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Basic Mathematics for Economists phần 2

các mô hình của Phần Người bán hàng gửi giá, nhưng người mua là phù hợp với một rong đó x là đầu ra, lấy được một chức năng cho lợi nhuận (π) của x. Gần đúng hình dạng chức năng này lợi nhuận sẽ mất? Một nhóm nhỏ của các công ty hoạt động trong một ngành công nghiệp | per week were worked then gross pay 40 hours @ 8 10 hours @ 12 320 120 440 tax payable 440 - 80 0.25 360 0.25 90 Therefore net pay 440 - 90 350 Using the expression derived in Example 3.14 if H 50 then net pay 9H - 100 9 50 - 100 450 - 100 350 This checks out with the answer above and so we know our expression works. It is rather more complicated to multiply pairs of brackets together. One method that can be used is rather like the long multiplication that you probably learned at school but instead of keeping all units tens hundreds etc. in the same column it is the same algebraic terms that are kept in the same column during the multiplying process so that they can be added together. Example 3.15 Simplify 6 2x 4 - 2x . Solution Writing this as a long multiplication problem 6 2x X 4 - 2x Multiplying 6 2x by -2x - 12x - 4x2 Multiplying 6 2x by 4 24 8x_ Adding together gives the answer 24 - 4x - 4x2 One does not have to use the long multiplication format for multiplying out sets of brackets. The basic principle is that each term in one set of brackets must be multiplied by each term in the other set. Like terms can then be collected together to simplify the resulting expression. Example 3.16 Simplify 3x 4y 5x - 2y . 1993 2003 Mike Rosser Solution Multiplying the terms in the second set of brackets by 3x gives 15x2 - 6xy 1 Multiplying the terms in the second set of brackets by 4y gives 20xy - 8y2 2 Therefore adding 1 and 2 the whole expression is 15x2 6xy 20xy 8y2 15x2 14xy 8y2 Example 3.17 Simplify x y 2. Solution x y 2 x y x y x2 xy yx y2 x2 2xy y2 The above answer can be checked by referring to Figure 3.1. The area enclosed in the square with sides of length x y can be calculated by squaring the lengths of the sides i.e. finding x y 2. One can also see that this square is made up of the four rectangles A B C and D whose areas are x2 xy xy and y2 respectively - in other words x2 2xy y2 which is the answer obtained above. Figure 3.1 1993 2003 Mike Rosser .