Direct & Inverse Proportions
By DarthVader
Date: 2022-03-28
Topic: 97 see comments
Post views: 1109
Direct Proportion
Two values are in direct proportion to one another when as one increases, so does the other.
Example:
y ∝ k∗x
‘y’ = Subject of the equation. (unknown you want to find)
‘∝’ = Directly proportional sign.
‘k’ = Constant proportionality.
‘x’ = Variable.
Example question:
"A stone is thrown into a well and after 0.5 seconds, it reaches a speed of 4.9 ms-1
Work out the ‘constant of proportionality’ ‘k’, then calculate the speed after 1.2 seconds. "
1. First set out the direct proportionality equation using the appropriate letters, in this case ‘v’ for velocity/speed, and ‘t’ for time:
v ∝ kt
2. Now plug in the information given in the question to calculate ‘k’:
4.9 = k ∗ 0.5
- Divide both sides by 0.5 to find ‘k’:
k = 4.9 ÷ 0.5
k = 9.8
3. Now we have the value of ‘k’ we can use the equation to find the speed after 1.2 seconds:
v = 9.8∗1.2
v = 11.76 ms-1
Inverse Proportion
Two values are inversly proportional when as one increases the other decreases, and vice versa.
Example:
y ∝ k/x
Example Question:
"4 people take 3 hours to paint a fence. How long will it take 6 people. "
1. First set out the equation for inverse proportions using appropriate letters, in this case ‘p’ for people and ‘t’ for time (hours):
t ∝ k ÷ p
2. Then work out ‘k’ by plugging in the values given in the question:
3 = k ÷ 4
- Multiply both sides by 4 to find ‘k’:
(4)3 = (4) ∗ k ÷ 4
k = 12
3. Now use the value of ‘k’ to find ‘t’ when ‘p is equal to 6’:
t = 12 ÷ 6
t = 2 hours
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