Ankoret 2 years ago nearsighted cow classic calculus problem

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1. IsTim

Are we suppose to find the derivative of its sight?

2. lgbasallote

maybe the integral of its periphery

3. Ankoret

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.

4. mickifree12

is this an optimization problem?

5. mickifree12

6. Ankoret

7. Ankoret

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.

12-5=×

9. Spacelimbus

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10. Spacelimbus

Behold! My drawing skills!

11. Spacelimbus

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 $\tan(y_2)=\frac{11}{x} \rightarrow y_2=\tan^{-1} \left(\frac{11}{x}\right)$

12. Spacelimbus

the rest is calculus,$f'(x)=0 \\ f''(x)<0 \longrightarrow \text{Max}$