30 large tiles.
30 large tiles to be used only.
The minimum cost is $135
A ratio is a fraction which is technically a division problem.
