標題:

maths f4

發問:

z varies as the square of x and inversely as y ,where x ,y and z are positive.when x=8 and y=4 ,z=2 a)express z in terms of x and y b)suppose x-2y-z=0, i)find x:y:z ii)find the increase of z if x is increased by 2. 點解AND 點做?

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最佳解答:

a) z=kx^2/y where k is a constant 2=k(8^2)/4 16k=2 k=1/8 Therefore z=x^2/(8y) b) i) x-2y-z=0 From a): z=x^2/(8y) x-2y-x^2/(8y)=0 8xy-16y^2-x^2=0 x^2-8xy+16y^2=0 (x-4y)^2=0 x-4y=0 x=4y Hence, z=x^2/(8y)=(4y)^2/(8y)=2y Therefore x:y:z=4y:y:2y=4:1:2 ii) x:z=4:2=2:1 i.e. x/z=2 (2x)/(2z)=2 Therefore the increase of z is 2, if x is increased by 2. 2011-05-28 13:30:30 補充: b) ii) x:z=4:2=2:1 i.e. x/z=2 Suppose when x is increased by 2, x becomes X and z becomes Z. Then X=x+2 and X/Z=2 X/Z=2 (x+2)/Z=2 Z=(x+2)/2=x/2+1=z+1 Therefore the increase of z is 1, if x is increased by 2. 2011-05-28 13:35:13 補充: z隨x的平方而正變和隨y而反變,其中x,y和z為正數。當x=8和y=4時,z=2。 a) 以x和y表示z。 b) 假設x-2y-z=0, i) 求 x:y:z ii) 若x增加2,求z的增加。

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