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DaniilM [7]
2 years ago
13

How, Let a = a rational number. Let b = an irrational number. Assume a + b = c and c is rational (attempting to disprove the con

jecture). a + b = c b = c - a Explain how Alfred's argument contradicts his initial assumption proving that the sum cannot be rational?
Mathematics
2 answers:
alisha [4.7K]2 years ago
7 0
If a and c are rational then a can be written as x/y and c  can be w/z  where w,x,y and z are integers

so as alfred said  if  b = c - a = x/y - w/z  =  (zx - wy) / yz  which is  rational.
So b cannot be irrational..
laiz [17]2 years ago
6 0
If 'a' is a rational number and c is rational, then 
a = p/q
c = r/s
where p,q,r,s are integers (q and s can't be zero)

Subtracting c-a gives
b = c-a
b = (p/q) - (r/s)
b = (ps/qs) - (qr/qs)
b = (ps - qr)/(qs)

The quantity pq - qr is an integer. The reason why is because ps and qr are both integers (multiplying any two integers leads to another integer). Subtracting any two integers results in another integer.

So we have (ps - qr)/(qs) in the form (integer)/(integer) = rational number

Therefore, b is a rational number, but this contradicts the given info that b is irrational. If b is irrational, then we CANNOT write it as a ratio of integers.

This contradiction proves the assumption "a+b = c and c is rational" is incorrect
The sum is irrational.

Therefore, if a+b = c, where 'a' is rational and b is irrational, then c is irrational.
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Mo had 14 tutoriang session. each session was 35 minutes long. How many minutes did Mo spend in the 14 session Combined?
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Uni made a model of a 1970 Ford Mustang using a scale of .5 inches = 9 in. If the actual car is 15 ft long, how long is the mode
kykrilka [37]

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The model car is 10 inches long

Step-by-step explanation:

To solve this question, we use conversion of units

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Each feet has 12 inches.

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Rule of three

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3 years ago
In 2001 the mint indoor pool vault record was 20 and 1/6 the women’s record for the indoor pool vault was 15 and 5/12 FT what is
blondinia [14]

Answer:

35 and 7/12 feet is the combined height of the two records.

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The combined height of the two records :

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35 and 7/12 feet is the combined height of the two records.

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