KiaunaF481016 KiaunaF481016
  • 03-11-2022
  • Mathematics
contestada

If pp is inversely proportional to the square of qq, and pp is 10 when qq is 10, determine pp when qq is equal to 5.

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NathaleeB334023 NathaleeB334023
  • 03-11-2022

Given that p is inversely proportional to the square of q, then these two variables are related by the next formula:

[tex]p=\frac{k}{q^2}[/tex]

where k is some constant.

Substituting with p = 10 and q = 10, and solving for k:

[tex]\begin{gathered} 10=\frac{k}{10^2} \\ 10=\frac{k}{100} \\ 10\cdot100=\frac{k}{100}\cdot100 \\ 1000=k \end{gathered}[/tex]

Substituting with q = 5 and k = 1000, we get:

[tex]\begin{gathered} p=\frac{1000}{5^2} \\ p=\frac{1000}{25} \\ p=40 \end{gathered}[/tex]

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