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Why is a constant of proportionality (usually the variable k) needed in variation problems?
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
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If it's direct proportion, then, as x increases so does y whilst keeping the ratio or proportion the same.
Let's say that x = 3 when y = 5.
If you double both then x = 6 and y = 10
Treble and you get x = 9 when y = 15
With fractions you already know that 3/5 = 6/10 = 9/15
With ratio you already know that 3:5 = 6:10 = 9:15
For the first pair, (3,5), you could write x = ky and work out that k = 3/5
For the second pair, (6,10) , you could write x = jy and work out that j = 6/10 = 3/5 = k
For the third pair, (9,15) ..... I'll leave you to finish this off.
So it is the properties of equivalent fractions that lead us to the general equation x = ky and we call k the constant of proportionality.
You can develop a similar argument for inverse proportion and for all the additional proprtions involving powers etc.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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If it's direct proportion, then, as x increases so does y whilst keeping the ratio or proportion the same.
Let's say that x = 3 when y = 5.
If you double both then x = 6 and y = 10
Treble and you get x = 9 when y = 15
With fractions you already know that 3/5 = 6/10 = 9/15
With ratio you already know that 3:5 = 6:10 = 9:15
For the first pair, (3,5), you could write x = ky and work out that k = 3/5
For the second pair, (6,10) , you could write x = jy and work out that j = 6/10 = 3/5 = k
For the third pair, (9,15) ..... I'll leave you to finish this off.
So it is the properties of equivalent fractions that lead us to the general equation x = ky and we call k the constant of proportionality.
You can develop a similar argument for inverse proportion and for all the additional proprtions involving powers etc.
Bob
For the pair (9, 15), I will let x = da.
I get d = 9/15 = 3/5.
Yes?
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
Offline
That's right.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
That's right.
Bob
Cooking with gas like Richie Cunningham used to say on Happy Days.
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
Offline
Pages: 1