標題:
Maths problem of variation[急]
發問:
1. The selling price of each copy of a weekly magazine is $x, and the total profit on selling the magazine is $y. It is given that one part of y varies directly as x, and the other part varies directly as the square of x. When x=42, y=79800. When x=50, y=75000.(a)Express y in term of x.(b)Find the value of y... 顯示更多 1. The selling price of each copy of a weekly magazine is $x, and the total profit on selling the magazine is $y. It is given that one part of y varies directly as x, and the other part varies directly as the square of x. When x=42, y=79800. When x=50, y=75000. (a)Express y in term of x. (b)Find the value of y when x=45. (c)Use the method of completing the square to write y in the form y=a+b(x+c)^2, where a, b, c are constants. I know how to calculate(a) and (b) but I don't know how to calaulate(c), so just show the calculation of (c) is enough. thx~
最佳解答:
(a) Let y=Ax+Bx^2 Sub. x=42, y=79800. When x=50, y=75000 79800=42A+1764B 75000=50A+2500B So from (2) 1500=A+50B=>A=1500-50B Sub, into (1) 79800=42(1500-50B)+1764B =>79800=63000-2100B+1764B =>B=-50 A=4000 So y=4000x-50x^2 (b) Sub. x=45, we have y=78750 (c) y =4000x-50x^2 =-50(x-40)^2+80000
其他解答:
Maths problem of variation[急]
發問:
1. The selling price of each copy of a weekly magazine is $x, and the total profit on selling the magazine is $y. It is given that one part of y varies directly as x, and the other part varies directly as the square of x. When x=42, y=79800. When x=50, y=75000.(a)Express y in term of x.(b)Find the value of y... 顯示更多 1. The selling price of each copy of a weekly magazine is $x, and the total profit on selling the magazine is $y. It is given that one part of y varies directly as x, and the other part varies directly as the square of x. When x=42, y=79800. When x=50, y=75000. (a)Express y in term of x. (b)Find the value of y when x=45. (c)Use the method of completing the square to write y in the form y=a+b(x+c)^2, where a, b, c are constants. I know how to calculate(a) and (b) but I don't know how to calaulate(c), so just show the calculation of (c) is enough. thx~
最佳解答:
(a) Let y=Ax+Bx^2 Sub. x=42, y=79800. When x=50, y=75000 79800=42A+1764B 75000=50A+2500B So from (2) 1500=A+50B=>A=1500-50B Sub, into (1) 79800=42(1500-50B)+1764B =>79800=63000-2100B+1764B =>B=-50 A=4000 So y=4000x-50x^2 (b) Sub. x=45, we have y=78750 (c) y =4000x-50x^2 =-50(x-40)^2+80000
其他解答:
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As a demonstration, let y = 4x^2 + 6x + 5 [actual value should be those in part (a)]. y = 4x^2 + 6x + 5 = 4(x^2 + 6x/4) + 5 = 4(x^2 + 3x/2) + 5 = 4[(x + 3/4)^2 - (3/4)^2] + 5 ( 3/4 is HALF of 3/2 and having same sign.) = 4[(x + 3/4)^2 - 9/16] + 5 = 4(x + 3/4)^2 - 9/4 + 5 = 4(x + 3/4)^2 + 11/4. so in this case, a = 11/4, b = 4 and c = 3/4. same method can be applied to any quadratic function y.
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