Question

How do I arrive at the answer ? What are the workings?

Answer 1

`y= (7√(10))/(5)`

Explanation:

If y is inversely proportional to
`√(x-2)`, then:

`\boxed{y \propto (1)/(√(x-2)) \implies y=(k)/(√(x-2))}`

for some constant k.

Given:

• y = 7 when x = 6

Substitute the given values into the found equation and solve for k:

`\implies 7=(k)/(√(6-2))`

`\implies 7=(k)/(√(4))`

`\implies 7=(k)/(2)`

`\implies 7 \cdot 2=(k)/(2)\cdot 2`

`\implies 14=k`

Therefore:

`y=(14)/(√(x-2))`

To find the value of y when x = 12, substitute x = 12 into the found equation and solve for y:

`\implies y=(14)/(√(12-2))`

`\implies y=(14)/(√(10))`

`\implies y=(14)/(√(10))\cdot (√(10))/(√(10))`

`\implies y= (14√(10))/(10)`

`\implies y= (7√(10))/(5)`