Project: Explain the mathematics of roller coaster construction. Imagine you are a roller coaster designer, and are asked to mathematically represent the curve of the first drop of a new ride. By looking at some of your favorite coasters, you determine that the optimal slope for the ascent, when the car is being pulled up the slope by a chain, is 0.7. The slope of the first drop that will be the most thrilling (without being dangerous) is –1.5. You decide to connect these two straight stretches, y = L1 and y = L2 , with a parabola of the form y = f(x) = ax 2 + bx + c, where x and f(x) are measured in meters. In order for the curve of the track to remain smooth, you must make sure that the linear segments, L 1 and L2 , have the same slope at each endpoint of the parabola, points P and Q. This ensures that the parabola is differentiable, as well as continuous at the endpoints. Choose point P, the left endpoint of your parabola, as your origin, to simplify calculations.

Micah solves a linear equation and concludes that x = 0 is the solution. his work is shown below. (1 – 3x) = 4(– + 2) 0 = x which statement is true about micah’s solution?

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 a flying disk is 139 meters in the air and travels at an average of 13 m/s how long is it in the air