X is directly proportional to the square of Y,what is the percentage change in X if y increases by25%
x = ky^2
(1.25y)^2 - y^2 = .5625 y^2
.5625y^2/y^2 = .5625 = 56.25%
Pls i want a full explaination
Please I want a full explanation
To determine the percentage change in X when Y increases by 25%, we need to understand the concept of direct proportionality.
In a direct proportion, as one variable (Y in this case) increases or decreases, the other variable (X) also changes in the same direction. In this scenario, X is directly proportional to the square of Y. This means that when Y increases by a certain percentage, X will also increase by a certain percentage.
To calculate the percentage change in X, we need to know the specific numerical relationship between X and Y. Let's assume that X = kY^2, where k is a constant.
If Y increases by 25%, the new value of Y would be 1.25Y (Y + 25% of Y).
Now, let's calculate the percentage change in X:
Percentage change in X = ((New X - Original X) / Original X) * 100
To find the new X value, we substitute the new Y value into the equation:
New X = k(1.25Y)^2 = 1.5625kY^2
Substituting back into the percentage change formula:
Percentage change in X = ((1.5625kY^2 - kY^2) / kY^2) * 100
Simplifying:
Percentage change in X = (0.5625kY^2 / kY^2) * 100
The term kY^2 cancels out:
Percentage change in X = 0.5625 * 100
Therefore, the percentage change in X when Y increases by 25% is 56.25%.
Note: The specific value of k was not defined in the question, so we couldn't determine the absolute value of the change in X, but we were able to find the percentage change.