Answer: f(120°) = (√3) + 1/2
Step-by-step explanation:
i will solve it with notable relations, because using a calculator is cutting steps.
f(120°) = 2*sin(120°) + cos(120°)
=2*sin(90° + 30°) + cos(90° + 30°)
here we can use the relations
cos(a + b) = cos(a)*cos(b) - sin(a)*sin(b)
sin(a + b) = cos(a)*sin(b) + cos(b)*sin(a)
then we have
f(120°) = 2*( cos(90°)*sin(30°) + cos(30°)*sin(90°)) + cos(90°)*cos(30°) - sin(90°)*sin(30°)
and
cos(90°) = 0
sin(90°) = 1
cos(30°) = (√3)/2
sin(30°) = 1/2
We replace those values in the equation and get:
f(120°) = 2*( 0 + (√3)/2) + 0 + 1/2 = (√3) + 1/2
So 2x+12=5x-9
you want all of the unknowns on one side and all of the known values on the other or
subtract 2x from both sides
12=3x-9
add 9 to both sides
21=3x
divide both sides by 3
7=x
-2, -1, 0
These would be the options
The domain is the limits of the function. Since time doesnt go negative, start with 0. At time 0, the height is
-16(0)^2 + 144 = 144ft
Then, solve for t to find the upper limit for t, which is when the height is zero (since you're dropping the object).
-16t^2 + 144 = 0
-16t^2 = -144
t^2 = 9
t = sqrt(9)
t = 3
The domain is 0 to 3 seconds.
