1) Since y is proportional to x², we can write the relationship as y = kx², where k is the constant of proportionality.
We are given that y = 18 when x = 3. Substituting these values into the equation:
18 = k * (3)²
18 = k * 9
Solving for k: k = 18 / 9 = 2
Therefore, the equation for y in terms of x is y = 2x².
2) (a) Since v is proportional to the square root of d, we can write v = k√d, where k is the constant of proportionality.
We are given that v = 14 m/s when d = 10 m. Substituting these values:
14 = k * √10
Solving for k: k = 14 / √10
The formula for v in terms of d is v = (14 / √10) * √d, which can also be written as v = 14√(d/10).
(b) We need to find d when v = 28 m/s. Using the formula from part (a):
28 = (14 / √10) * √d
Dividing both sides by 14: 2 = √d / √10
Multiplying both sides by √10: 2√10 = √d
Squaring both sides: (2√10)² = d
4 * 10 = d
d = 40
Therefore, the distance the stone has fallen is 40 meters.
3) Since S ∝ 1/R, we can write S = k/R, where k is the constant of proportionality.
We are given that S = 29.6 when R = 4.5. Substituting these values:
29.6 = k / 4.5
Solving for k: k = 29.6 * 4.5 = 133.2
Now, we need to find S when R = 7.2. Using the equation S = k/R with k = 133.2:
S = 133.2 / 7.2 = 18.5
Therefore, S = 18.5 when R = 7.2.
Parent Tip: Review the logic above to help your child master the concept of inverse proportion worksheet.
