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Stolb23 [73]
3 years ago
11

A slice of pizza whose edges form a 32degrees angle with an outer crust edge 4 inches long was found in a gym locker. What was t

he diameter of the original​ pizza?g
Mathematics
1 answer:
liq [111]3 years ago
5 0

Answer:

The diameter was d=\frac{45}{\pi } in.

Step-by-step explanation:

The arc of a circle is given by

s=r\theta

where

s = arc length

r = radius of the circle

θ = measure of the central angle in radians.

From the information given

s = 4 in

θ = 32º

To find the diameter of the original​ pizza, we use the formula of the diameter of a circle

d=2r

First, we need to convert the angle to radians

\theta=32\º \cdot \frac{\pi}{180\º} =\frac{8\pi }{45}

Next, solve for r from the arc formula

r=\frac{s}{\theta} =\frac{4}{\frac{8\pi }{45}} =\frac{45}{2\pi }

Then, we use the diameter of a circle formula

d=2r=2(\frac{45}{2\pi })=\frac{45}{\pi }

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Step-by-step explanation:

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3 years ago
Consider the matrices -2 -1 1 4 1 A = B = 4 -2 4 -2 -2 4 -2 1 -1 (a) Verify that they are diagonalizable and that they commute.
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Answer:

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Step-by-step explanation:

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Read 2 more answers
What is the volume of a certain cube? (1) The sum of the lengths of the edges of the cube is 36. (2) The surface area of the cub
german

Answer:

(1) The sum of the lengths of the edges of the cube is 36.

A cube has 12 equal edges. Sum = 36. Length of each edge = 36/12 = 3

Volume = 3*3*3 = 27

(2) The surface area of the cube is 54.

A cube has 6 identical faces. Area of each face = s^2 (s is the length of the side)

6s^2 = 54

s = 3

Volume = 3*3*3 = 27

Step-by-step explanation:

All you need to uniquely define a cube is any one measurement - length of a side/edge, area of a surface, volume etc. If you have any one of them, you can uniquely determine the others. So each statement alone is sufficient here.

To show how,

(1) The sum of the lengths of the edges of the cube is 36.

A cube has 12 equal edges. Sum = 36. Length of each edge = 36/12 = 3

Volume = 3*3*3 = 27

(2) The surface area of the cube is 54.

A cube has 6 identical faces. Area of each face = s^2 (s is the length of the side)

6s^2 = 54

s = 3

Volume = 3*3*3 = 27

8 0
3 years ago
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