1. Ms. Ortiz sells tomatoes wholesale. The function p(x) = -80x^2 + 320x - 10, graphed below, indicates how much profit she makes on a load of tomatoes if she sells them for 4 - x dollars per kilogram. What should Ms. Ortiz charge per kilogram and tomatoes to make the maximum profit, and what is the maximum profit she can make on a load of tomatoes.

A - $230 at $3 per kilogram

B - $310 at $2 per kilogram

C - $320 at $2 per kilogram

D - $320 at $3 per kilogram

2. A football is kicked into the air from an initial height of 3 feet. The height, in feet, of the football above the ground is given by s(t) = - 16t^2 + 35t + 3, where t is the time in seconds and t ≥ 0. Which is the closest to the time when the football will be 20 feet above the ground.

A - 2.72 seconds

B - 0.73 seconds or 1.46 seconds

C - 0.53 seconds

D - 0.53 seconds or 2.72 seconds

3 through 6 are in a picture below.

An empty bucket is placed under a faucet dripping at a constant rate of 4 milliliters per minute. with the given information, which of these statements is a reasonable conclusion? a there will be 24 milliliters of water in the bucket after 16 hour. b there will be 60 milliliters of water in the bucket after 14 hour. c there will be 160 milliliters of water in the bucket after 20 minutes. d there will be 100 milliliters of water in the bucket after 40 minutes.

For this option, you will work individually. the pythagorean theorem can be used in many real-world scenarios. part 1 write your own real-world scenario where the pythagorean theorem can be applied to find a missing piece. you may choose to write a problem that is two- or three-dimensional in nature. be sure that you will be able to draw a diagram of your scenario. write out your problem and submit it for part 1. be sure to end your scenario with a question. part 2 draw a diagram of the scenario you created in part 1. you may draw by hand and scan and upload your drawing or create a computer-generated drawing for submission. be sure to label all parts and dimensions of the drawing. part 3 solve the question that you posed in part 1. show all of your steps in answering the question. for this option, you will need to submit all three parts for full credit—your real-world problem and question, the diagram that you created, and your work solving the problem, showing all steps. * note that your instructor is looking for your own original idea. while it is acceptable to use the internet for research and inspiration, academic integrity policies apply.

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).