The wave heights in the open sea depend on the speed v of the wind and the length of time that the wind has been blowing at that speed. Values of the function h = ƒ(v, t) are recorded in feet in the...

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The wave heights in the open sea depend on the speed v of the wind and the length of time that the wind has been blowing at that speed. Values of the function h = ƒ(v, t) are recorded in feet in the following table.


Duration (hours)























































































Wind speed (knots)




v     t



5



10



15



20



30



40



50



10



2



2



2



2



2



2



2



15



4



4



5



5



5



5



5



20



5



7



8



8



9



9



9



30



9



13



16



17



18



19



19



40



14



21



25



28



31



33



33



50



19



29



36



40



45



48



50



60



24



37



47



54



62



67



69



(a) What are the meanings of the partial derivatives ∂h/∂v and ∂h/∂t?


(b) Estimate the values of ƒv(40, 15) and ƒt(40, 50). What are the practical interpretations of these values?


(c) What appears to be the value of the following limit?



Answered Same DayDec 24, 2021

Answer To: The wave heights in the open sea depend on the speed v of the wind and the length of time that the...

David answered on Dec 24 2021
121 Votes
represents the rate of change of h when we fix t and consider h as a function of v which
describes
how quickly the wave heights change when the wind speed changes for a fixed time
duration.

represents the rate of change of h when we fix v and consider h as a function of t which describes
how quickly the wave heights change when the duration of time changes, but the...
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