Exploring Direct, Inverse, and Joint Variation

The video tutorial covers the calculation of materials needed for care packages, followed by an introduction to direct variation, including its definition and application in solving mathematical problems. It then explores inverse and joint variation, providing examples and equations for each type. The tutorial emphasizes understanding the constant of variation and how to apply it in different scenarios.

How many pens are needed to make one complete care package?

• 5 pens

• 12 pens

• 20 pens

• 30 pens

What is the constant of variation if the equation is y = kx and y = 8 when x = -4?

• -4

• 2

• 4

• -2

In the context of direct variation, what does the equation y = kx imply about the relationship between y and x?

• They are inversely proportional

• They are conditionally proportional

• They are directly proportional

• They are not related

If y = 5/3x, what is y when x = 12?

• 20

• 7.5

• 18

• 15

Which equation represents a direct variation?

• y = 5x/2

• y = x/3

• y = 7 - x

• y = k/x

What is the constant of variation for the equation y = 5x/2?

• 2/5

• 5

• 5/2

• 2

What does it mean if z varies jointly with x and y?

• z = k*x/y

• z = k*x*y

• z = k/(x*y)

• z = k/x*y

If z = 3xy and x = 4, y = 5, what is z?

• 15

• 60

• 45

• 20

If the intensity of sound varies inversely with the square of the distance, what is the intensity at 15 meters if it is 10 watts per square meter at 1 meter?

• 0.67 watts/m^2

• 10 watts/m^2

• 0.044 watts/m^2

• 1.5 watts/m^2

In a direct variation scenario, if k = 1/60 and d = 100, what is t?

• 0.6 minutes

• 100 minutes

• 60 minutes

• 1.67 minutes