What is the probability that BD < 4?
P=ADBCAABD
fAC(x)=√52−x2fBC(x)=√32−(x−7)225−x2=9−x2+14x−4914x=65xC=4.6429yC=1.8558C(4.6429,1.8558)A(0,0)B(7.0)
fAD=1.85584.6429xfBD=√42−(x−7)21.85584.6429x=42−(x−7)21.85584.6429x=16−x2+14x−49
x2−13.6003x+33=0x=6.8001±√46.2420−33xD=3.1661yD=1.2635D(3.1661,1.2635)
AABC=72⋅1.8558AABC=6.4953AABD=72⋅1.2635AABD=4.4224ADBC=AABC−AABD=6.4953−4.4224ADBC=2,0729
P=ADBCAABD=2.07294.4224:2.07292.0729=1:2.1334
The probability that BD < 4 is P=1:2.1334
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