Question

Y is directly proportional to the square root of ( x-3 ). When x = 28, y = 20. Find y when x = 39.

Answer 1

y = 24

Explanation:

Given y is directly proportional to
`√(x-3)` then the equation relating them is

y = k
`√(x-3)` ← k is the constant of proportion

To find k use the condition when x = 28, y = 20 , then

20 = k ×
`√(28-3)` = k ×
`√(25)` = 5k ( divide both sides by 5 )

4 = k

y = 4
`√(x-3)` ← equation of proportion

When x = 39 , then

y = 4 ×
`√(39-3)` = 4 ×
`√(36)` = 4 × 6 = 24

Answer 2

• 24

Explanation:

y is directly proportional to the square root of ( x-3):

• y = k
  `√(x-3)`, where k is the coefficient of proportionality

Given:

• y is 20 when x is 28

Find k:

• 20 = k
  `√(28-3)`
• 20 = k* 5
• k = 20/5
• k = 4

Find y when x = 39:

• y = 4
  `√(39-3)`
• y =4
  `√(36)`
• y = 4*6
• y = 24