The function f(x) varies inversely with x and f(x)=1.6 when x=0.5. what is f(x) when x=3.2

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  f2(3.2) = 1.4

Discussion:

f2(x) varies inversely with x means that f2(x) = k\x where "k" is a constant.

As f2(x) = 1.6 when x = 0.5 substitution gives

f2(.5) = 1.6  = k/(.5)  = k /(1/2) = 2k

so k = 1.6/2 = .8

(end of part 1)

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1