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A sweet potato pie in a 10.50 in diameter plate is placed upon a rotating tray. Then, the tray is rotated such that the rim of th plate moves through a distance of 183 in. Express the angular distance that the pie plate has moved through in revolutions, radians, and degrees. angular distance: angular distance: angular distance: If the pie is cut into 10 equal slices, express the angular size of one slice in radians, as a fraction of π. angular size =π Incorrect

User Ben Pap
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To calculate the angular distance that the sweet potato pie plate has moved through, we can use the formula:

Angular Distance = Distance Traveled / Radius

Given that the rim of the plate moves through a distance of 183 inches, and the diameter of the plate is 10.50 inches, we can calculate the radius of the plate:

Radius = Diameter / 2

Radius = 10.50 / 2

Radius = 5.25 inches

Now we can calculate the angular distance in revolutions, radians, and degrees.

1. Angular distance in revolutions:

To convert the distance traveled into revolutions, we need to find the circumference of the circular path.

Circumference = 2 * π * Radius

Circumference = 2 * 3.14 * 5.25

Circumference ≈ 32.94 inches

Angular Distance (in revolutions) = Distance Traveled / Circumference

Angular Distance (in revolutions) = 183 / 32.94

Angular Distance (in revolutions) ≈ 5.55 revolutions

2. Angular distance in radians:

To convert the angular distance from revolutions to radians, we need to multiply by 2π (since there are 2π radians in one revolution).

Angular Distance (in radians) = Angular Distance (in revolutions) * 2π

Angular Distance (in radians) ≈ 5.55 * 2 * 3.14

Angular Distance (in radians) ≈ 34.78 radians

3. Angular distance in degrees:

To convert the angular distance from radians to degrees, we need to multiply by 180/π (since there are 180 degrees in one π radians).

Angular Distance (in degrees) = Angular Distance (in radians) * (180/π)

Angular Distance (in degrees) ≈ 34.78 * (180/3.14)

Angular Distance (in degrees) ≈ 1995.54 degrees

If the sweet potato pie is cut into 10 equal slices, the angular size of one slice can be calculated by dividing the angular distance of the pie plate by the number of slices.

Angular Size (in radians) = Angular Distance (in radians) / Number of Slices

Angular Size (in radians) ≈ 34.78 / 10

Angular Size (in radians) ≈ 3.48 radians

Therefore, the angular size of one slice is approximately 3.48 radians, which can be written as 3.48/π when expressed as a fraction of π.

User Ajanth
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