A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at C.A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C diametrically opposite A on the other side of the lake in

来源：学生作业帮助网编辑：六六作业网时间：2024/11/27 12:08:12

AwomanatapointAontheshoreofacircularlakewithradius2miwantstoarriveatC.AwomanatapointAontheshoreofaci

A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at C.A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C diametrically opposite A on the other side of the lake in
A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at C.
A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C diametrically opposite A on the other side of the lake in the shortest possible time (see the figure). She can walk at the rate of 4 mi/h and row a boat at 2 mi/h.For what value of the angle θ shown in the figure will she minimize her travel time?求 θ 度数

A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at C.A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C diametrically opposite A on the other side of the lake in
连接OB、BC,

∴∠BOC=2∠A=2θ,
∴AB=AC▪cosθ=4cosθ,
弧BC=πAC▪(2θ/2π)=4θ,
设”the woman's travel time“为T(θ),
则T(θ)=AB/2+BC/4=2cosθ+θ,
∴T(θ)的导函数T'(θ)=1-2sinθ,
令T'(θ)=0,sinθ=1/2,θ=π/6,
当θ∈(0,π/6)时,T'(θ)>0,T(θ)单调递增,
当θ∈(π/6,π/2)时,T'(θ)<0,T(θ)单调递减,
T(0)=2,T(π/2)=π/2,

∴T(0)>T(π/2),
∴the woman should walk around the lake from Point A to Ponint C．
故答案为：π/2．
//--------------------------------------------------------------------------------------------------------------------
【明教】为您解答,
如若满意,请点击【采纳为满意回答】;如若您有不满意之处,请指出,我一定改正!
希望还您一个正确答复!
祝您学业进步!

30度

gosh!!!!!!!!!!!!!!!!!!!!!!!!!!

A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at C.A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C diametrically opposite A on the other side of the lake in a point It's unfriendly ____others .A.point at B.pointing at C.to point at A man starts walking north at 6 ft/s from a point P.Five minutes later,a woman starts walking south at 4 ft/s from a point 470 ft due east of P.At what rate ( in ft/s ) are the people moving apart 15 min after the woman starts walking?Please round yo a scerck makes woman woman 求帮翻译make a break through at my point gain a skill point at fishing什么意思 we are at a tipping point in violent crime many cities这里tipping point mark a high point the point of a You have a point point ( )a sign. issue a point forecast after a point翻译 after a point翻译 a secret make a woman woman A secrt mekes a woman woman a secret nakes a woman woman