Does Doubling y in an Inverse Proportion Problem Halve the Constant?

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In summary, the inverse proportion problem is a mathematical concept where two variables have a relationship in which one variable increases while the other decreases. This can be solved using the formula y = k/x, where k is a constant. Examples of real-life inverse proportion problems include speed and time, and the number of workers and time to complete a task. The main difference between direct and inverse proportion is the relationship between the variables. Inverse proportion is useful in scientific research to model and understand relationships between variables, such as volume and pressure in chemistry, and the number of predators and prey in biology.
  • #1
e44-72
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Hello

if y [itex]\propto[/itex] 1/x
would 2y [itex]\propto[/itex] 1/0.5x
or 2y [itex]\propto[/itex] 1/2x

thank you for any replies
 
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  • #2
e44-72 said:
Hello

if y [itex]\propto[/itex] 1/x
would 2y [itex]\propto[/itex] 1/0.5x
or 2y [itex]\propto[/itex] 1/2x

thank you for any replies

if y [itex]\propto[/itex] 1/x then
y [itex]\propto[/itex] 2y [itex]\propto[/itex] 1/0.5x [itex]\propto[/itex] 1/x [itex]\propto[/itex] 1/2x
 
  • #3
y ∝ 1/x means y = k/x for some constant k. For your question, it means simply change the constant.
 

Related to Does Doubling y in an Inverse Proportion Problem Halve the Constant?

What is the inverse proportion problem?

The inverse proportion problem is a mathematical concept that involves two variables that are related in such a way that when one variable increases, the other variable decreases, and vice versa.

How do you solve an inverse proportion problem?

To solve an inverse proportion problem, you can use the formula y = k/x, where y and x are the two variables and k is a constant. You can find the value of the constant by plugging in the given values for y and x and solving for k. Then, you can use this value of k to find the missing variable in the problem.

What are some real-life examples of inverse proportion problems?

Some real-life examples of inverse proportion problems include the relationship between speed and time, where the faster you travel, the less time it takes to reach a destination, and the relationship between the number of workers and the time it takes to complete a task, where the more workers there are, the less time it takes to complete the task.

What is the difference between direct and inverse proportion?

The main difference between direct and inverse proportion is the relationship between the two variables. In direct proportion, both variables increase or decrease at the same rate, while in inverse proportion, one variable increases as the other decreases, and vice versa.

How can inverse proportion be useful in scientific research?

Inverse proportion can be used in scientific research to model and understand relationships between variables. For example, in chemistry, the inverse proportion between volume and pressure can help predict the behavior of gases. In biology, the inverse proportion between the number of predators and prey can help understand population dynamics.

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