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Brut [27]
4 years ago
12

While placing a compact disc into a CD player, you notice a small chip on it\'s edge. But you attempt to play the CD anyway by p

lacing the CD into the player\'s deck with the chip at θ0 = 10.0° as measured from the x axis. The CD begins to rotate with angular acceleration α = 2.49 rad/s2. If the CD has been spinning for t = 3.51 s and the disc has a radius of r = 6.00 cm, what are the x–y coordinates of the chip after this time, assuming the center of the disc is located at (0.00,0.00).
According to my calculations it should be x = -2 and y = 5.8 but those were incorrect.
Mathematics
1 answer:
Vera_Pavlovna [14]4 years ago
8 0

Answer:

  (x, y) ≈ (-5.89, 1.16)

Step-by-step explanation:

We assume the CD is still accelerating at the same rate at the end of the given time period. The angular position will be found from ...

  θ(t) = θ₀ + (1/2)a·t²

Filling in the numbers given, we get

  θ(3.51) = (10π/180) + (1/2)(2.49)(3.51²) = 15.51306 . . . radians

The x-y coordinates will be found from ...

  (x, y) = radius·(cos(θ), sin(θ)) ≈ 6·(-0.981066, 0.193674)

  (x, y) ≈ (-5.89, 1.16)

_____

For the trig functions, the calculator must be in radians mode, unless you have converted the angles to degrees.

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Answer:

a) (11/7, 9/7)

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Step-by-step explanation:

a) x - 2y + 1 = 0

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To find the point of intersection, we need to solve the system of equations  and the result will be the point of intersection (x,y)

x-2y+1=0\\x= 2y-1

Now we substitute x in the second equation:

2x+3y-7=0\\2(2y-1)+3y-7=0\\4y-2+3y-7=0\\7y-9=0\\y=9/7

Now we substitute y in our first equation.

x-2y+1=0\\x-2(9/7)+1=0\\x-18/7+1=0\\x=18/7-1\\x=11/7.

The point of intersection is (11/7, 9/7)

b) x -2y +11 =0

-x + 2y - 13 =0

We are going to follow the same procedure:

x-2y+11=0\\x=2y-11

-(2y-11)+2y-13=0\\-2y+11+2y-13=0\\0y=2\\0=2

Since this system of equations doesn't have a solution, the system has no point of intersection.

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