Answer:
- x = 2/√y or y = 4/x²
- x = 2/3
- y = 1/36
Step-by-step 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
