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標題:

(急)(F.5 數)求解!!

發問:

1)已知Y為兩部分之和,一部分為常數,叧一部分則隨X正變.當X=-1時,Y=2;而當X=5時,Y=8. 求聯繫x及y的方程. 2)A)已知Y的一部分隨x正變,叧一部分則隨X反變.當X=1時,Y=15;而當X=2時,Y=45. 求聯繫x及y的方程. B)求當X=5時Y的值. 3)已知z隨y及x^3聯變,若x減少5%而y增加15%,求z的百分增減. 4)已知y隨(x+2)成反變,且當x=2時,y=75.若y減少25,求x的變化.

最佳解答:

1) Y=k1+k2x when x=-1, y=2 2=k1-2(k2) ----(1) when x=5, y=8 8=k1+5(k2) -----(2) (1)-(2): -6=-7(k2) (k2)=6/7 sub(k2)=6/7 into (1): 2=k1-12/7 k1=26/7 so, y=26/7 + 6/7x 2)y=(k1)x+(k2)/x when x=1,y=15, 15=(k1)+(k2) -----(1) when x=2,y=45, 45=2(k1)+(k2)/2 -----(2) (1)x2-(2): -15=2(k2)+(k2)/2 5(k2)=-30 (k2)=-6 sub (k2)=-6 into (1): (k1)=21 so, y=21x-6/x 3)z=kyx^3 new value of x: 0.95x new value of y: 1.15y new value of z:k(1.15y)(0.95x)^3 =0.98598125kyx^3 Percentage change: (0.98598125kyx^3-kyx^3)/kyx^3 =kyx^3(0.98598125-1)/kyx^3 =-1.40% (cor. to 3 sig. fig.) 4)y=k/(x+2) when x=2, y=75, 75=k/3 k=225 so,y=225/(x+2) y(x+2)=225 x=(225/y)-2 new value of y:0.75y new value of x=(225/0.75y)-2 =(300/y)-2 percentage change of x: (225/y)-2 - (300/y)+2 / (300/y)+2 =(225/y)(-2-(4/3)+2)/(300/y)+2 =-133% 2014-11-14 11:15:32 補充： not sure if correct or not. Just for your reference :)

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