## 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

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

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2 weeks 2021-09-10T08:56:33+00:00 2 Answers 0

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

The expression for x in terms of y and z is x = or x =

Step-by-step explanation:

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

x α

x = C × , where C is a constant of proportionality

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

6 = C ×

6 = C ×

C = 6 × = 2.5 or

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

x = or