2條 f4 maths.... (15pt)

2010-05-20 5:28 pm

1)the height and the perimeter of a right-angled triangle are xcmand 40cm respectively. ifthe length if its base is 1cm less than twice its height, find the value of x.

2)ABCD is a squre of side 8cm.P and Q are point on AB and BC respectively such that AP=QC=xcm.

b)if the ares of triangleADP is two-thirds of the area of triangleBPQ, find the val ue of x.(corr.3 sig.fig.)

3)Solve th following simultaneous equation.
{ 3^(x+1)-2^(y+1)=1
{ 4(3^x)+3(2^y)=24

回答 (1)

用戶2053

2010-05-21 3:56 am

✔ 最佳答案

1) base = 2x - 1 ,
(2x - 1)^2 + x^2 = [40 - x - (2x-1)]^2
4x^2 - 4x + 1 + x^2 = (41 - 3x)^2
5x^2 - 4x + 1 = 9x^2 - 246x + 1681
4x^2 - 242x + 1680 = 0
2x^2 - 121x + 840 = 0
(2x - 105)(x - 8) = 0
x = 105/2 = 52.5(rejected since it is > 40) or x = 8

2b)
△ADP = (2/3)△BPQ
(1/2)AP*AD = (2/3) (1/2)BP*BQ
x * 8 = (2/3) (8-x)(8-x)
12x = x^2 - 16x + 64
x^2 - 28x + 64 = 0
x = [28 ± √(28^2 - 4*64)]/2
x = 25.5(rejected since it is > 8) or 2.51

3)Solve th following simultaneous equation.
{ 3^(x+1)-2^(y+1)=1
3(3^x) - 2(2^y) = 1......(1)
{ 4(3^x)+3(2^y)=24......(2)
(1)*3 + (2)*2 :
9(3^x) + 8(3^x) = 3 + 48
3^x = 51/17
3^x = 3
x = 1
sub it to (1) :
3(3^1) - 2(2^y) = 1
2(2^y) = 8
2^y = 4 = 2^2
y = 2

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