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:
The expression for x in terms of y and z is x = [tex]\frac{2.5z}{sqrt(y)}[/tex] or x = [tex]\frac{5z}{2sqrt(y)}[/tex]
Step-by-step explanation:
The relationship between x, y and z can be expressed as;
x α [tex]\frac{z}{sqrt(y)}[/tex]
x = C × [tex]\frac{z}{sqrt(y)}[/tex], where C is a constant of proportionality
Now, given the values of x, y and z, we can have that;
6 = C × [tex]\frac{12}{sqrt(25)}[/tex]
6 = C × [tex]\frac{12}{5}[/tex]
C = 6 × [tex]\frac{5}{12}[/tex] = 2.5 or [tex]\frac{5}{2}[/tex]
Putting the value of C in the equation, we have;
x = [tex]\frac{2.5z}{sqrt(y)}[/tex] or [tex]\frac{5z}{2sqrt(y)}[/tex]
