x varies directly as the product of u and v and inversely as their sum.If x=3 when u=3 and v=1.
x = kuv/(u+v)
when you come up with a question, this should help answer it.
To understand how x varies with u and v, let's break down the information given:
1. x varies directly as the product of u and v: This means that x is directly proportional to the product of u and v. In other words, if we increase the value of u or v, x will increase proportionally.
2. x varies inversely as their sum: This means that x is inversely proportional to the sum of u and v. In other words, if we increase the value of u or v, x will decrease proportionally.
Now, let's use this information to find the value of x when u=3 and v=1.
Since x varies directly as the product of u and v and inversely as their sum, we can express this relationship mathematically as:
x = k * (u * v) / (u + v)
where k is a constant of proportionality.
Using the given values, we can substitute u=3 and v=1 into the equation:
3 = k * (3 * 1) / (3 + 1)
Simplifying the equation further, we get:
3 = k * 3 / 4
Now, we can solve for the constant k:
k = (3 * 4) / 3
k = 4
So, the constant of proportionality is 4.
Now, substituting this value of k back into the equation, we can find the value of x:
x = 4 * (3 * 1) / (3 + 1)
Simplifying the equation further, we get:
x = 4 * 3 / 4
x = 3
Therefore, when u=3 and v=1, the value of x is 3.