Exponential Problem: Finding Exponents in a Tricky Equation

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Homework Help Overview

The problem involves determining the values of exponents in the equation A=BnCm, where the dimensions of A, B, and C are provided. The dimensions are expressed in terms of length (L) and time (T), and the task is to find the exponents n and m based on these dimensional relationships.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to set up the dimensional equation but expresses uncertainty about the next steps. Some participants question the setup of the equation and suggest that the dimensions of B should be considered in the exponentiation. Others discuss the implications of not having direct answers in a test scenario and the need for additional information to solve for n and m.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the problem. There is a mix of attempts to substitute values and concerns about the adequacy of the provided information. Some guidance has been offered regarding the setup of the equation, but no consensus has been reached on how to proceed without additional data.

Contextual Notes

Participants note the potential lack of information typically provided in homework or test settings, which may affect the ability to solve for the exponents n and m. There is also a mention of the need for either a known value or a ratio between n and m to facilitate the solution.

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Can anyone help me with this problem?

Homework Statement


Supposed A=BnCm, where A has dimensions LT, B has dimensions L2T-1, and C has dimensions LT2. Then the exponents n and m have the values:

a. 2/3; 1/3
b. 2; 3
c. 4/5; 3/5
d. 1/5; 3/5


Homework Equations


N/A


The Attempt at a Solution


Tried to set up the equation as below:
since:
A=BnCm
so,
LT= L2T-1*LT2
I don't know what to do next?
 
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You didn't set your equation up correctly. If B has dimensions L2T-1, then Bm has dimension (L2T-1)m.
 
Oh, I found the answer! It's (d). I just have to try to substitute each choice into the equation to find the right answer. ^^Thanks a lot.
 
Last edited:
But what if this were a problem on a test, and you weren't give the answer? Your technique wouldn't help you any. Cristo has given you a good start.
 
hihihi. Yes, he you're right! However, I thought, if they don't give us the answer,they will at least give us the value of either n or m, or the ratio b/t these two variables in order to solve the equation. Thanks for your comment, Mark. You have a nice day!
 
The question is do you know how, by following cristo's comment, to find m and n even if you aren't given possible answers?
 
Thank you all!
 
Do you understand that I asked a question?


You have not yet answered my question.
 

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