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Two quantities x and y are said to be in ___________ if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.
- a)inverse proportion
- b)mix proportion
- c)direct proportion
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Two quantities x and y are said to be in ___________ if they increase ...
Correct answer is C because when two quantities increase or decrease in such a manner that the ratio remains same so it is direct proportion.
Here there are two quantities x and y which are decreasing or increasing in such a manner that there ratio is same.
Here there are two quantities x and y which are decreasing or increasing in such a manner that there ratio is same.
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Two quantities x and y are said to be in ___________ if they increase ...
Direct Proportion
Direct proportion is a relationship between two quantities in which they increase or decrease together in such a way that the ratio of their corresponding values remains constant. This means that if one quantity doubles, the other quantity also doubles. Similarly, if one quantity triples, the other quantity also triples. The constant ratio is also known as the constant of proportionality.
Example:
Let's say we have a car that travels at a constant speed. The distance traveled and the time taken are two quantities that are directly proportional. If the car travels at a speed of 60 km/h, it will cover a distance of 120 km in 2 hours. If the speed remains constant, the car will cover a distance of 180 km in 3 hours.
In this example, the ratio of distance to time remains constant at 60 km/h. As the time increases, the distance also increases proportionally.
Mathematical Representation:
In mathematical terms, if two quantities x and y are in direct proportion, we can represent it as:
x = ky
where k is the constant of proportionality. This equation states that as y increases, x also increases in proportion to y.
Graphical Representation:
When two quantities are in direct proportion, their graph is a straight line passing through the origin (0, 0) on a Cartesian plane. The slope of the line represents the constant of proportionality.
Conclusion:
In direct proportion, two quantities increase or decrease together in such a way that their ratio remains constant. This concept is widely used in various fields such as physics, economics, and everyday life. Understanding direct proportion helps in solving problems related to ratios, rates, and proportions.
Direct proportion is a relationship between two quantities in which they increase or decrease together in such a way that the ratio of their corresponding values remains constant. This means that if one quantity doubles, the other quantity also doubles. Similarly, if one quantity triples, the other quantity also triples. The constant ratio is also known as the constant of proportionality.
Example:
Let's say we have a car that travels at a constant speed. The distance traveled and the time taken are two quantities that are directly proportional. If the car travels at a speed of 60 km/h, it will cover a distance of 120 km in 2 hours. If the speed remains constant, the car will cover a distance of 180 km in 3 hours.
In this example, the ratio of distance to time remains constant at 60 km/h. As the time increases, the distance also increases proportionally.
Mathematical Representation:
In mathematical terms, if two quantities x and y are in direct proportion, we can represent it as:
x = ky
where k is the constant of proportionality. This equation states that as y increases, x also increases in proportion to y.
Graphical Representation:
When two quantities are in direct proportion, their graph is a straight line passing through the origin (0, 0) on a Cartesian plane. The slope of the line represents the constant of proportionality.
Conclusion:
In direct proportion, two quantities increase or decrease together in such a way that their ratio remains constant. This concept is widely used in various fields such as physics, economics, and everyday life. Understanding direct proportion helps in solving problems related to ratios, rates, and proportions.
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Two quantities x and y are said to be in ___________ if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.a)inverse proportionb)mix proportionc)direct proportiond)None of theseCorrect answer is option 'C'. Can you explain this answer?
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