SOLUTION: suppose y varies directly with x and inversely with the square of z ,and x=48 when y=8 and z=3 find x when y=12 and z=2 please help me

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Question 1059370: suppose y varies directly with x and inversely with the square of z ,and x=48 when y=8 and z=3 find x when y=12 and z=2 please help me
Answer by MathTherapy(10552) About Me  (Show Source):
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suppose y varies directly with x and inversely with the square of z ,and x=48 when y=8 and z=3 find x when y=12 and z=2 please help me 
Based on what's given, we get: y+=+kx%2Fz%5E2, with k being the CONSTANT of PROPORTIONALITY

8+=+k%2848%29%2F3%5E2 ------ Substituting 48 for x, 8 for y, and 3 for z

8+=+48k%2F9

8+=+16k%2F3

16k = 24 ------ Cross-multiplying

matrix%281%2C3%2C+k+=+24%2F16%2C+or%2C+1.5%29



y+=+kx%2Fz%5E2

12+=+%281.5%29%28x%29%2F2%5E2 ------ Substituting 12 for y, matrix%281%2C3%2C+1.5%2C+for%2C+k%29, and 2 for z

1.5x+=+12%282%5E2%29 ------ Cross-multiplying

highlight_green%28matrix%281%2C5%2C+x%2C+%22=%22%2C+12%284%29%2F1.5%2C+or%2C+32%29%29