Answer:
To determine the percentage decrease in W when x is decreased by 9.75%, we need to first determine the relationship between w and x. Since w is proportional to the square root of x, we can write an equation to represent this relationship as follows:
w = k * √x
where k is the proportionality constant.
If the value of x is decreased by 9.75%, we can write the new value of x as follows:
x' = x * (1 - 0.0975) = x * 0.9025
Substituting this expression for x' into the equation above, we get:
w' = k * √(x * 0.9025)
To determine the percentage decrease in w, we can divide the new value of w by the original value of w and multiply by 100% to get the percentage change, or:
percentage decrease in w = (w' / w) * 100%
Substituting the expressions for w' and w into this equation, we get:
percentage decrease in w = [(k * √(x * 0.9025)) / (k * √x)] * 100%
Simplifying this expression, we get:
percentage decrease in w = (√(0.9025)) * 100%
Since the square root of 0.9025 is approximately 0.95, we can say that the percentage decrease in w is approximately 5%. This means that the value of w decreases by approximately 5% when the value of x decreases by 9.75%.