ANSWER
[tex] \\ [/tex]
If v varies directly as o and inversely as the square of p. If v=20 when o=10 and p=4, Find v when o =15 and p=4.
[tex] \\ v = \frac{ko}{ {p}^{2} } \\ \\ [/tex]
Evaluate the values
[tex] \\ 20 = \frac{k(10)}{ {4}^{2} } \\ \\ [/tex]
Square 4
[tex] \\ 20 = \frac{k(10)}{16} \\ \\ [/tex]
Multiply 16 to both sides
[tex] \\ (16)(20) = \frac{k(10)}{16} (16) \\ \\ [/tex]
Cancel both 16 from the right side
[tex] \\ (16)(20) = \frac{k(10)}{ \cancel{16}} ( \cancel{16}) \\ \\ [/tex]
[tex] \\ 320 = k(10) \\ \\ [/tex]
Divide 10 to both sides
[tex] \\ \frac{320}{10} = \frac{k(10)}{10} \\ \\ [/tex]
Cancel both 10 to the right side
[tex] \\ \frac{320}{10} = \frac{k( \cancel{1 0})}{ \cancel{10}} \\ \\ [/tex]
Divide
[tex] \\ \boxed{k = 32} \\ \\ [/tex]
Finding the value of v when o =15 and p=4. Use the k value of the first problem.
[tex] \\ v = \frac{ko}{ {p}^{2} } \\ \\ [/tex]
Evaluate values
[tex] \\ v = \frac{(32)(15)}{ {4}^{2} } \\ \\ [/tex]
Square 4
[tex] \\ v = \frac{(32)(15)}{16} \\ \\ [/tex]
Multiply 32 to 15
[tex] \\ v = \frac{480}{16} \\ \\ [/tex]
Divide
[tex] \\ \huge \green{ \boxed{ \bold{v = 30}}} \\ \\ \\ [/tex]
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