Answer:
3
Step-by-step explanation:
Intersections on the x axis occur when y = 0. f(x) is another term for y, so set f(x) equal to zero and solve for the two possible x's.
0 = x^2 - 3x - 40
0 = (x-8)(x+5)
By solving for x, you get 8 and -5. 8 and -5 added together will equal 3.
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
Answer:
(14, 2 )
Step-by-step explanation:
Use the midpoint formula
[0.5(x₁ + x₂), 0.5(y₁ + y₂) ]
with (x₁, y₁ ) = (16, 7) and (x₂, y₂ ) = (12, - 3)
midpoint = [0.5(16 + 12), 0.5(7 - 3) ] = [0.5(28), 0.5(4) ] = (14, 2 )
