Respuesta :
The proportionality shows the relation between two values. The value of the constant of variation is 5.
What is proportionality?
The proportionality shows the relation between two values.
As given in the question the quantity q varies inversely with the square of m and directly with the product of r and x. Therefore, the proportionality can be written as,
[tex]q \propto \dfrac{rx}{m^2}[/tex]
Now to remove the proportionality add a constant to the equation which is the constant of variation.
[tex]q =k\dfrac{rx}{m^2}[/tex]
When m is 4 and the product of r and x is 8 then the value of q is 2.5. Therefore, the value of k can be written as,
[tex]q =k\dfrac{rx}{m^2}\\\\2.5 = k\dfrac{8}{4^2}\\\\\dfrac{2.5 \times 16}{8}=k\\\\k=5[/tex]
Thus, the value of the constant of variation is 5.
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