Question

The variable z is directly proportional to x, and inversely proportional to y. When x is 4 and y is 13, z has the value 1.2307692307692. What is the value of z when x= 9, and y= 20

Answer 1

`&\boxed{\text{1.800 000 000 0000}}`

Explanation:

`z \propto x\\\\z \propto (1)/(y)\\\\z \propto (x)/(y)\\\\z = k \left ((x)/(y) \right )`

Solve for k

`\begin{array}{rcl}1.2307692307692& = & k\left ((4)/(13) \right )\\\\16.000000000000 & = & 4k\\k & = & 3.9999999999999\\\\z & = & 3.9999999999999\left ((x)/(y)\right )\\\end{array}`

Calculate the new value of z

`\begin{array}{rcl}z & = & 3.999 999 999 9999 \left ((9)/(20)\right )\\\\& = &\boxed{\textbf{1.800 000 000 000}}\\\end{array}`

Answer 2

Explanation:

1.2307692307692.

The first step is to find the proportionality constant.

The formula is

z = kx/y

1.2307692307692 = k * 4/13 Multiply both sides by 13

1.2307692307692 * 13 = 4k

16 = 4*k Divide by 4

k = 16/4

k = 4

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z = k*x/y

x = 9

y = 20

k = 4

z = 4 *9/20

z = 36/20

z = 1.8