Final answer:
To find the new value of y in a direct variation where y=5 1/4 when x=14, first determine the constant of variation k, then use it to calculate y when x=44/3, resulting in y=11/2 or 5.5.
Step-by-step explanation:
The question involves direct variation, which in mathematics is a relationship between two variables wherein one is a constant multiple of the other. In your case, y varies directly with x, which means as x increases or decreases, y does so proportionally. The direct variation can be represented by the equation y = kx, where k is the constant of variation. First, we'll find k using the given values of y and x, and then we'll use this constant to calculate the new value of y when x is 44/3.
- Start with the direct variation equation: y = kx.
- Plug in the given values: 5 1/4 = k(14).
- Convert 5 1/4 to an improper fraction: 21/4 = k(14).
- Solve for k: k = (21/4) / 14 = 21/56 = 3/8.
- Now that we have k, we can find the new value of y using x = 44/3: y = (3/8)(44/3).
- Multiply and simplify: y = (3 × 44) / (8 × 3) = 44/8 = 11/2.
Therefore, the value of y when x equals 44/3 is 11/2 or 5.5.