(a) Show that y Superscript 8 Baseline plus x minus 3 equals 0 is an implicit solution to StartFraction dy Over dx EndFraction equals negative StartFraction 1 Over 8 y Superscript 7 EndFraction on the interval (negative infinity comma 3 ). (b) Show that xy Superscript 9 Baseline minus xy Superscript 9 Baseline cosine x equals 1 is an implicit solution to the differential equation StartFraction dy Over dx EndFraction equals StartFraction (negative x sine x plus cosine x minus 1 )y Over 9 (x minus x cosine x )EndFraction on the interval (0 comma 2 pi ). (c) To verify the solution and the interval, convert y Superscript 8 Baseline plus x minus 3 equals 0 to explicit function(s). yequals RootIndex 8 StartRoot x plus 3 EndRoot (Use a comma to separate answers as needed.)

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.

Reagan lives five miles farther from school than vanessa lives. write an expression to describe how far reagan lives from school

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =