An open-top box is created by cutting out corners from a piece of cardboard as pictured below. Find a function that models the surface area as a function of x.

Outside temperature over the course of a day can be modeled as a sinusoids function. Suppose the temperature is 50 degrees at midnight and the high temperature for the day will be 60 degrees and low will be 40 degree ax Assuming t is the number of hours since midnight, find a function for the temperature, D, in terms of t.

During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)

The water from an outdoor fountain follows a path that is shaped like a parabola. The arch created by the water is 32 inches wide and 27 inches high. If the arch were 32 inches wide but 44 inches high, how could you modify your function W to model the new arch? Explain or show your reasoning.