Cambridge International Mathematics

Discussion Possible models

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abc

In some cases, we know what type of variation exists. We use the data values given to find the exact equation

for the model.

Example 11 Self Tutor

Check the other

data points on

the graph to

make sure they

obey this model.

The areaAof a sector of given

angle is directly proportional to

the square of its radiusr.

Find the equation of the

variation model given the data

on the graph.

Since A_r^2 , A=kr^2 wherekis a constant.

From the graph we see that when r=2, A=3

) 3=k£ 4 and so k=^34

The model is A=^34 r^2.

In the previous sections we observed that:

If y_xn then:

² y=kxn wherekis the proportionality constant

² the graph ofyagainstxnis a

straight line with gradientk.

O

y

x O

y

x O

y

x

r

r

2 4 6 8

8

6

4

2

A

O

O

y

xn

ykx¡=¡ n

616 Variation and power modelling (Chapter 30)

Why do the following graphs not represent direct or inverse variation models?

IGCSE01

cyan magenta yellow black

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100 100
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Y:\HAESE\IGCSE01\IG01_30\616IGCSE01_30.CDR Wednesday, 29 October 2008 3:48:49 PM PETER