Solution of equation 3x-5y= 4 4x+3y=15
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Question:
Abel planned for a garden to be 42 m long but found that it needs to be 24 m long to fit in his backyard. He found the change of scale below.
Which is Abel’s error?
Abel should have written the ratio as
Abel should have written the ratio as
Abel should have divided both numbers by 6.
Abel should have divided both numbers by 4.
Answer:
Abel should have divided both numbers by 6.
Step-by-step explanation:
Given
Measured Length of backyard = 42m
Actual Length of backyard = 24m
Measured Ratio:
Required
Error in calculation of measured ratio
From Abel's calculation:
It can be observed that He divided both numbers by 7
Though 42/7 = 6 but that's not so for 24/7
24/7≠4;
Instead 24/7 = 3.43 (Approximated)
To get the actual ration, he has to divide both numbers by the highest common factor
The common factors of 42 and 24 include 2,3,6 of which the highest is 6
Hence; HCF of 42 and 24 = 6
So, we can conclude that the error in his calculation is having not dividing both numbers by 6
Fermat's little theorem states that
≡a mod p
If we divide both sides by a, then
≡1 mod p
=>
≡1 mod 17
≡1 mod 17
Rewrite
mod 17 as
mod 17
and apply Fermat's little theorem
mod 17
=>
mod 17
So we conclude that
≡1 mod 17
If we divide both sides by a, then
=>
Rewrite
and apply Fermat's little theorem
=>
So we conclude that