F.4數學考試題目,唔識做(10題)(2)

12)設x為小徑的闊(20+2x)(16+2x)=572 4x^2+72x+320=572 4x^2+72x-252=0 x^2+18x-63=0 (x-3)(x+21)=0x= 3 or -21闊度冇可能負數，所以x=3 13a)L的方程:(y-4)/[x-(-2)]=-1 y-4=-2-x x+y=2// 13b)相交於y-axis代表x座標=0 0+y=2 y=2P的座標=(0,2)//13c)與L垂直代表:(2-y)/(0-x) *-1=-1 2-y=-x y-x=2//
14)(a+3i)^2=a^2+6ai-9Ans=純虛數代表將沒有i的刪除掉a^2=9 a=3 or -3//
15a) x^2-3x+4=0x=1.5±(√-7)/2α=1.5+(√7)i/2 ； β=1.5-(√7)i/2設1.5=a (√7)i/2=b α^2+β^2=[1.5+(√7)i/2]^2+[1.5-(√7)i/2]^2 =(a+b)^2+(a-b)^2 =a^2+2ab+b^2+a^2-2ab+b^2 =2a^2+2b^2 =2*(1.5)^2+2[(√7)i/2]^2 =4.5+2*(-7/4) =4.5-3.5 =1//15b)(α-β)^2=[1.5+(√7)i/2-(1.5-(√7)i/2)]^2 =[(√7)i]^2 =-7//

16ai)T(0)=2(0)^2-8(0)+32
=32
開冷氣前的溫度=32 C//
aii)T(3)=2(3)^2-8(3)+32
=18-24+32
=26
開冷氣3小時候的溫度=26 C//
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2) Cosine Theorem:
Let a be AB
6^2=5^2+a^2-2(5)(a)cos 55
36-25=a^2-10a cos 55
a^2-10a cos 55-11=0
a=[10cos55±√(100cos^2 55+44)]/2
=5cos 55±√(25cos^2 55+11)
∵5cos 55-√(25cos^2 55+11<0 ∴a=5cos 55+√(25cos^2 55+11) 5^2=6^2+a^2-2(6)(a)cosθ -11=a^2-12a cosθ


cos^-1 [(a^2+11)/12a]=θ
θ=43.0 (corr.to 3sig.fig.)

3)1/2 (5)(x) sin 111=17
5x sin 111=34
x=34/(5sin 111)
=7.28(corr .to 3sig.fig.)
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4)設x 為PR:
x^2=8^2+15^2-2(8)(15) cos 60
=64+225-120
=169
x=13
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13^2=11^2+20^2-2(11)(20)cos∠S
169=121+400-440cos∠S
-352=-440cos∠S
cos∠S=0.8
∠S=36.9(corr.to 3sig.fig.)
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5)5識做-.-
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6)提示？無視吧
Area=1/2 (16)(10) sin(cos^-1 8/10)
=80*0.6
=48sq.units//