If y=-6.3 when x=2/3, how do you find y when x=8 given that y varies inversely as x?

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Answer 1 · 2017-06-06T12:45:35

#y=-21/40#

Given that #" "y=kxx1/x" "# where #k# is the constant of variation.

Known condition:

#y" "=" "kxx1/x" "->" "-6 3/10" "=" "kxx1/(2/3)#

#" "->" "-63/10" "=" "kxx3/2#

Multiply both sides by #2/3#

#" "->" "-63/10xx2/3" "=" "kxx1#

But 2 will divide exactly into 10 by 5 and 3 will divide exactly into 63 by 21 giving:

#" "->" "-(cancel(63)^(21))/(cancel(10)^5)xx(cancel(2)^1)/(cancel(3)^1)" "=" "k#

So #k=-21/5#

Thus we have:#" "y=-21/5xx 1/x" "->" "y=-21/(5x)#
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Let #x=8# giving:

#y=-21/(5xx8)=-21/40#