Question

1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.​

Answer 1

Problem Solving:-

1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.

Solution:-

`\sf{The \: relation \: y \: varies \: inversely \: as \: x \: translates \: to \: y = (k)/(x).}`

Substitute the values to find k:

`\sf\rightarrow{y= (k)/(x) }`

`\sf\rightarrow{6= (k)/(18) }`

`\sf\rightarrow{k=(6)(18)}`

`\sf\rightarrow{K={\color{magenta}{108}}}`

Answer:-

`\sf{The \: equation \: of \: variations \: is \: y={ \color{red}{ (108)/(x) }}}`

`{\huge{\color{blue}{━━━━━━━━━━━━}}}`

#CarryOnMath⸙

Answer 2

An inverse function is y = k/x

replace x and y with the given values:

6 = k/18

Solve for k by multiplying both sides by 18:

k = 108