Question

y is directly proportional to the positive square root of x when x = 9, y= 12 find y when x =1/2​

Answer 1

y = 2
`√(2)`

Explanation:

Given y is directly proportional to
`√(x)` then the equation relating them is

y = k
`√(x)` ← k is the constant of variation

To find k use the condition when x = 9, y = 12

12 = k
`√(9)` = 3k ( divide both sides by 3 )

4 = k

y = 4
`√(x)` ← equation of variation

When x =
`(1)/(2)` , then

y = 4
`\sqrt{(1)/(2) }` = 4 ×
`(1)/(√(2) )` ← rationalise the denominator by multiplying by
`(√(2) )/(√(2) )`

y =
`(4)/(√(2) )` ×
`(√(2) )/(√(2) )` =
`(4√(2) )/(2)` = 2
`√(2)`

Answer 2

Y =k√x

12 = 3k

k = 4

now X = 1\2

y = 4√1/2

y = 2√2