ANSWER
[tex] \\ \\ [/tex]
If p varies directly as A and p= 2 when A= 40. Find p when A= 100.
[tex] \\ \sf{p = kA} \\ \\ [/tex]
Evaluate the values
[tex] \\ 2 = k(40) \\ \\ [/tex]
Divide 40 to both sides
[tex] \\ \frac{2}{40} = \frac{k(40)}{40} \\ \\ [/tex]
Cancel both 40 from the right side
[tex] \\ \frac{2}{40} = \frac{k( \cancel{40})}{ \cancel{40}} \\ \\ [/tex]
Simplify
[tex] \\ k = \frac{1}{20} \\ \\ [/tex]
Finding the value of p. Use the constant of variation from the first problem.
[tex] \\ \texttt{p = kA} \\ \\ [/tex]
Evaluate values
[tex] \\ p = ( \frac{1}{20} )(100) \\ \\ [/tex]
Multiply
[tex] \\ \large\boxed{ \green{ \sf{p = 5}}} \\ \\ \\ [/tex]
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