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Suppose r varies directly with the square of m and inversely as s. If r= 12 when m = 6 and s=4, find r when m = 4 and s 10

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Sagot :

semsee45

Answer:

[tex]r=\frac{32}{15}[/tex]

Step-by-step explanation:

If r varies directly with the square of m and inversely as s,

then [tex]r=\frac{km^2}{s}[/tex] where k is some constant

Given r = 12 when m = 6 and s = 4:

       [tex]r=\frac{km^2}{s}[/tex]

⇒    [tex]12=\frac{k6^2}{4}[/tex]

⇒ [tex]\frac{12\times4}{6^2} =k[/tex]

⇒     k = [tex]\frac{4}{3}[/tex]

Therefore, substituting the found value of k into the original equation: [tex]r=\frac{4m^2}{3s}[/tex]

Find r when m = 4 and s = 10:

   [tex]r=\frac{4m^2}{3s}[/tex]

⇒ [tex]r=\frac{4\times4^2}{3\times10}[/tex]

⇒ [tex]r=\frac{32}{15}[/tex]

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