If y varies directly s the square root of (x + 1) and y = 6 when x = 3, find x when y = 9
Answer Details
We are given that y varies directly with the square root of (x+1), which can be written as y=k√(x+1), where k is the constant of variation. To find k, we use the given values of x and y:
y=k√(x+1)
6=k√(3+1)
6=k√4
6=2k
k=3
So the equation for y in terms of x is y=3√(x+1). To find x when y=9, we substitute these values into the equation and solve for x:
9=3√(x+1)
3=√(x+1)
9=x+1
x=8
Therefore, x = 8 when y = 9.