Question

Y is inversely proportional to X^2. Given that Y = 2 when X = 3,

i) Express Y in terms of X
ii) Find the value of Y when X = 5.
a) i) Y = 18/X^2, ii) Y = 0.08
b) i) Y = 2X^2, ii) Y = 0.22
c) i) Y = 2/X^2, ii) Y = 0.08
d) i) Y = 18X^2, ii) Y = 0.22

Answer 1

Y is inversely proportional to X² is represented by the equation Y = k/X². For Y = 2 when X = 3, we find k = 18, so the equation is Y = 18/X². Then, the value of Y when X = 5 is calculated to be 0.72.

Step-by-step explanation:

If Y is inversely proportional to X², it means that whenever X increases, Y decreases, and vice versa. We use the relationship Y = k/xX², where k is the constant of proportionality. To express Y in terms of X, we need to find the value of k using the given values: Y = 2 when X = 3.

By substituting the given values into the equation, we get 2 = k/9. Solving for k, we find that k = 18. Hence, the equation that expresses Y in terms of X is Y = 18/X².

To find the value of Y when X = 5, we substitute X with 5 in the equation: Y = 18/25. After calculating, we get Y = 0.72. Therefore, the value of Y when X = 5 is 0.72.