1. the table shows the soil density of several soil samples at different depths.
depth (m)
1
5
6
8
10
12
14
21
23
24
28
soil density ()
1052
1073
1112
1149
1171
1252
1219
1244
1267
1251
1264

(a) write the equation of the regression line that models the data. let x = depth below the surface and let y = soil density. (use the highlighted points to calculate your equation)
(b) use the equation to estimate the soil density of a sample at a depth of 20 m. show your work.

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).