作业帮一道数学题目,关于相关变化率的,跪求讲解~
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一道数学题目,关于相关变化率的,跪求讲解~
A man 1.8m tall is walking at the rate of 0.9m/s toward a streetlight pole 5.4m igh.(a)At what rate is his shadow length decreasing?(b)How fast is the tip of his shadow moving?
A man 1.8m tall is walking at the rate of 0.9m/s toward a streetlight pole 5.4m igh.(a)At what rate is his shadow length decreasing?(b)How fast is the tip of his shadow moving?
AB=5.4,CD=C'D'=1.8,经过t时间后CD移动到C'D',则CC'=0.9t,设影长EC为x,由相似三角形可以得到,BE=3x,则BC=2x,从而C'B=2x-0.9t,再根据相似三角形得到E'C'=x-0.45t,
EE'=EB-E'B=1.35t.
（1）求影子缩短的速率.经过t时间,影子长度由EC变为E'C',故（EC-E'C'）/t=0.45
（2）求影子顶端的移动速率.经过t时间,影子顶端由E运动到E',则EE'/t=1.35