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)
121 different ways. I would just simply multiply 11 songs and 11 different placements so 11 x 11 = 121
Answer:
1. a=2.3
2. b=2.6
3. c=2.3
4.d=2.6
5. e=40
6. f=1/6
7. g=85
Step-by-step explanation:
Answer:
Step-by-step explanation:
X=8.50
y=9.50
Answer:
Mean = 8 gerbils
MAD = 4.29 gerbils
Step-by-step explanation:
Find the mean:
Mean= 0+3+6+9+11+13+14 ÷ 7
Mean = 56 ÷ 7
Mean = 8 gerbils
To get the MAD we have to find the distance of each value of gerbil from the mean
8,5,2,1,3,5,6
MAD = 9+6+3+0+2+4+5 ÷ 7
MAD = 30 ÷ 7
MAD = 4.29 gerbils