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directly as Vi and inversely as y°. If: = 61 when = 36 and y = 9, find a if r = 64 and y = 6. (Round off your answer to the nearest hundredth.)

Directly As Vi And Inversely As Y If 61 When 36 And Y 9 Find A If R 64 And Y 6 Round Off Your Answer To The Nearest Hundredth class=

Sagot :

Given: z directly varies as √x and inversely varies as y³

when x = 36 and y = 9 then z = 61

To find:

when x = 64 and y = 6 then z = ?

explanation:

z ∝ √x / y³

z = k √x / y³

when x = 36 and y = 9 then z = 61

[tex]z=\text{ }\frac{k\text{ }\sqrt{x}}{y^3}[/tex][tex]\begin{gathered} 61=\frac{k\text{ * }\sqrt{36}}{9^3} \\ 61=\frac{k*6}{729} \\ k=\frac{61*729}{6}=\frac{61*243}{2}=\frac{14823}{2} \end{gathered}[/tex]

when x = 64 and y = 6

[tex]z=\text{ }\frac{14823}{2}*\frac{\sqrt{64}}{6^3}=\frac{14823*8}{2*216}=\frac{4941*4}{72}=\frac{4941}{18}=274.5[/tex]

the value of z = 274.5

final answer:

z = 274.5 ≈ 300 when rounded off to the nearest hundredth

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