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

Question

asked Jun 7, 2023 17.4k views

1 Answer

Tyrone Wilson · Answer 1 · 2023-06-13T07:15:12+0000

Answer:

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:

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:

$\implies y=(14)/(√(12-2))$

$\implies y=(14)/(√(10))$

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

$\implies y= (14√(10))/(10)$

$\implies y= (7√(10))/(5)$