If Y varies directly as the square of X, it means that the relationship between Y and X can be expressed as Y = kX^2, where k is the constant of variation.
To find the value of k, we can use the given information that Y = 18 when X = 12. Plugging these values into the equation, we get:
18 = k(12)^2
18 = k(144)
k = 18/144
k = 1/8
Now that we have the value of k, we can find Y when X = 13 by substituting it into the equation:
Y = (1/8)(13)^2
Y = (1/8)(169)
Y = 169/8
Y = 21.125
Therefore, when X = 13, Y is approximately equal to 21.125.
Answers & Comments
Answer:
If Y varies directly as the square of X, it means that the relationship between Y and X can be expressed as Y = kX^2, where k is the constant of variation.
To find the value of k, we can use the given information that Y = 18 when X = 12. Plugging these values into the equation, we get:
18 = k(12)^2
18 = k(144)
k = 18/144
k = 1/8
Now that we have the value of k, we can find Y when X = 13 by substituting it into the equation:
Y = (1/8)(13)^2
Y = (1/8)(169)
Y = 169/8
Y = 21.125
Therefore, when X = 13, Y is approximately equal to 21.125.