The height of a buoy on a lake is changing during a storm. The height's rate of change can be modeled by r(t) = 0.5 cos(0.2t) feet per second where t is measured in seconds. Is the buoy's height increasing or decreasing at time t = 10 seconds? Why?

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Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 5.15 ft at midnight, rises to a high of 10.2 ft, falls to a low of 0.1 ft, and then rises to 5.15 ft by the next midnight. What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the situation? Enter your answer in the box. f (x): %3D Basic 7 8. 9. y Activate Windows Go to Settings to activate W 2 士 2$ CO 3. LO

arcsin (0.3)=

A hot air balloon rising upwards is noticed by an observer who is 4 miles from where it is released. At this exact moment, the angle between the observer's line of sight and the horizontal is pi/3 radians. The angle of elevation is changing at 0.3 radians per minute. How fast is the hot air balloon rising right now?

The Pampanga Eye, in Sky Ranch Pampanga, is the tallest Ferris wheel in the Philippines. It has a diameter of 213 feet. When the Pampanga Eye is in uniform motion, it completes one revolution every 20 minutes, The height h, in feet above the ground, of a person riding on the Pampanga Eye can be estimated by h(t)=118-95 cos (π/10 t) where t is the time in minutes since the person started the ride. a. How high is the person at the start of the ride (t = 0)? b. How high is the person after 15 minutes?

The Eiffel Tower, in Paris France, is approximately 324 meters tall. A camera is 85 meters from the base of the tower and is moving along the horizontal ground away from the tower while keeping the top of the tower in view. What is the camera's horizontal velocity when the angle of elevation (to the top of the tower) is decreasing at 0.11 radians per second? m/s You may round your final response to two decimal places.

The actual temperature inside an oven varies around the selected temperature. This variation can be modeled with a sine function. If the cook selected a temperature of 375°F, then the actual temperature T in the oven is given by T = 5 sin(57x) + 375, where it is the number of hours since the oven first hit the selected temperature of 375°F. What is the highest actual temperature in the oven? 'F What is the lowest actual temperature in the oven? What is the period of this function? Give your answer in minutes. minutes When is the first time the oven will hit the highest temperature? Give your answer in minutes. minutes

cos[arccos(−0.1)]

A camera on the ground is 10 km away from a launch pad. From there it tracks a rocket launched vertically into the atmosphere. At a certain instant, the angle of elevation from the camera to the rocket is 21/3 radians and is changing at a rate of 0.5 radians per second. Determine the rocket's velocity at that instant.