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

Question

Ethan Adkins · Accepted Answer

undefined To find y when x=8, we can use the inverse variation formula: y = k/x.

First, we need to find the constant of variation, k.

Given that y = -6.3 when x = 2/3, we can substitute these values into the formula: -6.3 = k / (2/3).

To solve for k, we can multiply both sides of the equation by (2/3): -6.3 * (2/3) = k.

Simplifying, we get: -4.2 = k.

Now that we have the value of k, we can substitute it back into the inverse variation formula: y = -4.2 / x.

To find y when x = 8, we substitute x = 8 into the formula: y = -4.2 / 8.

Simplifying, we get: y = -0.525.

Therefore, when x = 8, y is equal to -0.525.

Eva Adamson · Answer

#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)# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Let #x=8# giving:

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