3. An industrial fly-wheel turns so that it is modeled with the function: 2л -t|+15, where h is in metres, and t is in seconds. 0.7 h(t) = 13 cos a) What is the maximum height of a point on the edge of the wheel? a) How long does one rotation of the wheel last? b) If the wheel turns for 10 minutes, how many cycles will the wheel make?

A new car worth $22,000 is depreciating in value by $2000 per year. Complete parts (a) through (c) a. Write a formula that models the car's value, y, in dollars, after x years. b. Use the formula from part (a) to determine after how many years the car's value will be $16,000. c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system Then, show your solution to part (b) on the graph. a. A formula that models the car's value, y, in dollars, after x years is (Type an equation.) b. After years, the car's value will be $16,000. (Type a whole number.) c. Choose the correct graph below. OA. OB. Oc. OD. Ay 22,000 Ay 10+ 10- 22,000- 0+ 10 2200 2200 Click to select your answer(s). P Type here to search A 4) C PrtSc Insert Delete F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F1 F2 @ & Backspace

The pressure (P) inside a cylinder is inversely proportional to the volume (V) of gas it contains. When the volume of gas is 50 ml, the pressure is 400 kPa.   a) Determine a function that represents the pressure (P) as a function of the volume (V).   b) Determine the pressure when the volume is 75 ml.   c) Explain, using the equation found in a), how the pressure inside the cylinder will be when the volume of the gas becomes very large.

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)

4. Max can earn $6/h as a waiter, plus an additional $9/h in tips. a) Graph Max's earnings from wages as a function of hours worked. Cb) Graph Max's earnings from tips as a function of hours worked. ) Develop an algebraic and a graphical model for Max's total earnings. d) How much can Max earn if he works 52 h in one week?

The yearly profit, "P" of your store can be estimated by the function P(n)=15n-45,000 where "n" is the number of items you sell per year, and P is measured in dollars. A) what is your estimated profit if you sell 5,280 items this year? B) Estimate the number of items you must sell to make $150,000 profit? C) Estimate the number of items you must sell to break even ($0 profit)

Suppose that there are initially 75 bacteria in a colony and after 3 hours, there are 300 bacteria in the colony.Assuming exponential growth, how many bacteria are there after 7 hours? Round to the nearest whole number.