Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified, exact value in terms o
f PI (no approximations). The figures are based on semicircles or quarter circles, and problems (b), (c), and (d) involve portions of a square. Calculate area and perimeter
1 answer:
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Complete Question
The complete question is shown on the first uploaded image
Answer:
The optimal point(i.e the position of P) that will allow Sally to reach the cabin as quickly as possible is from the cabin.
Step-by-step explanation:
From the question we are told that
The speed from the point Sally is standing to the point P is
The speed from the point P to the cabin is
Let denote the distance from the bottom left corner to the P be y ft
Generally according to Pythagoras theorem the distance from Sally's first position to point P is mathematically represented as
Generally the distance from that point P to the cabin is mathematically represented as
Generally the time it takes Sally to cover that distance s is mathematically represented as
=>
Generally the time it takes Sally to cover that distance d is mathematically represented as
=>
So the total time taken is
Generally the minimum time taken with respect to the distance is mathematically evaluated by differentiating and equating the derivative to 0
So
=>
=>
=>
=>
So the distance from point P to the cabin is
=>
So the optimal point(i.e the position of P) that will allow Sally to reach the cabin as quickly as possible is from the cabin
