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.

see explanation

Step-by-step explanation:

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

y = k ← k is the constant of proportionality

(i)

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

k = = = = 5, hence

y = 5 ← equation of proportionality

(ii)

When x = 25, then

y = 5 × = 5 × 5 = 25

(iii)

When y = 8, then

5 = 8 ( divide both sides by 5 )

= ( square both sides )

x =