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Ratios are really useful

March1

We are on to Chapter 2, titled Ratios. The pyramid at Giza has some amazing mathematical properties and was probably constructed to scale using ratios from a model or sketch (I showed how this works in class). Last period we learned how to simplify ratios and also how to use the cool ratio method that my Dad taught me, using (e.g.) 2:5::7:x
So, a Ratio is a comparison of two or more values/amounts/quantities. A ratio of 1:1 would be lifesize, whereas a ratio of 1:50 would be a scale of 1/50th the real size. Homework was pg 35, Qu 4 and 5 – finding ratios of areas and volumes. Today we move on to some practical problems in Ex 2B (pg 36). Also check out this link and your Maths Online exercises. Enjoy!

 

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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