Question

y varies directly as square root of x. When x = 16, y = 24. Find the constant of variation and equation of variation.

Answer 1

Hi,

Answer:
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Equation of variation:
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$y \: \: \alpha \: \sqrt{x} \\ \\ y \: \: = c \: \: \sqrt{x}$
Constant of variation:
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$c \: = 6$


solution:
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As y is directly proportional to √x,
so we can write
$y \: \: \alpha \: \sqrt{x}$


to remove symbol of proportionality , replace a constant here,let the constant is c.

$y \: \: = \: c \: \sqrt{x}$
Now to find value of variation constant

$x = 16 \\ \\ y = 24 \\ \\ c = \frac{y}{ \sqrt{x} } \\ \\ c = \frac{24}{ \sqrt{16} } \\ \\ c = \frac{24}{4} \\ \\ c = 6$
hope it helps you.

Answer 2

Hi ,

It is given that ,

y varies directly as square root of x .

x = 16 , y = 24

y = k × √x ( k is a constant )

24 = k × √16

24 = 4k

24/4 = k

6 = k

Therefore ,

Required constant = k = 6

And

Equation y = 6√x

I hope this helps you.

: )