y varies directly with the square x. If y=8 when x=2, find y when x=3.
y = k x^2
8 = k *4
k = 2
y = 2 x^2
2*9 = 18
How do you get it.explain better
Geyyeyeueusj
To solve this problem, we need to use the direct variation equation, which states that when two quantities vary directly, their ratio remains constant. In this case, y varies directly with the square of x, so we can write the equation as:
y = kx^2
where k is the constant of variation.
To find the value of k, we can use the given information that when x = 2, y = 8:
8 = k(2)^2
8 = 4k
k = 2
Now that we know the value of k, we can substitute it back into the direct variation equation to find y when x = 3:
y = 2(3)^2
y = 2(9)
y = 18
Therefore, when x = 3, y = 18.