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w varies directly as the sqare of x and inversely as p and q. if w=12 when x=4,p=2 and q=20,find when w when x=3,p=8 and q=5

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Answer:

w varies directly as the square of x and inversely as p and q. If w=12 when x=4,p=2 and q=20, find when w when x=3,p=8 and q=5.

[tex]w = \frac{k {x}^{2} }{pq} \\ [/tex]

Evaluate the values

[tex]12 = \frac{k( {4}^{2} )}{(2)(20)} \\ [/tex]

square 4

[tex]12 = \frac{k(16)}{40} \\ [/tex]

Multiply 40 both sides

[tex](40)(12) = \frac{k(16)}{40} (40) \\ [/tex]

[tex]480= \frac{k(16)}{ \cancel{40}} ( \cancel{40}) \\ [/tex]

[tex]480= k(16) \\ [/tex]

Divide both sides by 16

[tex] \frac{480}{16} = \frac{k(16)}{16} \\ \frac{480}{16} = \frac{k( \cancel{16})}{ \cancel{16}} \\ [/tex]

[tex] \\ \boxed{k = 30} \\ \\ [/tex]

Find when w when x=3,p=8 and q=5. Use k=30

[tex]w = \frac{k {x}^{2} }{pq} \\ [/tex]

Evaluate the values

[tex]w = \frac{(30)( {3}^{2} )}{(8)(5)} \\ [/tex]

Square 3

[tex]w = \frac{(30)( 9 )}{(8)(5)} \\ [/tex]

Mutiply 8 by 5

[tex]w = \frac{(30)( 9 )}{(40)} \\ [/tex]

Mutiply 30 by 9

[tex]w = \frac{(270 )}{(40)} \\ [/tex]

Simplify

[tex] \\ \green{\boxed{ \boxed{ \bold{w = \frac{27}{4} }}}} \\ \\ [/tex]

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