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A meteorologist sketched the path of the jet stream on a map of the northern U.S. and southern Canada on which all latitudes were parallel and all longitudes were parallel and equally spaced. A computer analysis showed this path to be given by:y=(6.0e^(-0.020x) )(sin0.20x)where 0≤x≤60
the the origin is 125.0°W,45.0°N and the point (60,0)is 65.0°W,45.0°N.
Find the locations of the maximum and minimum latitudes of the jet stream between 65°W and 125°W for that day.
can you show how to solve this step by step Thanks.
If the path is y = 6[e^(0.02x)][sin(0.2x)], find y' to see where the maxes and mins are at.
Once y' is found, set it to 0 and solve. Once this is done, do the conversioin to the units.
Note that for f = e^(0.02x), f' = 0.02*e^(0.02x) and
for g = sin0.2x, g' = 0.2*cos0.2x,
From here, y' = fg' + gf'. Since both f and f' have a e^(0.2x) in them, factor it out.
This gives [e^(0.02x)](0.2*cos0.2x + 0.02*sin0.2x).
The 1st term is never 0, since exponentials are always positive.
The 2nd term can be set to 0. so we have 0.2*cos0.2x + 0.02*sin0.2x = 0.
Subtracting the 1st term from both sides gives 0.02*sin0.2x = -0.2*cos0.2x.
Dividing both sides by 0.02 and by cos0.2x gives tan0.2x = -10.
I'll let you look that up and then convert the units.
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