The 1st, 4th, and 7th terms make an arithmetic sequence of their own. The 4th term is the average of the 1st and 7th, so ...
(1st +7th)/2 = 4th
1st + 7th = 2×4th
1st = 2×4th - 7th
The first term is ...
2*141 - 132 = 150
Answer: 119°
Step-by-step explanation:
From the positive y-axis, all angles are measured clockwise
PR = PQ + QR = 5[150°] + 3[60°]
X = 5*sin150 + 3*sin60 = <u>5.1</u>
Y = 5*Cos150 + 3*Cos60 = <u>-2.83</u>
TanA = X/Y
A = -61° = 61° East of South = 119° Clockwise
Therefore, the bearing of R from P is 119°
Initially, Ball A of 10 kg will have velocity x, while Ball B of 30 kg has velocity -10 m/s.
After collision, Ball A will have a velocity of -30 m/s, while Ball B will have velocity 10 m/s. We assume their masses do not change.
(10 kg)(x m/s) + (30 kg)(-10 m/s) = (10 kg)(-30 m/s) + (30 kg)(10 m/s)
10x - 300 = -300 + 300
x = 30 m/s (to the right)
6x+3>3x+30
The thing about solving inequalities, you just need to treat the symbol, which is the less than symbol in this case, as an equal sign.
So our problem becomes: 6x+3=3x+30
Now we solve this like a normal algebra problem.
First, get all the variables on one side. Since 3x is smaller than 6x, we'll get rid of that by subtracting it from each side.
3x+3=30 is what we end up with.
Now to get the variable alone and get rid of that constant. To do that, we are going to subtract 3 from each side.
We end up with 3x=27
Now, to get the 'x' alone, we need to divide each side by 3.
x=9 is what we end up.
BUT WE FORGOT TO DO SOMETHING
We started this as an inequality problem, so we need to end it as an inequality solution.
Since there wasn't any negatives we need to worry about (Which is something else entirely) we just need to transfer the symbol we started with down.
x>9
Any Questions?