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Len [333]
3 years ago
8

To which set of numbers does the following number belong 6.3 repeating

Mathematics
1 answer:
kenny6666 [7]3 years ago
5 0

6.3333... belongs to rational numbers.

Any number which can be represented in the form of p/q where q\neq 0 is known as rational number.

Any repeating number is rational.

Proof:

Let x= 6.3333..........  -(i)

Multiply both sides by 10

10 x= 63.3333........... -(ii)

Subtracting equation i from equation ii

9x= 57

x=  57/9 which is in p/q form.

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9514 1404 393

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  about 44.5 feet

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We can write relations for the height of the rail as a function of initial length and expanded length, but the solution cannot be found algebraically. A graphical solution or iterative solution is possible.

Referring to the figure in the second attachment, we can write a relation between the angle value α and the height of the circular arc as ...

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Then the length of the expanded rail is ...

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Rearranging this last equation, we have ...

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It is this equation that must be solved iteratively. We find the solution to be ...

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So, the height of the circular arc is ...

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<em>Additional comments</em>

Note that s and c in the diagram are half the lengths of the arc and the chord, respectively. The ratio of half-lengths is the same as the ratio of full lengths: c/s = 2640/2640.5 = 5280/5281.

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