r proptional to a^2/b
if b => 2b
then a^2 needs to become 2a^2
so the new 'a' we need, lets call it 'A', should equal SQRT(2)
if thats not obvious you can try equations:
a^2/b = A^2/(2b)
A^2 = 2a^2
A=SQRT(2)*a
sqrt2 = 1.41 => 40% increase
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AleksandrM
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AleksandrM
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jason,
When I cross-multiply I arrive at a^2 * 2b = A^2 * b
If you are dividing boths sides by b, you still end up with a b left over because you have a b on one side and 2b on the other.
When I cross-multiply I arrive at a^2 * 2b = A^2 * b
If you are dividing boths sides by b, you still end up with a b left over because you have a b on one side and 2b on the other.
Hi AleksandrM,
I think the following will remove your doubt:
R=k*A^2/B, where k=constant of proportionality.
Now when B is doubled, to keep the rate constant the numerator has to be multiplied with 2 which means an increase of A by sqrt2
Now, the increase in A=(1.4-1)=0.4*100=40%
I think the following will remove your doubt:
R=k*A^2/B, where k=constant of proportionality.
Now when B is doubled, to keep the rate constant the numerator has to be multiplied with 2 which means an increase of A by sqrt2
Now, the increase in A=(1.4-1)=0.4*100=40%
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llewellyn27
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Easy way to solve this problem is to plug in numbers
Assume
A = 10 and B = 5
A1 = ? and B1 = 10 (given a 100% increase)
The ratio stays the same. So,
A^2/ B = 100/5
A1^2 / B1 = A1^2/10
Solve for A1 which comes to 10* sqrt2
% Increase = (A1-A)/A * 100
= (sqrt2 -1) * 100
= 41% increase
Assume
A = 10 and B = 5
A1 = ? and B1 = 10 (given a 100% increase)
The ratio stays the same. So,
A^2/ B = 100/5
A1^2 / B1 = A1^2/10
Solve for A1 which comes to 10* sqrt2
% Increase = (A1-A)/A * 100
= (sqrt2 -1) * 100
= 41% increase
