Let f(x, y,t) represent temperature at a position a miles east and y miles north of New York City and time t hours after noon. Suppose that temperature increases by .01° for every mile south and decreases by .02° for every mile east. But temperature everywhere also depends on time of day and thus contains a term of the form 12 cos (t). Suppose you drive southwest at 6mph at 4pm (Yes, you are driving pretty slowly). Is it getting hotter or cooler?
Let f(x, y,t) represent temperature at a position a miles east and y miles north of New York City and time t hours after noon. Suppose that temperature increases by .01° for every mile south and decreases by .02° for every mile east. But temperature everywhere also depends on time of day and thus contains a term of the form 12 cos (t). Suppose you drive southwest at 6mph at 4pm (Yes, you are driving pretty slowly). Is it getting hotter or cooler?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:) Let f(x,y, t) represent temperature at a position r miles east and y miles
north of New York City and time t hours after noon. Suppose that temperature
increases by .01° for every mile south and decreases by .02° for every mile east. But
temperature everywhere also depends on time of day and thus contains a term of
the form 12 cos (t). Suppose you drive southwest at 6mph at 4pm (Yes, you are
driving pretty slowly). Is it getting hotter or cooler?
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