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Ankoret
nearsighted cow classic calculus problem
Are we suppose to find the derivative of its sight?
maybe the integral of its periphery
Supposed to find "the vertical angle subtended by the billboard at her eye in terms of x" and also the distance the cow must be standing from the billboard to maximize the first thing.
is this an optimization problem?
also it would help if you gave us more information
yes, optimization. hang on, getting more info.
Rectangular billboard 5 ft in height is 12 ft above the ground. Nearsighted cow with eye level at 4 ft above ground stands x ft from the billboard. Express theta in terms of x, then find the distance the cow must stand from the billboard in order to maximize theta.
|dw:1343007462718:dw|
Behold! My drawing skills!
Anyway, since it is barely decipherable, I will add what I think is best to do. I have chosen f(x) to be the angle in which the cow sees the board, y_2 should be the entire angle since there should be substitutions involved. \[ y_2=f(x)+y_1 \rightarrow f(x)=y_2-y_1 \] now for the angles \[ \tan(y_1)=\frac{8}{x} \rightarrow y_1 = \tan^{-1}\left(\frac{8}{x}\right)\] and \[ \tan(y_2)=\frac{11}{x} \rightarrow y_2=\tan^{-1} \left(\frac{11}{x}\right)\]
the rest is calculus,\[ f'(x)=0 \\ f''(x)<0 \longrightarrow \text{Max}\]