An empty building's temperature on a cold morning drops to 48 degree at 1: 00 a. m. at that time the furnace is turned on with the thermostat set at 66 degree. the time constant for the building is 2 hours and for the building along with its heating system is 1/4 hour. assuming that the outside temperature varies as a cosine wave with a maximum 54 degree at 1: 00 p. m. and a minimum of 27 degree at 1: 00 a. m., set up the initial value problem (with initial condition) that describes this problem. do not solve this ivp.

Dee used 2 1/3 cups of sugar for a cake recipe. if the amount of sugar the container holds is 3 times the amount she used, does the container hold more than, less than, or equal to 3 cups of sugar? explain.

Idon’t understand this.. will someone ? will mark brainliest along with 20 points.

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d.what is the height of the tide after 93 hours?