Question

Three quantities x,y and z are connected so that x varies directly as z and inversely as the square root of y.If x=6 when z=12 and y=25,find the expression for x in terms of y and z

Answer 1

Answer:

the expression is x= 2.5 * z/√y  

Step-by-step explanation:

since x is proportional to z and since x varies inversely as the square root of y

x= a * z/√y  

then

a = x*√y /z

replacing values

a = x*√y /z = 6*√25 /12 = 30/12 = 10/4=2.5

therefore

x= 2.5 * z/√y  

Answer 2

Answer:

The expression for x in terms of y and z is x = $\frac{2.5z}{sqrt(y)}$ or x = $\frac{5z}{2sqrt(y)}$

Step-by-step explanation:

The relationship between x, y and z can be expressed as;

x α $\frac{z}{sqrt(y)}$

x = C × $\frac{z}{sqrt(y)}$, where C is a constant of proportionality

Now, given the values of x, y and z, we can have that;

6 = C × $\frac{12}{sqrt(25)}$

6 = C × $\frac{12}{5}$

C = 6 × $\frac{5}{12}$ = 2.5 or $\frac{5}{2}$

Putting the value of C in the equation, we have;

x = $\frac{2.5z}{sqrt(y)}$ or $\frac{5z}{2sqrt(y)}$