f.4 maths variations

2009-03-26 7:00 am

1) Given that y varies directly (ax+1), and y=15 when x=1; y=27 when x=2,find

(a) the value of the constant a,
(b) the value of y when x=3.

ans:
(a) 4
(b) 39

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2)Given that V varies directly as square root H, find the % change in H if V is increased by 5%.

ans:+10.25%
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3) R varies directly as the square root of V and inversely as the square root of H. If H increases by 40% and V decreases by 65%, find the % change in R.

ans:-50%

please show steps by steps
thanks a lot!

回答 (1)

myisland8132

2009-03-26 10:10 am

✔ 最佳答案

1 Let y=K(ax+1)
15=K(a+1)
27=K(2a+1)
27(a+1)=15(2a+1)
a=4
K=3
when x=3,y=39
2 V=K√H
if V is increased by 5%.
Then V1=1.05V
=>V/√H=1.05V/√H1
H1=(1.05)^2H
So H increased by 10.25%
3 R=K√(V/H)
H1=1.4H,V1=0.35V
R√(H/V)=R1√(H1/V1)
R√(H/V)=R1√(1.4H/0.35V)
R=2R1
So the % change in R is -50%

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