ANSWER
[tex] \\ [/tex]
if g varies directly as h and inversely as i. If g=20 when h=25 and i=45, Find g when h =15 and l=23.
[tex] \\ \bold{g = \frac{kh}{ i} } \\ \\ [/tex]
Evaluate the values
[tex] \\ 20 = \frac{k(25)}{45} \\ \\ [/tex]
Multiply 45 to both sides
[tex] \\ (45)(20) = \frac{k(25)}{45} (45) \\ \\ [/tex]
Cancel both 45 from the right side
[tex] \\ (45)(20) = \frac{k(25)}{ \cancel{45}} ( \cancel{45}) \\ \\ [/tex]
Multiply 45 to 20
[tex] \\ 900 = k(25) \\ \\ [/tex]
Divide 25 to both sides
[tex] \\ \frac{900}{25} = \frac{k(25)}{25} \\ \\ [/tex]
Cancel both 25 from the right side
[tex] \\ \frac{900}{25} = \frac{k( \cancel{25})}{ \cancel{25}} \\ \\ [/tex]
Divide
[tex] \\ \large \boxed{k = 36} \\ \\ [/tex]
Find g when h =15 and i=23. Use the constant of variation of the first problem.
[tex] \\ \bold{g = \frac{kh}{ i} } \\ \\ [/tex]
Evaluate values
[tex] \\ g = \frac{(36)(15)}{23} \\ \\ [/tex]
Multiply 36 to 15
[tex] \\ \bold{ans.} \\ \longrightarrow \huge \green{ \boxed{ \bold{g = \frac{540}{23}}} }[/tex]
The answer couldn't be simplified.
[tex] \\ \\ \\ [/tex]
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