2022-04-08
A man 6 ft tall walks at a rate of 5 ft/sec away from a lamppost that is 12 ft high. At what rate is the length of his shadow changing when he is 25 ft away from the lamppost?
nick1337
Expert2022-06-08Added 777 answers
Let be the distance between the man and the street light and let be the length of his shadow. Note that we have two similar right triangles and . Hence using the similar triangle property, we get
Differentiating with respect to time partially, we get
Now Since the man is walking away's from the lamp at a rate ot .
Hence at the moment when he is aways from the lamppOst, the length of his shadow is changing at a rate of
Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
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