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# If y varies directly as the square root of x and y is 10 when x = 1, find y when...

### Question

If y varies directly as the square root of x and y is 10 when x = 1, find y when x = 4.

### Options

A) 18

B) 20

C) 30

D) 40

The correct answer is B.

### Explanation:

$$y \approx \sqrt{x}$$
$$y = k\sqrt{x}$$
At $$y = 10, x = 1$$
$$10 = k\sqrt{1}$$
$$k = 1$$
$$\rightarrow y = \sqrt{x}$$
At $$x = 4, y = \sqrt{4} = 2$$

## Dicussion (1)

• $$y \approx \sqrt{x}$$
$$y = k\sqrt{x}$$
At $$y = 10, x = 1$$
$$10 = k\sqrt{1}$$
$$k = 1$$
$$\rightarrow y = \sqrt{x}$$
At $$x = 4, y = \sqrt{4} = 2$$