X varies directly as the product of u and v and inversely at their sum. If x=3 when v=3and u=1. What is the value of x if v=3 and u=3
We are given that X varies directly as the product of u and v and inversely as their sum. This can be written as:
X ∝ (u * v) / (u + v)
Or, in equation form:
X = k(u * v) / (u + v)
where k is the constant of variation.
We are also given that x = 3 when v = 3 and u = 1. Plugging these values into the equation, we can solve for k:
3 = k(1 * 3) / (1 + 3)
3 = 3k / 4
12 = 3k
k = 4
Now, we can use this value of k to find the value of x when v = 3 and u = 3:
X = 4(3 * 3) / (3 + 3)
X = 4(9) / 6
X = 36 / 6
X = 6
Therefore, the value of x when v = 3 and u = 3 is 6.