## anonymous 4 years ago nearsighted cow classic calculus problem

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1. IsTim

Are we suppose to find the derivative of its sight?

2. anonymous

maybe the integral of its periphery

3. anonymous

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. anonymous

is this an optimization problem?

5. anonymous

also it would help if you gave us more information

6. anonymous

yes, optimization. hang on, getting more info.

7. anonymous

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.

8. anonymous

12-5=×

9. anonymous

|dw:1343007462718:dw|

10. anonymous

Behold! My drawing skills!

11. anonymous

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. anonymous

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

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