X=6y
sum of their reciprocals
(1/x)+(1/y)=7
x=6y
1/6y+1/y=7
1/6y+6/6y=7
7/6y=7
times both sides by 6y
7=42y
divide both sides by 42
1/6=y
x=6y
x=6(1/6)
x=6/6
x=1
the numbers are 1 and 1/6
You can find counterexamples to disprove this claim. We have positive integers that are perfect square numbers; when we take the square root of those numbers, we get an integer.
For example, the square root of 1 is 1, which is an integer. So if y = 1, then the denominator becomes an integer and thus we get a quotient of two integers (since x is also defined to be an integer), the definition of a rational number.
Example: x = 2, y = 1 ends up with 
which is rational. This goes against the claim that 
is always irrational for positive integers x and y.
Any integer y that is a perfect square will work to disprove this claim, e.g. y = 1, y = 4, y= 9, y = 16. So it is not always irrational.
Answer:
The check digit is 7.
Step-by-step explanation:
Check digit can be calculated by the following way:
- Add all the digits except the check digit that is the last digit on the right side.
Total = 0 + 2 + 4 + 6 + 7 + 9 + 3 + 6 + 1 + 6 + 3
Total = 47
- Add the digits at odd starting from left, double this amount and finally add it with the total from step 1.
= 0 + 4 + 7 + 3 + 1 + 3
Sum = 18
Doubling the sum = 36
Adding it with the total from step 1, we get
Total = 36 + 47
Total = 83
- Subtract the last digit of the total from step 2 with 10, and this will be check digit.
Check Digit = 10 - 3
Check Digit = 7
The length is 14
Just count the spaces in between to get the result of 14
This becomes...........
[(y+7)/7y] x [(14y-5)/(3y^2+21y)]= [(y+7)/7y] x [(14y-5)/3y(y+7)]= [1/7y] x [(14y-5)/3y]= [(14y-5)/21y]
