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Lorico [155]
2 years ago
15

Alex says that there is no numbers between 1/3 and 1/4 . Why might he think that and what would you tell him? Is there a number

that falls between these?
Mathematics
1 answer:
Thepotemich [5.8K]2 years ago
8 0

Answer:

<em>Why might he think that and what would you tell him?</em>

He thought perhaps that numbers were formed by rational numbers of the form \frac{1}{x}, where x\in \mathbb{N}. I would tell him that there are rational numbers \frac{y}{z}, such that \frac{1}{x}\le \frac{y}{z} \le \frac{1}{x+1}, where x, y, z \in \mathbb{N}.

<em>Is there a number that falls between these?</em>

\frac{7}{24} is a rational number between \frac{1}{3} and \frac{1}{4}.

Step-by-step explanation:

<em>Why might he think that and what would you tell him?</em>

He thought perhaps that numbers were formed by rational numbers of the form \frac{1}{x}, where x\in \mathbb{N}. I would tell him that there are rational numbers \frac{y}{z}, such that \frac{1}{x}\le \frac{y}{z} \le \frac{1}{x+1}, where x, y, z \in \mathbb{N}.

<em>Is there a number that falls between these?</em>

Indeed, the average number of \frac{1}{3} and \frac{1}{4}, for instance. That is:

\frac{y}{z} = \frac{\frac{1}{3}+\frac{1}{4}  }{2}

\frac{y}{z} = \frac{\frac{7}{12} }{2}

\frac{y}{z} = \frac{7}{24}

\frac{7}{24} is a rational number between \frac{1}{3} and \frac{1}{4}.

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Answer: 44

Step-by-step explanation:

we will find RN and NQ, then add together to give us RQ.

To find RN;

RP= 17 PN = 15 and RN =?

using pythagoras theorem,

adj^2 = hyp^2 - opp^2

RN^2 = RP^2 - PN^2

?^2 = 17^2 - 15^2

?^2 = 17^2 - 15^2

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?^2 = 64

? = √64

? = 8

RN=8

To find NQ,

PN = 15 PQ=39 and NQ=?

using pythagoras theorem

NQ^2 = PQ^2 - PN^2

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?^2 = 1521 - 225

?^2 = 1296

? = √1296

? = 36

NQ= 36

RQ = RN + NQ

RQ= 8 + 36

RQ=44

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