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Mathematics
Study Set
Calculus Concepts and Contexts
Exam 4: Extension E: Applications of Differentiation
Path 4
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Question 1
Multiple Choice
A piece of wire 10 m long is cut into two pieces.One piece is bent into a square and the other is bent into an equilateral triangle.How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.
Question 2
Essay
Find an equation of the line through the point (8,16) that cuts off the least area from the first quadrant.
Question 3
Multiple Choice
Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L = 9 cm if one side of the rectangle lies on the base of the triangle. Round your answer to the nearest tenth.
Question 4
Multiple Choice
A woman at a point A on the shore of a circular lake with radius
wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time.She can walk at the rate of
and row a boat at
How should she proceed? (Find
) .Round the result,if necessary,to the nearest hundredth.
Question 5
Multiple Choice
Find the point on the line
that is closest to the origin.
Question 6
Short Answer
The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares?
Question 7
Short Answer
Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length L = 8 and width W = 3.
Question 8
Short Answer
A farmer with 710 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.What is the largest possible total area of the four pens?