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Ankoret Group Title

nearsighted cow classic calculus problem

  • 2 years ago
  • 2 years ago

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  1. IsTim Group Title
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    Are we suppose to find the derivative of its sight?

    • 2 years ago
  2. lgbasallote Group Title
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    maybe the integral of its periphery

    • 2 years ago
  3. Ankoret Group Title
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    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.

    • 2 years ago
  4. mickifree12 Group Title
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    is this an optimization problem?

    • 2 years ago
  5. mickifree12 Group Title
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    also it would help if you gave us more information

    • 2 years ago
  6. Ankoret Group Title
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    yes, optimization. hang on, getting more info.

    • 2 years ago
  7. Ankoret Group Title
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    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.

    • 2 years ago
  8. AmberADamas Group Title
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    12-5=×

    • 2 years ago
  9. Spacelimbus Group Title
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    |dw:1343007462718:dw|

    • 2 years ago
  10. Spacelimbus Group Title
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    Behold! My drawing skills!

    • 2 years ago
  11. Spacelimbus Group Title
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    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 \[ \tan(y_2)=\frac{11}{x} \rightarrow y_2=\tan^{-1} \left(\frac{11}{x}\right)\]

    • 2 years ago
  12. Spacelimbus Group Title
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    the rest is calculus,\[ f'(x)=0 \\ f''(x)<0 \longrightarrow \text{Max}\]

    • 2 years ago
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