7. On Planet Math, Veronica is skipping. The height of her feet while skipping, can be modelled by the equation y(x) = sin²x + 2sinx + 1, where y is the height of Veronica's feet above from the ground in centimetres, and x is the time of the number of seconds that have passed since Veronica started jumping. a) How many times does Veronica's feet hit the ground in the first 25 seconds? b) How many centimetres is Veronica off the ground after 3 seconds?

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)

A ferris wheel has a radius of 28 feet and completes 3 revolution in 1.5 minutes. Assume the nder begins at the lowest point of the wheel, 2 feet above ground level. Model the height of the rider, in feet above the ground, as a function of time in seconds, using a sine equation with only positive numbers in the final equation.