6. Find the period and sketch graph of the function. Show all asymptotes or amplitude if applicable and sketch the fundamental period. y = tan (2.x) a.
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- A Ferris wheel has a radius of 30 m. Its center is 31 m above the ground. It rotates once every 40 s. Suppose you get on the bottom at t = 0. Write an equation that expresses your height as a function of elapsed time. Oh = 31 cos 2T- - O h = 30 cos 2T (t - 40) 40 = (t - 20) 40 Oh 31 cos 2T- = (t - 20) 40 (t – 20) 40 Oh 30 cos 2π- 2T +30 +1 +30 +31Put the function in the form y = ab' and state the values a and b. Enter the exact answers. a = b= M. y = (√5)" 2In a tidal river, the time between high and low tide is 5.8 hours. At high tide the depth of water is 17.7 feet, while at low tide the depth is 4.1 feet. Assume the water depth as a function of time can be expressed by a trigonometric function (sine or cosine). (a) Graph the depth of water over time if there is a high tide at 12:00 noon. Label your graph indicating low and high tide. Select the letter of the graph which best matches your graph. Assume that t = 0 is noon. Choose v A B (b) Write an equation for the depth f(t) of the tide (in feet) t hours after 12:00 noon. f(t) = help (formulas) (c) A boat requires a depth of 8 feet to set sail, and is docked at 12:00 noon. What is the latest time in the afternoon it can set sail? Round your answer to the nearest minute. For example, if you find f(t) = 8 when t = 1.25, you would answer at 1:15 PM (since this is 1 and a quarter hours after noon). D The latest the boat can leave is at PM E
- Suppose that you are on the beach on December 25 and notice that the high tide occurs at 2:00 pm with a depth of 1.6 meters. You then return at 7:00 in the evening and notice it is low tide at 0.2 meters. Since tides vary sinusoidally over time, find a cosine function that represents the depth of the tide as a function of time x measured in hours after 12:00 AM on December 25th. 1a) Draw the graph to represent this situation. Remember that x = 0 represents 12 AM, the beginning of December 25. 1b) Determine the following characteristics of the cosine function from the graph and the given information: > Maximum Value = _____m ? > Minimum Value = _____m ? > Period T = ____hours ? > Horizontal shift (for cosine function) =____hours ? 1c) Now compute the relevant parameters for the equation: > Amplitude A = _____m ? > Average value D = _____m ? > Frequency B = ______ ?In a tidal river, the time between high and low tide is 6.8 hours. At high tide the depth of water is 16.2 feet, while at low tide the depth is 4.1 feet. Assume the water depth as a function of time can be expressed by a trigonometric function (sine or cosine). (a) Graph the depth of water over time if there is a high tide at 12:00 noon. Label your graph indicating low and high tide. A В Select the letter of the graph which best matches your graph. Assume that t = 0 is noon. Choose v (b) Write an equation for the depth f(t) of the tide (in feet) t hours after 12:00 noon. f(t) help (formulas) (c) A boat requires a depth of 8 feet to set sail, and is docked at 12:00 noon. What is the latest time in the afternoon it can set sail? Round your answer to the nearest minute. For example, if you find f(t) = 8 when t = 1.25, you would answer at 1:15 PM (since this is 1 and a quarter hours after noon). The latest the boat can leave is at PM E FA stone is dropped into a lake, creating a circular ripple thattravels outward at a speed of 60 cm/s.(a) Express the radius of this circle as a function of thetime t(in seconds).(b) If A is the area of this circle as a function of the radius,find A °r and interpret it.
- In a tidal river, the time between high and low tide is 6.6 hours. At high tide the depth of water is 15.7 feet, while at low tide the depth is 4.1 feet. Assume the water depth as a function of time can be expressed by a trigonometric function (sine or cosine).(a) Graph the depth of water over time if there is a low tide at 12:00 noon. Label your graph indicating low and high tide. (b) Write an equation for the depth ?(?)f(t) of the tide (in feet) ?t hours after 12:00 noon.?(?)= (c) A boat requires a depth of 8 feet to set sail, and is docked at 12:00 noon. What is the earliest time in the afternoon it can set sail? Round your answer to the nearest minute. For example, if you find ?(?)=8f(t)=8 when ?=1.25, you would answer at 1:15 PM (since this is 1 and a quarter hours after noon).The earliest the boat can leave is at __:__ PMGraph the function y=-sin2x on [-pi,0]The graph attached shows the curves y = x^3 and y^3=x. a.) Explain why both of these curves are functions. b.) For the curve y^3=x, write y as a function of x.
