1.If a partly varies directly as the square root of b and partly varies inversely as the square of c,and a=3 when b=c=1,a=5/2 when b=4 and c=2,find
(a) an equation connecting a,b and c,
(b) the value of a when b=16 and c=3.
Maths question
2007-05-08 5:33 am
回答 (2)
2007-05-09 12:45 am
✔ 最佳答案
(a)Let h & k are constant
Suppose the equation is a = H(b)^0.5 + K/(c^2)
For a=3 when b=c=1,
3 = H + K ---(Eqn. 1)
For a=5/2 when b=4 and c=2
(5/2) = 2H + 0.25K
=> Mutlipy 4 to both side => 10 = 8H + K ---(Eqn. 2)
(Eqn. 2) - (Eqn. 1)
=> 7 = 7H => H = 1
=> K = 2
The equation is a = (b)^0.5 + 2/(c^2)
(b)
when b=16 and c=3
a
= (16)^0.5 + 2/(3^2)
= 4 + 2/9
= 38/9
2007-05-08 5:50 am
(a). let k be the constant
a=kb^1/2+K/(c^2)
3=k+K------1
5/2=2k+K/4-----2
k=3-K-----3
sub 3 into 2
10=24-8K+K
K=2
k=1
so a=b^1/2+2/(c^2)
(b). a=16^1/2+2/3^2
=4+2/9
=38/9
a=kb^1/2+K/(c^2)
3=k+K------1
5/2=2k+K/4-----2
k=3-K-----3
sub 3 into 2
10=24-8K+K
K=2
k=1
so a=b^1/2+2/(c^2)
(b). a=16^1/2+2/3^2
=4+2/9
=38/9
參考: ans.我唔肯定.......對自己超沒自信的說
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