The cosine of an angle is the x-coordinate of the point where its terminal ray intersects the unit circle. So, we can draw a line at x=-1/2 and see where it intersects the unit circle. That will tell us possible values of θ/2.
We find that vertical line intersects the unit circle at points where the rays make an angle of ±120° with the positive x-axis. If you consider only positive angles, these angles are 120° = 2π/3 radians, or 240° = 4π/3 radians. Since these are values of θ/2, the corresponding values of θ are double these values.
a) The cosine values repeat every 2π, so the general form of the smallest angle will be
... θ = 2(2π/3 + 2kπ) = 4π/3 + 4kπ
b) Similarly, the values repeat for the larger angle every 2π, so the general form of that is
... θ = 2(4π/3 + 2kπ) = 8π/3 + 4kπ
c) Using these expressions with k=0, 1, 2, we get
... θ = {4π/3, 8π/3, 16π/3, 20π/3, 28π/3, 32π/3}
Answer:
$95-$5m
Step-by-step explanation:
after m months the has to pay $5m
so then you just need to subtract 5m from $95
Answer:
therefore the correct options are:
B. the equation is an exponential decay equation.
F. $28000 represents the initial cost of an automobile that depreciates 27% per year over the course of t years.
Step-by-step explanation:
i) the cost of an automobile is given by the equation is
C(t) = 
, where C(t) represents the cost and t represents the time in years
ii) the above equation is an exponential decay equation. It is a decay equation because growth rate is 0.73 which is less than 1 and greater than zero.
ii) when t = 0 then the cost is C(0) = 28000 represents the initial cost.
iii) from the equation in i) we can understand that the cost depreciates 27% per year over the course of t years.
therefore the correct options are:
B. the equation is an exponential decay equation.
F. $28000 represents the initial cost of an automobile that depreciates 27% per year over the course of t years.
Answer:
Your original account balance before you made the deposit is $6
Step-by-step explanation:
Let x = your original account balance.
You triple your account balance by making a deposit. This means
New account balance = 3 × x = 3x
Then you withdraw $28.50 from your bank account. This means that you have $(3x - 28.5) left.
Now your account is overdrawn by $10.50. This means you have withdrawn beyond what you have in your account. Your new account balance is -$10.5. Therefore,
3x - 28.5 = - 10.5
3x = -10.5 + 28.5 = 18
x = 18/3 = 6
Your original account balance before you made the deposit is $6
Answer:
The case reached the Supreme Court in June 1971. The Supreme Court has, at times, ruled that the government can restrict speech that presents a “clear and present danger.”
