Q128 of 147 Page 8

Height of a place A is 1800 m above sea level. Another place B is 700 m below sea level. What is the difference between the levels of these two places?

We have the diagram:


The diagram makes the question clearer that the difference between these two places is the total distance between point A to the sea level and the distance between point B and the sea level.


Notice, the distance between point A and the sea level = 1800 m


The distance between point B and the sea level = 700 m


The distance between the points A and B, AB = AO + OB


⇒ AB = 1800 + 700


⇒ AB = 2500


Thus, Difference between the levels of A and B = 2500 m


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126

If ∆ is an operation such that for integers a and b we have

a ∆ b = a × b – 2 × a × b + b × b (–a) × b + b × b


then find (i) 4 (– 3)


(ii) (– 7) ∆ (– 1)


Also show that 4 ∆ (– 3) ≠ (– 3) ∆ 4


and (– 7) ∆ (– 1) ≠ ( – 1) ∆ (– 7)

 127

Below u, v, w and x represent different integers, where u = –4 and x ≠ 1. By using following equations, find each of the values:

u × v = u


x × w = w


u + x = w


(a) v


(b) w


(c) x


Explain your reasoning using the properties of integers.

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130

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