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Can I help with this problem. If z varies inversely as w^2 and z = 10 when w = 2. Find z when w = 6

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First, we need the find the value of the constant k:


z=(k)/(w^2)

Then, we use the given values to find k. Therefore:

z = 10 when w = 2


10=(k)/(2^2)

And solve for k:


\begin{gathered} 10=(k)/(4) \\ 10\cdot4=4\cdot(k)/(4) \\ k=40 \end{gathered}

Now, when w = 6, z will be:


z=(k)/(w^2)=(40)/(6^2)=(40)/(36)=(10)/(9)

Answer:


z=(10)/(9)

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