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 =k√x

12 = 3k

k = 4

now X = 1\2

y = 4√1/2

y = 2√2

Answer 2

Answer:

y = 2$\sqrt{2}$

Step-by-step explanation:

Given y is directly proportional to $\sqrt{x}$ then the equation relating them is

y = k$\sqrt{x}$ ← k is the constant of variation

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

12 = k$\sqrt{9}$ = 3k ( divide both sides by 3 )

4 = k

y = 4$\sqrt{x}$ ← equation of variation

When x = $\frac{1}{2}$ , then

y = 4$\sqrt{\frac{1}{2} }$ = 4 × $\frac{1}{\sqrt{2} }$ ← rationalise the denominator by multiplying by $\frac{\sqrt{2} }{\sqrt{2} }$

y = $\frac{4}{\sqrt{2} }$ × $\frac{\sqrt{2} }{\sqrt{2} }$ = $\frac{4\sqrt{2} }{2}$ = 2$\sqrt{2}$