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Allisa [31]
3 years ago
12

In what diffrent ways can 440 be written as the product of two positve integers

Mathematics
1 answer:
tekilochka [14]3 years ago
8 0

 440    = 1 x 2 x 2 x 2 x 5 x 11

(1):            1 x 440

(2):           2 x 220

(2 x 2):     4 x 110

(5):           5 x 88

(2x2x2):   8 x 55

(2 x 5):    10 x 44

(11):          11 x 40

(2x2x5): 20 x 22

No need to continue because the next number is 2 x 11 = 22 and we already have that on the right side, so we have found all of the multiplicative pairs of 440.



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Answer:

1) The area of the circle pizza is approximately 161.64 in.²

2) The area of the octagon shaped pizza is approximately 145.52 square inches

Step-by-step explanation:

The 8 slices of pizza combine to form the composite octagon

The parameters of the pizza are;

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The length of each (outer) edge of the octagon = 5.49 inches

The outer edge of the octagon = The base of the triangle shaped pizza

Let θ represent the vertex angle of the triangle shaped pizza

Therefore, we have;

θ = (The angle at the center point of the pizza)/8 = 360°/8 = 45°

The vertex angle of the triangle shaped pizza, θ = 45°

We note that a triangle shaped pizza is isosceles shaped, therefore, the base angles are given as follows;

The base angles of a piece of pizza = (180° - (angle at vertex))/2

∴ The base angles of a piece of pizza = (180° - 45°)/2 = 67.5°

The length, 'l', of the other sides of the triangle shaped pizza is given by sine rule as follows;

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l = (sin 67.5°) × 5.49/(sin(45°) ≈ 7.173

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1) The length of the other sides of the triangle shaped pizza, l = The radius of the circle, r

The area of the circle = π·l²

∴ The area of the circle ≈ π × (7.173 in.)² ≈ 161.64 in.²

2) The area of each triangle piece of pizza is given as follows;

The area of a triangle, A = 1/2×l·b·sin(C)

∴ A = 1/2× 5.49 × 7.173 × sin(67.5°) ≈ 18.19

The area of each triangle piece of pizza, A ≈ 18.19 inches²

The total area of 8 slices of octagon shaped pizza, TA ≈ 8 × A

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The total area of 8 slices of octagon shaped pizza, TA ≈ 145.52 inches²

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Step-by-step explanation:

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