solve for y?
z=0.3(y-6)^2
please can you explain your working,
Many thanks,
Wendy.
I'm sorry. Really don't understand this. Where did the 10/3 come from in the first step?
To solve for y in the equation z = 0.3(y-6)^2, we can use the following steps:
1. Divide both sides of the equation by 0.3 to isolate the expression (y-6)^2:
z/0.3 = (y-6)^2
2. Take the square root of both sides to remove the exponent of 2:
√(z/0.3) = √(y-6)^2
3. Simplify the right side of the equation by taking the square root of both the base and the exponent:
√(z/0.3) = |y-6|
4. Now we have two cases to consider:
Case 1: y-6 is positive
In this case, |y-6| = y-6, so the equation becomes:
√(z/0.3) = y-6
Add 6 to both sides of the equation to isolate y:
y = √(z/0.3) + 6
Case 2: y-6 is negative
In this case, |y-6| = -(y-6), so the equation becomes:
√(z/0.3) = -(y-6)
Multiply both sides of the equation by -1 to isolate y:
-√(z/0.3) = y-6
Add 6 to both sides of the equation to isolate y:
y = -√(z/0.3) + 6
Therefore, the solutions for y are:
y = √(z/0.3) + 6 or y = -√(z/0.3) + 6
(10/3)z = (y-6)^2
y = sqrt[(10/3)z] +6
= 1.826 sqrt z + 6