(急)(F.5 數)求解!!

慕恩

2014-11-13 6:25 am

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.

回答 (1)

用戶73917

2014-11-14 7:04 pm

✔ 最佳答案

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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