A Quantity \[$ P \$\] Varies Jointly With \[$ R \$\] And \[$ S \$\]. Which Expression Represents The Constant Of Variation, \[$ K \$\]?A. \[$\frac{r S}{p}\$\] B. \[$p + R + S\$\] C. \[$prs\$\]
Introduction
In mathematics, joint variation is a concept where a quantity varies in proportion to two or more other quantities. This means that if one or more of the quantities change, the varying quantity will also change in a predictable way. In this article, we will explore the concept of joint variation and how it can be represented mathematically.
What is Joint Variation?
Joint variation is a type of variation where a quantity, denoted as { p $}$, varies in proportion to two or more other quantities, denoted as { r $}$ and { s $}$. This can be represented mathematically as:
{ p = krs $}$
where { k $}$ is the constant of variation.
Understanding the Constant of Variation
The constant of variation, denoted as { k $}$, is a mathematical constant that represents the ratio of the varying quantity to the product of the other quantities. In other words, it is a measure of how much the varying quantity changes in response to changes in the other quantities.
Representing the Constant of Variation
To represent the constant of variation, we need to isolate { k $}$ in the equation. We can do this by dividing both sides of the equation by { rs $}$:
{ \frac{p}{rs} = k $}$
This equation shows that the constant of variation, { k $}$, is equal to the ratio of the varying quantity, { p $}$, to the product of the other quantities, { rs $}$.
Solving for the Constant of Variation
Now that we have isolated { k $}$, we can solve for it by multiplying both sides of the equation by { rs $}$:
{ p = krs $}$
{ k = \frac{p}{rs} $}$
This equation shows that the constant of variation, { k $}$, is equal to the ratio of the varying quantity, { p $}$, to the product of the other quantities, { rs $}$.
Conclusion
In conclusion, the constant of variation, { k $}$, is a mathematical constant that represents the ratio of the varying quantity to the product of the other quantities. It can be represented mathematically as { k = \frac{p}{rs} $}$. This equation shows that the constant of variation is equal to the ratio of the varying quantity to the product of the other quantities.
Answer
Based on the equation { p = krs $}$, we can see that the constant of variation, { k $}$, is represented by the expression { \frac{p}{rs} $}$.
Final Answer
The final answer is: A. {\frac{r s}{p}$}$
A quantity { p $}$ varies jointly with { r $}$ and { s $}$. Which expression represents the constant of variation, { k $}$? A. {\frac{r s}{p}$}$ B. {p + r + s$}$ C. {prs$}$
Q: What is joint variation?
A: Joint variation is a concept in mathematics where a quantity varies in proportion to two or more other quantities. This means that if one or more of the quantities change, the varying quantity will also change in a predictable way.
Q: How is joint variation represented mathematically?
A: Joint variation can be represented mathematically as:
{ p = krs $}$
where { p $}$ is the varying quantity, { r $}$ and { s $}$ are the other quantities, and { k $}$ is the constant of variation.
Q: What is the constant of variation?
A: The constant of variation, denoted as { k $}$, is a mathematical constant that represents the ratio of the varying quantity to the product of the other quantities.
Q: How is the constant of variation represented mathematically?
A: The constant of variation can be represented mathematically as:
{ k = \frac{p}{rs} $}$
Q: Which expression represents the constant of variation, { k $}$?
A: The correct expression is:
{ \frac{p}{rs} $}$
This is because the constant of variation is equal to the ratio of the varying quantity to the product of the other quantities.
Q: What is the difference between the correct and incorrect expressions?
A: The correct expression, { \frac{p}{rs} $}$, represents the ratio of the varying quantity to the product of the other quantities. The incorrect expressions, { p + r + s $}$ and { prs $}$, do not represent the constant of variation.
Q: Why is it important to understand joint variation and the constant of variation?
A: Understanding joint variation and the constant of variation is important because it allows us to model and analyze real-world phenomena that involve multiple variables. It is a fundamental concept in mathematics and has many practical applications in fields such as physics, engineering, and economics.
Q: Can you provide an example of joint variation in real-world applications?
A: Yes, joint variation is used in many real-world applications, such as:
- Modeling the relationship between the distance traveled by a car and the time taken to travel that distance, assuming a constant speed.
- Analyzing the relationship between the cost of a product and the quantity produced, assuming a constant price.
- Modeling the relationship between the temperature of a substance and the amount of heat energy transferred to it, assuming a constant specific heat capacity.
These are just a few examples of how joint variation is used in real-world applications.
Conclusion
In conclusion, joint variation is a fundamental concept in mathematics that involves a quantity varying in proportion to two or more other quantities. The constant of variation is a mathematical constant that represents the ratio of the varying quantity to the product of the other quantities. Understanding joint variation and the constant of variation is important for modeling and analyzing real-world phenomena that involve multiple variables.