Dimensions, Unit Operations Homework (True/False)

AI Thread Summary
X and Y are dimensionally different, leading to specific conclusions about various operations. The operations X/Y and X*Y are considered physically meaningful, while X+Y and X-Y are not, as they involve adding incompatible units. Exponential functions like e^(X/Y) and e^(X+Y) are also deemed physically meaningless due to the dimensional inconsistency. Squaring the quantities, such as X^2 and Y^2, is valid, as is taking the cube root of each, X^(1/3) and Y^(1/3). Overall, the discussion confirms the importance of dimensional analysis in determining the validity of mathematical operations involving different units.
FAJISTE
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Homework Statement



X and Y are dimensionally different. (They have different units.) Select ALL the physically meaningful operations. State which are true or false
1. X/Y or X*Y
2. X+Y or X-Y
3. e^(X/Y) or e^(X+Y)
4. X^2 +Y^2 or X^X + Y^Y
5. X^2 or Y^2
6. X^(1/3) or Y^(1/3)

Homework Equations





The Attempt at a Solution



I'm assuming

1. True because you could have like velocity/second, etc.
2. False, you can't add apples and oranges
3. False no idea though
4. False
5. True
6. True

An explanation along with the correct answers would be greatly appreciated.
 
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FAJISTE said:
1. True because you could have like velocity/second, etc.
2. False, you can't add apples and oranges
3. False no idea though
4. False
5. True
6. True

I believe you have all correct so far.

For 3, I don't think it is possible to raise a constant to the power of a quanity.
Else it'd be like saying 2^(4 kilograms) or e^(2 Newtons), it is physically meaningless.
 
thanks a lot, if I could just have a complete confirmation since I only have one last try to get it right in the computer
 
N/m i was right, thanks for the confirm tho
 
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