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Differential Equations, Chain Rule, and Rate of Change

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1. A ladder 10 feet long rests against a vertical wall. If the top of the ladder slides down at a rate of 1 ft/sec how fast is the bottom of the ladder sliding away when the bottom of the ladder is 8 ft away from the wall?

2. Two people start from the same point. One runs west at 13 km/hr and the other walks north at 2 km/hr. How fast is the distance between the people changing after 10 minutes?

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1. A ladder long rests against a vertical wall. If the top of the ladder slides down at a rate of how fast is the bottom of the ladder sliding away when the bottom of ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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