According to kepler's first law, a comet should have an elliptic, parabolic, or hyperbolic orbit (with gravitational attractions from the planets ignored). in suitable polar coordinates, the position (r,ϑ) of a comet satisfies an equation of the form r=β+e(r⋅cosϑ) where β is a constant and e is the eccentricity of the orbit, with 0≤e< 1 for an ellipse, e=1 for a parabola, and e> 1 for a hyperbola. suppose observations of a newly discovered comet provide the data below. determine the type of orbit, and predict where the comet will be when ϑ=4.6 (radians).3 ϑ.881.101.421.772.14 r3.002.301.651.251.01

Part one: measurements 1. measure your own height and arm span (from finger-tip to finger-tip) in inches. you will likely need some from a parent, guardian, or sibling to get accurate measurements. record your measurements on the "data record" document. use the "data record" to you complete part two of this project. name relationship to student x height in inches y arm span in inches archie dad 72 72 ginelle mom 65 66 sarah sister 64 65 meleah sister 66 3/4 67 rachel sister 53 1/2 53 emily auntie 66 1/2 66 hannah myself 66 1/2 69 part two: representation of data with plots 1. using graphing software of your choice, create a scatter plot of your data. predict the line of best fit, and sketch it on your graph. part three: the line of best fit include your scatter plot and the answers to the following questions in your word processing document 1. 1. which variable did you plot on the x-axis, and which variable did you plot on the y-axis? explain why you assigned the variables in that way. 2. write the equation of the line of best fit using the slope-intercept formula $y = mx + b$. show all your work, including the points used to determine the slope and how the equation was determined. 3. what does the slope of the line represent within the context of your graph? what does the y-intercept represent? 5. use the line of best fit to you to describe the data correlation.

17. a researcher measures three variables, x, y, and z for each individual in a sample of n = 20. the pearson correlations for this sample are rxy = 0.6, rxz = 0.4, and ryz = 0.7. a. find the partial correlation between x and y, holding z constant. b. find the partial correlation between x and z, holding y constant. (hint: simply switch the labels for the variables y and z to correspond with the labels in the equation.) gravetter, frederick j. statistics for the behavioral sciences (p. 526). cengage learning. kindle edition.

Find the value of x. give reasons to justify your solutions! l, m ∈ kn