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Two quantities x and y are said to be in _________ if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant.
- a)inverse proportion
- b)direct proportion
- c)mix proportion
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two quantities x and y are said to be in _________ if an increase in x...
The correct answer is option A, inverse proportion. Two quantities x and y are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant.
In inverse proportion, the ratio of the two quantities is always constant. If x and y are inversely proportional, then x/y is always equal to some constant value, k. In mathematical terms, this is represented as x*y = k.
For example, if x represents the distance between two points and y represents the time taken to travel between those two points, then x and y are inversely proportional. As the distance increases, the time taken to travel the distance increases, and vice-versa.
In contrast, two quantities are said to be in direct proportion if an increase in x causes a proportional increase in y and vice-versa.
Most Upvoted Answer
Two quantities x and y are said to be in _________ if an increase in x...
Inverse Proportion
Inverse proportion is a mathematical relationship between two variables, x and y, where an increase in one variable leads to a proportional decrease in the other variable (and vice versa). In this relationship, the product of their corresponding values remains constant.
Explanation:
When two quantities, x and y, are said to be in inverse proportion, it means that as one quantity increases, the other quantity decreases in such a way that their product remains constant. This can be expressed mathematically as:
x × y = k
where k is a constant.
Example:
Let's consider an example to understand inverse proportion better. Suppose we have a car traveling at a constant speed, and we want to determine the relationship between the time taken and the distance traveled.
In this case, time taken (x) and distance traveled (y) are inversely proportional because as the time taken to travel a certain distance increases, the speed of the car decreases, resulting in a proportional increase in the distance traveled.
Let's assume the car travels at a speed of 60 km/h. If the time taken to travel a distance of 120 km is 2 hours, we can set up the equation:
x × y = k
2 × 60 = k
k = 120
Now, if we want to find the time taken to travel a distance of 240 km, we can rearrange the equation:
x × y = k
x × 240 = 120
x = 120/240
x = 0.5 hours
Therefore, the time taken to travel a distance of 240 km is 0.5 hours.
Conclusion:
Inverse proportion is a mathematical relationship where an increase in one quantity causes a proportional decrease in the other quantity, and vice versa, such that the product of their corresponding values remains constant. It is important to understand this concept in order to solve problems involving inverse proportion in various fields such as physics, mathematics, and economics.
Inverse proportion is a mathematical relationship between two variables, x and y, where an increase in one variable leads to a proportional decrease in the other variable (and vice versa). In this relationship, the product of their corresponding values remains constant.
Explanation:
When two quantities, x and y, are said to be in inverse proportion, it means that as one quantity increases, the other quantity decreases in such a way that their product remains constant. This can be expressed mathematically as:
x × y = k
where k is a constant.
Example:
Let's consider an example to understand inverse proportion better. Suppose we have a car traveling at a constant speed, and we want to determine the relationship between the time taken and the distance traveled.
In this case, time taken (x) and distance traveled (y) are inversely proportional because as the time taken to travel a certain distance increases, the speed of the car decreases, resulting in a proportional increase in the distance traveled.
Let's assume the car travels at a speed of 60 km/h. If the time taken to travel a distance of 120 km is 2 hours, we can set up the equation:
x × y = k
2 × 60 = k
k = 120
Now, if we want to find the time taken to travel a distance of 240 km, we can rearrange the equation:
x × y = k
x × 240 = 120
x = 120/240
x = 0.5 hours
Therefore, the time taken to travel a distance of 240 km is 0.5 hours.
Conclusion:
Inverse proportion is a mathematical relationship where an increase in one quantity causes a proportional decrease in the other quantity, and vice versa, such that the product of their corresponding values remains constant. It is important to understand this concept in order to solve problems involving inverse proportion in various fields such as physics, mathematics, and economics.
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Two quantities x and y are said to be in _________ if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant.a)inverse proportionb)direct proportionc)mix proportiond)None of theseCorrect answer is option 'A'. Can you explain this answer?
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