The tide is the regular rising or falling of the ocean’s surface. This is due in large part to the gravitational forces of the moon. The following table represents water level of the tide off the coast of Kings Point, N. Y., for a 24 hour period, February 9th through February 10th of 2009. Hour
Measurement in feet above the average low tide
0
-0.98
2
5.83
4
7.78
6
7.34
8
2.33
10
-0.47
12
-0.21
14
5.32
16
8.83
18
8.31
20
3.80
22
-0.28
24
0.53

Use your graphing calculator to produce a sine regression model for the data in the table. Round a, b, c, and d to the nearest 0.001.
a.
y = 0.519 sine (4.974 x minus 3.965) + 0.812
b.
y = 4.974 sine (0.519 x minus 0.812) + 3.965
c.
y = 0.519 sine (4.974 x minus 0.812) + 3.965
d.
y = 4.974 sine (0.519 x minus 3.965) + 0.812

What is true about the dilation? it is a reduction with a scale factor between 0 and 1. it is a reduction with a scale factor greater than 1. it is an enlargement with a scale factor between 0 and 1. it is an enlargement with a scale factor greater than 1.

Find the values of the variables in the kite

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).