Calculus

A rotating beacon is located 1 kilometer off a straight shoreline. If the beacon rotates at a rate of 3 revolutions per minute, how fast (in kilometers per hour) does the beam of light appear to be moving to a viewer who is 1/2 kilometer down the shoreline.

I need to show work, so formatting answers in this manner would be most appreciated. Thanks in advance! :) :)

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  1. Evaluate the limit as h -> 0 of:

    [tan (pi/6 + h) - tan(pi/6)]/h

    I thought the answer was √3/3, or tan(pi/6, but apparently that is wrong, any tips here?

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  2. Sorry, I mean to make a new question, disregard above 'answer'.

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  3. Gee, now you're going to make people who open this topic think the answer has already been provided. Thanks a ton...

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  4. You're a .

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  5. tan(θ)=x/1
    cos(θ)=1/sqrt(x^2+1)
    sec^2(θ)=x^2+1

    dθ/dt=3 rev/min=6π rad/min

    x=tan(θ)
    dx/dt=sec^2(θ) dθ/dt

    At x=0.5 km

    dx/dt=(0.5^2+1)*6π=23.6 km/min=1414 kph

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