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serious [3.7K]
3 years ago
13

Classify each number below as a rational number or an irrational number.

Mathematics
1 answer:
FrozenT [24]3 years ago
6 0

Answer:

87.84(repeating) irrational

-(sqrt[11]) irrational

-(sqrt[36]) rational

72.28 rational

11pi irrational

Step-by-step explanation:

If you can ever see the whole number, it is rational. For example, 5.194291497129471290410247912094142 is rational, although not very pleasant to look at. Repeating decimals, square roots of prime numbers, and special numbers (like pi in your question) are irrational because they go on infinitely.

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Po The diameter of a circular fountain in a city park is 28 feet. A sidewalk that is 3.5 feet will be built around the fountain.
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Answer:

Area of sidewalk = 346.5 ft^2

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Step-by-step explanation:

The diameter of the circular fountain is 28 ft. Radius = 28 / 2 = 14 ft

The thickness of the sidewalk is 3.5 ft. This means they want to add 3.5 ft to each radius of the fountain.

To find the area of the sidewalk alone, we have to find the area of the sidewalk alone and then subtract it from the area of the sidewalk and fountain.

That is:

A_s = A_{s+f} - A_f

The fountain is circular and its radius is 14 ft. Hence, its area will be:

A_f = \pi r^2

A_f = \pi *14^2 = 616 ft^2

The sidewalk and fountain together also form a circular shape. Their joint radius will be:

R = 14 + 3.5 = 17.5 ft

Hence, the area will be:

A_{s + f} = \pi R^2 \\A_{s + f} = \pi * 17.5 * 17.5 = 962.5 ft^2

Hence, the area of the sidewalk alone will be:

A_s = 962.5 - 616 = 346.5 ft^2

This is the area of the sidewalk.

For every square foot (ft^2), 0.8 bag of concrete will be used. This means that for 346.5 ft^2:

Bags of concrete = 0.8 * 346.5 = 277.2 ≅ 277

At least 277 bags of concrete will be used for the new sidewalk.

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