Inverse Variation flashcard

Front

What is inverse variation?

Back

Inverse variation is a relationship between two variables where an increase in one variable results in a decrease in the other, and vice versa. It can be expressed mathematically as y = k/x, where k is a constant.

Front

If y varies inversely with x, what is the equation that represents this relationship?

Back

The equation representing inverse variation is y = k/x, where k is the constant of variation.

Front

In the context of inverse variation, what does the constant of variation (k) represent?

Back

The constant of variation (k) represents the product of the two variables in an inverse relationship. It remains constant for all pairs of values.

Front

How do you determine the constant of variation from given values of x and y?

Back

To find the constant of variation (k), multiply the values of x and y together: k = x * y.

Front

Given y = 6/x, what is the value of y when x = 2?

Back

When x = 2, y = 6/2 = 3.

Front

If 8 workers can complete a task in 6 hours, how long will it take for 12 workers to complete the same task?

Back

It will take 4 hours for 12 workers to complete the task.

Front

What is the relationship between pressure and volume in an inverse variation scenario?

Back

In an inverse variation scenario, as the volume of a gas increases, the pressure decreases, and vice versa, following the equation P * V = k.

Front

If the pressure of a gas is 4 atm when the volume is 2 L, what will be the pressure when the volume is 8 L?

Back

The pressure will be 1 atm when the volume is 8 L.

Front

Given the data points (5, 10), (10, 5), (15, 3.33), do they represent an inverse variation relationship?

Back

Yes, these data points represent an inverse variation relationship with a constant of variation k = 50.

Front

Identify the inverse variation equation from the following: y = 2x, y = 5x^2, y = x/6, y = 4/x.

Back

The inverse variation equation is y = 4/x.