Proportionality Question

Therefore, p is proportional to r^2.In summary, we can conclude that if P is proportional to q^2 and q is inversely proportional to r, then p is proportional to r^2. This is determined by the equations p = kq^2 and q = c/r, where k and c are proportional constants. Even if we assume k = c, p is still inversely proportional to r^2, with the constant of kc^2. Therefore, p is proportional to r^2.
  • #1
297
0

Homework Statement


If P is proportional to q^2
and q is inversely proportional to r

Show that p is proportional to r^2


Homework Equations


p = kq^2
q = c/r

where k and c are proportional constants


The Attempt at a Solution



I'd say this is impossible. This is all the information given to me. This was found in an exam paper.

But even if we assume

k = c

p is not proportional to r^2.

-.-

Any ideas?
 
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  • #2
You might have read the question wrong. If p ∝ q², and q ∝ 1/r, then p ∝ 1/r².
 
  • #3
p=kq^2
q=c/r
therefore
p=k(c/r)^2
or
p=(kc^2)/r^2

So p should be inversely proportional to r^2, with the constant of kc^2.
 

1. What is a proportionality question?

A proportionality question is a type of mathematical problem that involves determining the relationship between two quantities. This can be done by setting up a proportion, which is an equation that shows that two ratios are equal.

2. How do I solve a proportionality question?

To solve a proportionality question, you first need to set up a proportion by writing two equal ratios. Then, cross-multiply and solve for the unknown variable. Finally, check your answer by plugging it back into the original equation.

3. What are some real-life applications of proportionality questions?

Proportionality questions are used in a variety of real-life situations, such as calculating recipe ingredients, determining exchange rates for currency, and finding the optimal mix of ingredients in a product. They are also commonly used in science and engineering fields for calculations involving rates and proportions.

4. What are some common mistakes to avoid when solving a proportionality question?

One common mistake is forgetting to include units when setting up the ratios. It is important to have consistent units on both sides of the proportion. Another mistake is not simplifying the ratios before solving, which can lead to incorrect answers. It is also important to check your final answer by plugging it back into the original equation to ensure it is correct.

5. Can you solve a proportionality question without using cross-multiplication?

Yes, there are other methods for solving proportionality questions, such as using equivalent fractions or setting up a proportionality table. However, cross-multiplication is the most commonly used method and can be easily applied to any proportionality question.

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