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.
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Answer 1

Answer:

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$\sqrt{x}$ ← k is the constant of proportionality

(i)

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

k = $\frac{y}{\sqrt{x} }$ = $\frac{20}{\sqrt{16} }$ = $\frac{20}{4}$ = 5, hence

y = 5$\sqrt{x}$ ← equation of proportionality

(ii)

When x = 25, then

y = 5 × $\sqrt{25}$ = 5 × 5 = 25

(iii)

When y = 8, then

5$\sqrt{x}$ = 8 ( divide both sides by 5 )

$\sqrt{x}$ = $\frac{8}{5}$ ( square both sides )

x = $\frac{64}{25}$