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Point B is located at ( 1, 0) If you've drawn out the 2 triangles, you will have noticed that A O B and P O Q are rotations of each other, and are therefore congruent, so we can say that P Q and A B are equal. Mathematically: A O B ≅ P O Q, ∴ P Q = A B. If you don't remember the Cartesian distance formula, here it is: d = ( x 2 − x 1.


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1 The temperature T(t)°C of an object at time t seconds is modelled using Newton's Law of Cooling, T(t) = 15 + 4e−3t. What is the initial temperature of the object? −3 4 15 19 2 A standard six-sided die is rolled 12 times. Let p ˆ be the proportion of the rolls with an outcome of 2.


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Title: Mathematics Advanced, Extension 1 and Extension 2 Reference Sheet Author: NSW Education Standards Authority Created Date: 11/7/2019 1:47:30 PM


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1 (ii) f(x) = + x + 2 (iv) f(x) = 2x 7 3 (v) g(x) = 2x 7 (vi) f(x) = 1 4 x2 Find the ranges in parts (iv) and (v). In each of the following find an explicit formula for the composite functions f(g(x)) and g(f(x)). Also find the natural domain of each composite function. f(x) = 3x + 2 and g(x) = 4x 6 f(x) = and g(x) = x2 1 x