PLS HELP I WILL GIVE BRAINLIEST 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).

Step-by-step explanation:

Domain of the rainbow is (-∞,+∞), which represents the horizontal distance of the rainbow, though it is reasonable to say that the real-world domain is [-6,6]

Range of the rainbow is (-∞,36], which represents the height of the rainbow from the ground, though it is reasonable to say that the real-world range is [0,36]

The y-int is (0, 36), and it represents the maximum of the rainbow's height

The x-intercepts are (-6,0) and (6,0), which represent the points on the ground at which the rainbow ends end.

the table:

x      y

-4   20

0     36

slope: (36-20)/(0-(-4))=16/4=4

function: y=4x+36

The function I've created is positive, since it represents the ascend of the plane and has a slope of 4

The solutions to the system of equations I've created are:

(-4,20) which represents the point 20 meters up in the air where the plane flew through the rainbow the first time

(0,36) which represents the point 36 meters up the air where the plane flew through the rainbow the final second time

f(x):

10 if x<0

-0.1x^2+10 if 0<x≤10

0 if>10

This piece wise function represents a slide of a person from a 10 ft slide, where it is 0 ever after, due to it being the ground

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

the first one, all those points on the line just make a strait line.