Question

If x varies inversly as the square root of y varies and x=1 when y=4, find;

relationship between x and y
the value of x when y =9
the value of y when x=12​

Answer 1

• x = 2/√y or y = 4/x²
• x = 2/3
• y = 1/36

Explanation:

When x varies inversely as the square root of y, and x=1 when y=4, you want to find ...

• the relationship between x and y
• the value of x when y =9
• the value of y when x=12​.

Inverse variation

The given relation can be written using a constant of proportionality as ...

x = k/√y . . . . x varies as the inverse of the square root of y

The value of k can be found from the given values for x and y:

1 = k/√4 = k/2

2 = k . . . . . . . . . multiply by 2

Relationship

The relationship between x and y can be written as ...

x = 2/√y

Solving for y, it can also be written as ...

y = 4/x²

For y = 9

The value of x is ...

x = 2/√9

x = 2/3

For x=12

The value of y is ...

y = 4/12² = 4/144

y = 1/36