## Quiz 4 :

Applications of Differentiation

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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.

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The sum of two positive numbers is . What is the smallest possible value of the sum of their squares?

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A car braked with a constant deceleration of 40 , producing skid marks measuring 60 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

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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.

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Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at is , find f (1) .

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Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Round your answer to four decimal places.)

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Find the position function of a particle moving along a coordinate line that satisfies the given conditions. , s (0) = 5, v (0) = 0

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Use Newton's method to approximate the given number correct to eight decimal places.

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Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Round your answer to four decimal places.)

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A particle is moving with the given data. Find the position of the particle. ,

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What constant acceleration is required to increase the speed of a car from 20 ft/s to 45 ft/s in s?

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Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.)

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Find the position function of a particle moving along a coordinate line that satisfies the given condition. , s(1) = -1

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Use Newton's method to approximate the indicated root of in the interval , correct to six decimal places.Use as the initial approximation.

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