Podcast
Questions and Answers
In an inverse variation, if one variable increases, what happens to the other variable?
In an inverse variation, if one variable increases, what happens to the other variable?
- It increases proportionally.
- It stays constant.
- It increases exponentially.
- It decreases. (correct)
Which equation represents an inverse variation, where $x$ and $y$ are variables and $k$ is a non-zero constant?
Which equation represents an inverse variation, where $x$ and $y$ are variables and $k$ is a non-zero constant?
- $x - y = k$
- $x/y = k$
- $xy = k$ (correct)
- $x + y = k$
If the time it takes to travel a certain distance varies inversely with speed, what happens to the travel time if the speed is doubled?
If the time it takes to travel a certain distance varies inversely with speed, what happens to the travel time if the speed is doubled?
- It remains the same.
- It quadruples.
- It is halved. (correct)
- It doubles.
If $y$ varies inversely as $x$, and $y = 6$ when $x = 4$, find the value of $y$ when $x = 8$.
If $y$ varies inversely as $x$, and $y = 6$ when $x = 4$, find the value of $y$ when $x = 8$.
If the time it takes for a group to complete a task varies inversely with the number of people working on it, what does this imply?
If the time it takes for a group to complete a task varies inversely with the number of people working on it, what does this imply?
If $a$ varies inversely as $b^2$, and $a = 3$ when $b = 2$, find $a$ when $b = 4$.
If $a$ varies inversely as $b^2$, and $a = 3$ when $b = 2$, find $a$ when $b = 4$.
The electrical current in a circuit with constant voltage varies inversely with the resistance. If the current is 2 amps when the resistance is 10 ohms, what is the current when the resistance is 5 ohms?
The electrical current in a circuit with constant voltage varies inversely with the resistance. If the current is 2 amps when the resistance is 10 ohms, what is the current when the resistance is 5 ohms?
Assume the number of seats in a room stay constant. How does the space allotted to each seat change with the number of people sitting in the seats?
Assume the number of seats in a room stay constant. How does the space allotted to each seat change with the number of people sitting in the seats?
The volume of a gas at constant temperature varies inversely with the pressure exerted on it (Boyle's Law). If the volume of a gas is 10 liters at a pressure of 2 atmospheres, what is the volume when the pressure is increased to 5 atmospheres?
The volume of a gas at constant temperature varies inversely with the pressure exerted on it (Boyle's Law). If the volume of a gas is 10 liters at a pressure of 2 atmospheres, what is the volume when the pressure is increased to 5 atmospheres?
In an inverse variation relationship, which statement is always true about the variables $x$ and $y$?
In an inverse variation relationship, which statement is always true about the variables $x$ and $y$?
The per capita share of expenses varies inversely with the number of people sharing the expenses. If four people share expenses and each pays $50, how much will each person pay if ten people share the same expenses?
The per capita share of expenses varies inversely with the number of people sharing the expenses. If four people share expenses and each pays $50, how much will each person pay if ten people share the same expenses?
The number of teeth on two connected gears varies inversely with the number of revolutions per minute (RPM) they make. If a large gear has 60 teeth and makes 30 RPM, how many RPM will a smaller gear with 20 teeth make?
The number of teeth on two connected gears varies inversely with the number of revolutions per minute (RPM) they make. If a large gear has 60 teeth and makes 30 RPM, how many RPM will a smaller gear with 20 teeth make?
Flashcards
Inverse Variation
Inverse Variation
A relationship where the product of two variables is constant.
Constant of Variation (k)
Constant of Variation (k)
The constant value in an inverse variation equation.
Inverse Variation Equation
Inverse Variation Equation
Expressed as xy = k, where k is a non-zero constant.
Relationship in Inverse Variation
Relationship in Inverse Variation
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Bike Ride Example
Bike Ride Example
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Formula for biking
Formula for biking
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Cooling Water Example
Cooling Water Example
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Breaking a Board Example
Breaking a Board Example
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Stringed Instruments
Stringed Instruments
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Study Notes
- Inverse variation describes relationships where one quantity increases as the other decreases.
Real-Life Example: Biking Speed and Time
- The time it takes to cover a specific distance varies inversely with speed.
- The equation rate × time = distance (or time = distance / rate) represents this scenario.
- For a 20-mile bike ride, averaging 20 mph results in a 1-hour ride. Reduced speed to 10mph doubles the time to 2 hours.
Definition of Inverse Variation
- An inverse variation is a relationship where the product of two variables equals a constant.
- Mathematically expressed as xy = k, where k is a non-zero constant.
Equations, Tables, and Graphs
- The inverse variation equation can be rewritten as y = k/x.
- When x is large, y is small, and when x is small, y is large.
- Inverse variation graphs are curves, not straight lines as seen in linear relationships.
Tables Examples
- k=1
- x = 1/4, y = 4
- x = 1/2, y = 2
- x = 1, y = 1
- x = 2, y = 1/2
- x = 10, y = 1/10
- k=100
- x = 1, y = 100
- x = 2, y = 50
- x = 10, y = 10
- x = 50, y = 2
- x = 100, y = 1
Other Real-Life Examples
- How quickly a glass of cold water cools down on a warm day varies inversely with the temperature.
- The force required to break a board varies inversely with its length.
- String length and vibration frequency have an inverse variance.
Lesson Summary
- Inverse variation occurs when the product of two variables is constant (xy = k, where k ≠0).
- When one variable increases, the other decreases proportionally.
- Examples include stringed instruments, warming water, and bike rides.
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