Question

Functions Acellus Suppose that y varies directly with and y = 10 when x = 8. What is when y = 30?

x = [?]

Answer 1

To find the value of x in a direct variation when y = 30, given y is 10 when x = 8, we calculate the constant of variation and then use it to determine the new x value, resulting in x being 24.

Step-by-step explanation:

The question asks about direct variation, which in mathematics, is a relationship where one variable is a constant multiple of another. Given that y varies directly with x and that y = 10 when x = 8, we can establish a proportionality constant k such that y = kx. To find the value of x when y = 30, we first find the constant of variation using the provided values, then apply it to find the new x value.

Steps to find x when y = 30:

1. Find the constant of variation k
2. Apply k to determine x when y = 30

Let's start:

1. Since y = 10 when x = 8, the constant k = y/x = 10/8 = 1.25.
2. Now, we use the equation with the known constant of variation to find the unknown value of x when y = 30: y = kx becomes 30 = 1.25x.
3. Finally, solve for x, which gives x = 30 / 1.25 = 24.

Therefore, when y = 30, the value of x is 24.