求助,这道题的解法 ,谢谢啦
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易知AE=4cm.
0<t<=4时AP=AQ=tcm,y=(1/2)t^2,其图像向上凹,弃A,D.
4<t<6时PC=6-t,CQ=2√3-(t-4)=4+2√3-t,
S△CPQ=(1/2)(6-t)(4+2√3-t)=(1/2)(t-5-√3)^2-(√3-1)^2/2,
S△AEP=√3(t-4),
S△ABQ=2(t-4),
S梯形ABCE=6√3,
∴y=6√3-(1/2)[24+12√3-(10+2√3)t+t^2]-(2+√3)(t-4)
=(-1/2)t^2+3t-4+4√3,
6<=t<4+2√3时y=2(4+2√3-t).
选C.
0<t<=4时AP=AQ=tcm,y=(1/2)t^2,其图像向上凹,弃A,D.
4<t<6时PC=6-t,CQ=2√3-(t-4)=4+2√3-t,
S△CPQ=(1/2)(6-t)(4+2√3-t)=(1/2)(t-5-√3)^2-(√3-1)^2/2,
S△AEP=√3(t-4),
S△ABQ=2(t-4),
S梯形ABCE=6√3,
∴y=6√3-(1/2)[24+12√3-(10+2√3)t+t^2]-(2+√3)(t-4)
=(-1/2)t^2+3t-4+4√3,
6<=t<4+2√3时y=2(4+2√3-t).
选C.
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