Point C moves along the top arc of a circle of radius 1 centered at the origin O(0, 0) from point A(

vrotterigzl 2022-06-24 Answered
Point C moves along the top arc of a circle of radius 1 centered at the origin O(0, 0) from point A(-1, 0) to point B(1, 0) such that the angle BOC decreases at a constant rate 1 radian per minute. How does the area of the triangle ABC change at the moment when |AC|=1? Answer: it increases at 1/2 square units per minute. Could you give me a hint how to solve this task? I don't even know what to begin with.
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Answers (2)

stigliy0
Answered 2022-06-25 Author has 21 answers
Say angle B O C is θ. Express the area of triangle A B C in terms of θ (use sin). This is an area A in terms of θ. Find d A d θ .Then find the point where C A = 1 and determine θ at that point. Evaluate d A d θ for that value of θ.
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polivijuye
Answered 2022-06-26 Author has 16 answers
and then use the chain rule to obtain d A d t = d A d θ d θ d t
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