Question

Use the given type of variation and the values for the independent variable x and the dependent variable y to find the value of k, the constant of variation.

Direct: (3 rightarrow 90, 30)
Inverse: (3 rightarrow 90, ?)
Direct: (4 rightarrow 20, ?)
Inverse: (4 rightarrow 20, ?)
Direct: (5 rightarrow 50, ?)

a) 180
b) 60
c) 5
d) 10

Answer 1

In direct variation, the constant of variation can be found by substituting the given values into the equation. For each given direct variation, we can solve for the constant of variation, k.

Step-by-step explanation:

In direct variation, the equation is of the form y = kx, where k is the constant of variation. To find the value of k, we can use the given values for x and y. For the first direct variation, (3, 90), we can substitute these values into the equation and solve for k. So, 90 = 3k, which gives us k = 30.

Similarly, for the second direct variation, (4, 20), we substitute these values into the equation and solve for k. So, 20 = 4k, which gives us k = 5.

Lastly, for the third direct variation, (5, 50), we substitute these values into the equation and solve for k. So, 50 = 5k, which gives us k = 10.