Notice that
• <em>π</em>/2 = <em>π</em>/3 + <em>π</em>/6
• <em>π</em>/6 = <em>π</em>/3 - <em>π</em>/6
Recall the angle sum identities for sine:
sin(<em>x</em> + <em>y</em>) = sin(<em>x</em>) cos(<em>y</em>) + cos(<em>x</em>) sin(<em>y</em>)
sin(<em>x</em> - <em>y</em>) = sin(<em>x</em>) cos(<em>y</em>) - cos(<em>x</em>) sin(<em>y</em>)
By adding these together, we get
sin(<em>x</em> + <em>y</em>) + sin(<em>x</em> - <em>y</em>) = 2 sin(<em>x</em>) cos(<em>y</em>)
==> sin(<em>x</em>) cos(<em>y</em>) = 1/2 (sin(<em>x</em> + <em>y</em>) + sin(<em>x</em> - <em>y</em>))
Now take <em>x</em> = <em>π</em>/3 and <em>y</em> = <em>π</em>/6 :
sin(<em>π</em>/3) cos(<em>π</em>/6) = 1/2 (sin(<em>π</em>/2) + sin(<em>π</em>/6))
So the blank should be filled with cos.
8.65
8.66
8.67
8.68
8.69
8.70
8.71
8.72
8.73
11 blue
2 green
7 brown
total is 20 card
7 out of that 20 are brown
so x out of 100% are brown
7/20=x/100 - cross multiply
700=20x
x=700/20
x=70/2
Answer:
A. 5
Step-by-step explanation:
Answer:
Rate at which the shadow is moving = -5 ft/s.
Step-by-step explanation:
I can do the second part for you:
If the distance of the woman from the wall is Xp , the length of the shadow is Xs and the distance from the tip of the shadow to the wall is X we have the relation:
X = Xp + Xs.
We need to find X' (the rate that the tip of the shadow is moving). at Xp = 16 and X'p = -4 ft/s.
We need a relation between X and Xp so we have to eliminate Xs.
By similar triangles 5.5 / 27.5 = Xs / x
1/5 = Xs/x
Xs = x /5 so substituting in the above relation:
X = Xp + X/5
4X/5 = Xp
X = 5Xp / 4
Taking derivatives:
X' = 5X'p / 4
Now X'p is given as - 4 so
X' = -20/4 = -5 ft/s.
