Answer:
n = π/6, π/4, 3π/4, 5π/6
Step-by-step explanation:
sin(3n) − sin n = cos(2n)
Use double and triple angle formulas:
(3 sin n − 4 sin³ n) − sin n = 1 − 2 sin² n
2 sin n − 4 sin³ n = 1 − 2 sin² n
4 sin³ n − 2 sin² n − 2 sin n + 1 = 0
Factor by grouping:
2 sin² n (2 sin n − 1) − (2 sin n − 1) = 0
(2 sin² n − 1) (2 sin n − 1) = 0
Solve:
2 sin² n − 1 = 0
2 sin² n = 1
sin² n = 1/2
sin n = √2/2
n = π/4, 3π/4
2 sin n − 1 = 0
2 sin n = 1
sin n = 1/2
n = π/6, 5π/6
Step 1: 6x - 2x - 5 = -6 + 21
Step 2: 6x - 2x - 5 = 15
Step 3: 4x - 5 = 15
The next step would be to add 5 to both sides of the equation.
so Step 3: 4x - 5 = 15 .......add 5 to both sides would make
Step 4: 4x = 20
So after the next step you would have 4x = 20
Hope this helps! :)
Answer: 12 = r
Step-by-step explanation: When we have this kind of a setup, we want to put our variables together on one side of the equation and our numbers together on the other side of the equation.
First, let's put our variables on the right side by subtracting 3r from both sides of the equation. That gives us 5 = 2r - 19.
Now we can move our numbers to the left by adding 19 to both sides of the equation and we get 24 = 2r.
Divide both sides by 2 and 12 = r
Note:
Don't just do this problem in your head. It's extremely important to develop the habit of putting all your steps down on paper or digitally. It will really pay off for you down the line.
Answer:
C. 2.865
Step-by-step explanation:
All you have to do in this situation is to subtract the amount he ran two weeks ago by the amount Thomas ran last week. It would look like so,
38.074 - 35.209
And once you do that you get the answer of 2.865
Hope that helps and have a great day!
