標題:
一題中四數學關於VARIATION附答案20分
發問:
The cost of a sourvenir of the surface area of A cm^2 is $C.It is given that C is the sum of two parts, one part varies directly as A while the other part varies directly as A^2 and inversely as n, where n is the number of souvenirs produced. When A=50 and n=500, C=350; when A=20 and n=400, C=100.a) express C in... 顯示更多 The cost of a sourvenir of the surface area of A cm^2 is $C.It is given that C is the sum of two parts, one part varies directly as A while the other part varies directly as A^2 and inversely as n, where n is the number of souvenirs produced. When A=50 and n=500, C=350; when A=20 and n=400, C=100. a) express C in terms of A and n. 答案: C=3A+[(40A^2)/n] b) the selling price of a souvenir of the surface area A cm^2 is $8A and the profit in selling the souvenir is $P. i) express P in terms of A and n. 答案:P=8A-C P=5A-[(40A^2)/n] ii) suppose P:n = 5:32. Find A:n. 答案: 1:16 iii) Suppose n=500. Can a profit of $100 be made in selling a sorvenir? Explain your answer. 答案: NO iV) Suppose n=400. Using the method of completing the square, find the greatest profit in selling a souvenir. 答案: $62.5 我淨係唔識 B既 ii) iii) 同iv) 麻煩你地給我詳細的steps. 唔該晒你啊!
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最佳解答:
bii) P:n = 5:32 P=5n/32 Put P = 5n/32 into P = 5A-[(40A^2)/n] 5n/32 = 5A-[(40A^2)/n] n^2 = 32An-256A^2 n^2-32An+256A^2 = 0 (n-16A)^2 = 0 n=16A A:n=1:16 biii) Put n=500 into P/n = 5/32 P/500 = 5/32 P= 78.125 which is less than $100 biv) Put n = 400 into P = 5A-[(40A^2)/n] P = 5A-[(40A^2)/400] P = 5A- A^2/10 P = -1/10 (A^2-50A) P = -1/10 (A^2-50A+625) + 625/10 P = -1/10(A-25)^2 + 62.5 P attains its greatest value at A=25 and the greatest profit in selling a souvenir is $62.5
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