Im pretty sure the answer is a, sorry if its incorrect.
Answer:
Consider the given equation.
4sinxsin2xsin4x=sin3x
2(2sin2xsinx)sin4x=sin3x
We know that
2sinAsinB=cos(A−B)−cos(A+B)
Therefore,
2[cos(2x−x)−cos(2x+x)]sin4x=sin3x
2[cosx−cos3x]sin4x=sin3x
2sin4xcosx−2sin4xcos3x=sin3x
We know that
2sinAcosB=sin(A+B)+sin(A−B)
Therefore,
sin(4x+x)+sin(4x−x)−[sin(4x+3x)+sin(4x−3x)]=sin3x
sin(5x)+sin(3x)−[sin(7x)+sin(x)]=sin3x
sin(5x)−sin(7x)=sin(x)
We know that
sinC−sinD=2cos(
2
C+D
)sin(
2
C−D
)
Therefore,
2cos(
2
5x+7x
)sin(
2
5x−7x
)=sinx
2cos(
2
12x
)sin(
2
−2x
)=sinx
2cos(6x)sin(−x)=sinx
−2cos(6x)sin(x)=sinx
cos6x=−
2
1
6x=2nπ±
3
2π
x=
3
nπ
±
9
π
Hence, the value is
3
nπ
±
9
π
.
Answer:
Describe the effects of gravity on objects in motion.
Describe the motion of objects that are in free fall.
Calculate the position and velocity of objects in free fall.
Step-by-step explanation:
Describe the effects of gravity on objects in motion.
Describe the motion of objects that are in free fall.
Calculate the position and velocity of objects in free fall.
Answer:
x = 1 + sqrt(89) or x = 1 - sqrt(89)
Step-by-step explanation:
Solve for x:
(x - 9) (x + 7) = 25
Expand out terms of the left hand side:
x^2 - 2 x - 63 = 25
Add 63 to both sides:
x^2 - 2 x = 88
Add 1 to both sides:
x^2 - 2 x + 1 = 89
Write the left hand side as a square:
(x - 1)^2 = 89
Take the square root of both sides:
x - 1 = sqrt(89) or x - 1 = -sqrt(89)
Add 1 to both sides:
x = 1 + sqrt(89) or x - 1 = -sqrt(89)
Add 1 to both sides:
Answer: x = 1 + sqrt(89) or x = 1 - sqrt(89)
The angle of rotation is the minimum angle in which you rotate a regular polygon such that the figure appears unchanged. The formula for that is dividing one angle of revolution by its number of sides.
Angle of Rotation = 360°/n
Angle of Rotation = 360°/72 = 5°
