Written Homework 2 1 4 1 5 2 1 Page 1 of 2 Math 140 PRINT YOUR NAME From the questions below please choose and solve 10 problems only The homework is worth 10 points Show all of your work and put a box around your nal answer Number each attempted question clearly Write legibly that is suitably large and suitably dark if the grader can t read your answer it s consider uncompleted Question 1 During the winter a smart thermostat is set to adjust the temperature on a 24 hour cycle It is programmed to reach a maximum of 71 F at 8PM and a minimum of 65 F at 8AM Let T t be the thermostat setting t hours after midnight a Find a possible formula for T t b At what times throughout the day is the thermostat set to 69 F Question 2 Find all solutions of the following equations a 5 cos 2x 3 sin 2x 3 b 20 90 sin cid 0 3 t 2 cid 1 100 c cos 6x 1 d 8 cos 5x 3 4 3 Question 3 During a year the length of a day from sunrise to sunset in Taloga Oklahoma varies from a short est day of approximately 9 6 hours to a longest day of approximately 14 4 hours while in Mon treal the day lengths vary from 8 3 hours to 15 7 hours For each location determine a function cid 19 cid 18 2 365 L t 12 A sin t that approximates the length of a day in hours where t represents the day in the year assuming t 0 is the spring equinox on March 21 Compare the day lengths in each location on April 15 July 30 and November 15 Question 4 A particular persons height oscillates throughout the day with a period of 24 hours Their average height is 170 cm and their maximum height is 173 cm At 4 AM their height is 170 cm and increasing a Find a possible formula for h t their height in cm t hours after midnight b Find a time when their height equals 169 cm Question 5 Sketch the graph y 2 sin 2 x 1 on 0 2pi Calculate the amplitude period mid line maximum and minimum value and the x intercepts cid 16 cid 16 cid 17 cid 17 2 cid 18 a sin Question 6 Find each value cos 1 1 3 cid 18 sin 1 3 7 cot 1 5 2 b tan c cos cid 18 cid 19 cid 19 cid 19 Math 140 Written Homework 2 1 4 1 5 2 1 Page 2 of 2 Question 7 Sketch the graph of the following functions State the domain and range for these functions a y arcsin x b y arccos x c y arctan x Question 8 A ball dropped from a state of rest at time t 0 travels a distance s t 4 9t2 m in t second a How far does the ball travel during the time interval 2 2 5 b Compute the average velocity over 2 2 5 c Compute the average velocity over 2 2 01 d Compute the average velocity over 2 2 005 e Compute the average velocity over 2 2 001 f Compute the average velocity over 2 2 0001 g Estimate the instantaneous velocity over t 2 Question 9 Use the sketch of y x below to nd a the of instantaneous rate of change at x 7 b the average rate of change on 0 3 HW2Picture1 png Question 10 Find an equation of the tangent line to the curve y x3 the point 2 8 Do not use derivative to calculate the slope of the tangent line Question 11 Draw a graph of a function y f x where the instantaneous velocity at t 2 is very di erent from the average velocity between t 2 and t 5 Question 12 Draw a graph of a function y f x so that the instantaneous velocity at t 2 is the same as the average velocity between t 2 and t 5