Express the statement as a formula that involves the variables w, z, u and a constant of proportionality k, and then determine the value of k from the condition : w varies directly as z and inversely as the square root of u, if z = 3 and u = 4, then w = 18
w=kz/sqrtU
k=w*sqrt(U)/z= 18*2/3=12? check that.
To express the statement as a formula, we use the concept of direct and inverse variation.
According to the condition, w varies directly as z and inversely as the square root of u. This means that if z increases, w will also increase, and if u decreases, w will increase. Mathematically, we can express this as:
w = k * (z / √u)
Here, k is the constant of proportionality that we need to determine.
Now, we can substitute the given values of z = 3 and u = 4 into the formula to solve for k:
18 = k * (3 / √4)
To simplify further:
18 = k * (3 / 2)
Now, we can solve for k by isolating it:
k = 18 * (2 / 3)
k = 36 / 3
k = 12
Therefore, the value of the constant of proportionality, k, is 12.