Can Someone Explain Proportional Reasoning to Me?

  • Thread starter crownedhues
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In summary, the conversation discusses the attempt to find the correlation between two solutions, using example values and equations. The suggestion is made to simplify the process and find a mathematical relationship between the values by replacing one variable and comparing the results. The advice is given to not overthink the problem.
  • #1
crownedhues
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Homework Statement
The question is asking what would happen to T if I double L. The answer has to be in words (i.e: “T is cut in half”)
Relevant Equations
T = 2𝝅√L/g
I already tried plugging in values I saw from example problems and tried to find the correlation between the two solutions I would get, but thus far haven’t been able to find any. Maybe I’m overcomplicating this or looking at this the wrong way?
 
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  • #2
If L=1, what is √L ?
 
  • #3
Replace L with 2L and compare the result to your original equation. Then find a way to express the mathematical relationship between those values in words.

Don’t overthink it.
 
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  • #4
berkeman said:
If L=1, what is √L ?
it should still be 1
 
  • #5
Oh sorry, I apologize. It's been a long day. Let me rephrase...

If L=2, what is √L ?

And the suggestion by @Emmo Amaranth is equivalent to my corrected question, BTW. :smile:
 
  • #6
berkeman said:
Oh sorry, I apologize. It's been a long day. Let me rephrase...

If L=2, what is √L ?

And the suggestion by @Emmo Amaranth is equivalent to my corrected question, BTW. :smile:
no worries, that’s understandable! i think i’m catching your drift. thank you for your quick response and your help :smile:
 
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  • #7
Emmo Amaranth said:
Replace L with 2L and compare the result to your original equation. Then find a way to express the mathematical relationship between those values in words.

Don’t overthink it.
thank you!
 
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  • #8
You're quite welcome! Glad to help.
 
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1. What is proportional reasoning?

Proportional reasoning is the process of comparing and analyzing quantities in relation to each other. It involves understanding how changes in one quantity affect another quantity, and vice versa.

2. Why is proportional reasoning important?

Proportional reasoning is important because it allows us to make predictions, solve problems, and make decisions based on relationships between quantities. It is also a fundamental concept in many fields of science and mathematics.

3. How is proportional reasoning used in real life?

Proportional reasoning is used in many aspects of daily life, such as calculating taxes, budgeting money, and determining the best deals when shopping. It is also used in fields such as engineering, finance, and statistics.

4. What are some strategies for improving proportional reasoning skills?

Some strategies for improving proportional reasoning skills include practicing with real-life scenarios, breaking down problems into smaller parts, and using visual aids such as graphs or diagrams. It is also helpful to understand the concept of proportionality and the relationship between ratios and proportions.

5. Are there any common misconceptions about proportional reasoning?

One common misconception about proportional reasoning is that it only involves multiplication and division. In reality, it also involves understanding ratios, fractions, and percentages. Another misconception is that proportional relationships always have a constant rate of change, when in fact they can have varying rates of change.

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