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Boats A and B are positioned in the ocean as shown in the figure . Measurements are in miles . Boat A 4 (0,400) The image shows the boat from In-Class Activity 17.B at two different moments as it is being reeled to the (1 and a2 . These lengths form the hypotenuses and legs , respectively , of two right triangles. In each case . Boat B (200.0) We will develop a formula for the change in distance AD - D2 - D, in terms of Aa - az - a1. This moves horizontallys to relate the speed at Boat A is traveling south at 40 miles per hour and Boat B is traveling east at 60 miles per hour. Part A: Use the Pythagorean theorem to provide the squares of the distances below, using the labels Part A: What is the initial distance between the boats? In the figure, the initial distance is indicated by the straightline connecting the boats. ( D2 ) 2 - Hint ( D1 ) 2 - Answer: miles Part B: Subtract the equations you generated for Part A. The constant terms should cancel. (D, ) 2 - Part B: What is the position of Boat A after 2.5 hours? Give your answer as an ordered pair. - (D, )2 - Hint (D 2 ) 2 - ( 1 1 ) ? - [ Answer: Part C: The left and right sides of your equations should each be differences of the left and right sides of your equation. ctored as x' - 12 - (x -yXx ->). Factor Part C: What is the position of Boat B after 2.5 hours? Answer : Answer: art D: Notice that the differences AD - D2 - D, and Aa - a2 - @) are factors in your equation. Part D: What is the distance between the boats after 2.5 hours? eplace each difference with its respective symbol. Hint Answer: Part E: Each difference shown in Part D is a change in distance. If we divide each side by At, we arrive at an equation that relates the speed that the cable is moving Ay . to the speed of the boat. Ar- Write the result of this division, Part E: If A D represents the difference in the distances from Parts A and D. and At is the time that Answer: assed, the average rate of change for the distance between the boats is What is the average rate of change in the distance between the boats over the 2.5-hour time period? Hint Part F: Solve the equation for the speed of the boat At mithr Search Table of Contents , Unit 4 : Preparing for Calculus with Rates of Change, Optimization, Related Rates ) Lesson 17 , 17.0 Seismic Waves -(D, ) - bread gundy theword from the Doing of origin The waves created by RF2_17C_Preview when and secondary s waves ) that price can be modeled approximately by circles of increasing ro (D2) 2 - (D, ) ? - lar with radius'r' and circumference"c Part C: The left and right sides of your equations ch be differences of two squared RF2_17C_Preview the left and reference of squares. like x' - y', can always be factored as x? - y? = (x + y)(x ->). Factor Score: 0/2 0/2 answered . Question 1 Answer: Part D: Notice that the differences AD - D2 - D, and Ad - a2 -a, are factors in your equation. replace each difference with its respective symbol. Answer: Part E: Each difference shown in Part D is a change in distance, if we divide each side by Af, we arrive at an equation that relates the speed that the cable is the cable is moving. Ay to the speed of the boat, Hint Write the result of this division. Part A: Give the formula for the circumfe Answer: Answer: Part B : Give the formula for the area enc Part F: Solve the equation for the speed of the boat, By using the scales on the *" and Answer: Hint Part C: When the radius of Answer: Use your formula to deteren son IS D, = 13 feet, and the boat is being reeled in at 2 feet se your formula to determine the average speed of the boat during the first 1.75 seconds of travel. Calculator Part D: When the radius of the wave is 2.3" miles, what is the ft/sec Answer: can Help: Messpee Instructor an: Your formula can be used for an instantaneous (no Submit Question velocity when it is 0.25 feet is the velocity at a single moment. Give the boat's instantaneous place . from the dock (aj - a2 - 0.25). Round your answer to the hundredths fu/sec Question Help: Message instructor Calculator PhotoG