Expand the target expression:
A sin(x + ϕ) = A (sin(x) cos(ϕ) + cos(x) sin(ϕ)) = -2 sin(x) + 4 cos(x)
Then we have
A cos(ϕ) = -2
A sin(ϕ) = 4
Recall that sin²(x) + cos²(x) = 1 for all x. Then
(A cos(ϕ))² + (A sin(ϕ))² = (-2)² + 4²
A² (cos²(ϕ) + sin²(ϕ)) = 4 + 16
A² = 20
A = √20 = 2√5
Also recall that tan(x) = sin(x)/cos(x) by definition. Then
(A sin(ϕ)) / (A cos(ϕ)) = 4 / (-2)
tan(ϕ) = -2
ϕ = arctan(-2) = -arctan(2)
6×500=3000
6×30=180
6×2=12
3000+180+12=3182
3182 is the final answer
If you divide 9 by 25 it equals .36
if you divide 18 by 50 it equals .36
if you divide 36 by 100 it equals .36
and if you divide 9 by 25 it equals .36
therefor it’s all equivalent. 18 divided by 50 is also .36
Answer:
So in order to find the missing number, we must find the difference with the numbers that we were given.
Problem #1
42-30= 12 and 84-69= 15. It's possible that each difference increases by one Let's see...
30+12= 42
42+13= 55
55+14 = 69
69+15 = 84
So for 1., all you have to do is keep adding the difference and increase it by 1 each time. If you wanted to keep increasing, you would add 84+16, then 100+17, etc.
Problem #2: As for the second one, I had trouble solving it, sorry :(.
Problem #3
3. For the third problem, 27-22= 5 and 9-1=8. It looks like each difference increased by 1.
27-22 = 5
22-6 = 16
16-7 = 9
9-8= 1