If y varies inversely as the cube of x and directly as the square of z and y = -6 when x=3 and z =9, how do you find y when x =6 and z= -4?

frobirrimupyx

frobirrimupyx

Answered question

2022-09-02

If y varies inversely as the cube of x and directly as the square of z and y = -6 when x=3 and z =9, how do you find y when x =6 and z= -4?

Answer & Explanation

Waylon Jenkins

Waylon Jenkins

Beginner2022-09-03Added 17 answers

If y varies inversely as the cube of x and directly as the square of z
then we can write:
y x 3 z 2 = c for some constant c
If ( x , y , z ) = ( 3 , - 6 , 9 ) is a solution for this equation, then
( - 6 ) 3 3 9 2 = c
= 162 81 = c
c = 2
When ( x , z ) = ( 6 , - 4 )
y x 3 z 2 = 2
becomes
y 216 16 = 2
y = 16 2 216
y = 4 27

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