Question

5.

If y is directly proportional to the square root of x and y = 20 when x = 16, find
(i) an equation connecting x and y,
(ii) the value of y when x = 25,
(iii) the value of x when y = 8.
​

Answer 1

see explanation

Explanation:

given that y is directly proportional to the square root of x, then the equation relating them is

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

(i)

To find k use the condition that y = 20 when x = 16

k =
`(y)/(√(x) )` =
`(20)/(√(16) )` =
`(20)/(4)` = 5, hence

y = 5
`√(x)` ← equation of proportionality

(ii)

When x = 25, then

y = 5 ×
`√(25)` = 5 × 5 = 25

(iii)

When y = 8, then

5
`√(x)` = 8 ( divide both sides by 5 )

`√(x)` =
`(8)/(5)` ( square both sides )

x =
`(64)/(25)`