Answer:
θ = 0.896 and 2.246.
Step-by-step explanation:
We will use the identity
sin²θ + cos²θ = 1
and the double angle formula
cos2θ = cos²θ - sin²θ = (1 - sin²θ) - sin²θ = 1 - 2sin²θ
1. Convert the equation to a more solvable form.
2. Solve the quadratic
a = 2; b = 1; c = -2
(a) Set up the equation.
(b) Evaluate the roots
3. Solve for θ
(a) The negative root
u = sinθ = -1.281
sinθ cannot be less than -1. No solution.
(b) The positive root
If sin(x) = a, then
x = arcsin(x) + 2πn and
x = π - arcsin(a) + 2πn
(i) Case 1
u = sinθ = 0.7808
θ = arcsin(0.7808) + 2πn
θ = 0.8959 ± 2πn
If n = 0,
θ = 0.8959
(ii) Case 2
θ = π - 0.8959 + 2πn
If n = 0,
θ = π - 0.8959 = 2.246
The solutions are θ = 0.8959 and θ = 2.246
The diagram below shows the graph of f(θ) with its roots at 0.896 and 2.246.
Answer: C) 165 annual members
Step-by-step explanation:
Those who will visit the garden more than 3 times in the next month will be those who visit 4, 5, and 6 or more times.
Out of the 75 surveyed, the total number of those are:
= 9 + 12 + 3
= 24
That would give a percentage of:
= 24 / 75
= 32%
This means that the best estimate for those who will visit more than 3 times is 32%.
Out of the total number of 516, that is:
= 32% * 516
= 165 members
Answer:
6
Step-by-step explanation:
In the slope intercept equation, y=mx+b, m stands for slope and b stands for y-intercept, therefore your y-intercept is 6.
Answer:
3 : 1
Step-by-step explanation:
ratio = teeth on front sprocket : teeth on rear sprocket
= 36 : 12 ( divide both parts of the ratio by 12 )
= 3 : 1 ← in simplest form
The slope of a line that is perpendicular to another line is the negative reciprocal of the other.
In this case, we know that the slope of the given equation is 2.
Since we're solving for a line perpendicular to it, we simply find the reciprocal of the 2 (It turns into 1/2) and make it negative.
y = -1/2x + b
Since the given states that the new y-intercept is 10, input it into 'b'.
y = -1/2x + 10
If you'd like me to explain anything I did here, just ask :)
-T.B.
