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

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    0
    2021-09-10T08:57:52+00:00

    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  

    0
    2021-09-10T08:58:12+00:00

    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)}

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