MATH 140 Lecture Notes - Lecture 13: Pythagorean Theorem, Ellipse

• School: University of Maryland
• Department: Mathematics
• Course: MATH 140
• Professor: Gulick

Document Summary

Practice problems: what we want to find, solution, known values and equations, (cid:498)a spherical bubble grows at a rate of (cid:884)(cid:3030)(cid:3040)(cid:3119)(cid:3046) . One second after the dog rate is the distance d changing one second after the cat begins its travelling? (cid:499) leaves, a cat starts from the same point and travels east at 8 feet per second. At what: after t seconds after the cat moves, the dog moves at 10(t+1, knowns, knowns, want to find, solution: feet/second and the cat moves at 8t feet/second above the ground and travels horizontally eastward. The string is being let out at 2 feet per second. Find the horizontal speed of the kite when 125 feet of string are let: (cid:4666)(cid:883)(cid:4667, pythagorean theorem: (cid:4666)(cid:1872)(cid:4667)= (cid:4666)(cid:883)(cid:882)+(cid:883)(cid:882)(cid:1872)(cid:4667)(cid:2870)+(cid:4666)8(cid:1872)(cid:4667)(cid:2870)= (cid:883)(cid:882)(cid:882)+(cid:884)(cid:882)(cid:882)(cid:1872)+(cid:883)(cid:882)(cid:882)(cid:1872)(cid:2870)+(cid:888)(cid:886)(cid:1872)(cid:2870)= (cid:883)(cid:888)(cid:886)(cid:1872)(cid:2870)+(cid:884)(cid:882)(cid:882)(cid:1872)+(cid:883)(cid:882)(cid:882) (cid:2870) (cid:2869)(cid:2874)(cid:2872)(cid:3047)(cid:3118)+(cid:2870)(cid:2868)(cid:2868)(cid:3047)+(cid:2869)(cid:2868)(cid:2868)(cid:4666)(cid:885)(cid:884)8(cid:1872)+(cid:884)(cid:882)(cid:882)(cid:4667: derive: (cid:4666)(cid:1872)(cid:4667)= (cid:2869, plug in t = 1: (cid:4666)(cid:1872)(cid:4667)= (cid:2870) (cid:2872)(cid:2874)(cid:2872) (cid:883)(cid:884). (cid:884)(cid:887)(cid:3033)(cid:3047)(cid:3046) (cid:2870) (cid:2874)(cid:2872)(cid:4666)(cid:2869)(cid:3118)(cid:4667)+(cid:2870)(cid:2868)(cid:2868)(cid:4666)(cid:2869)(cid:4667)+(cid:2869)(cid:2868)(cid:2868)= (cid:2873)(cid:2870)(cid:2876) (cid:2871)(cid:2870)(cid:2876)(cid:4666)(cid:2869)(cid:4667)+(cid:2870)(cid:2868)(cid:2868, (cid:498)the spool of a kite is held fixed at 5 feet above the ground.