The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds: Part A: During what interval(s) of the domain is the water balloon's height increasing? (2 points) Part B: During what interval(s) of the domain is the water balloon's height staying the same? (2 points) Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer. (3 points) Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds. Use complete sentences to support your answer. (3 points)

A)0 sec to 2 sec

B) 2 sec - 3 sec.

C)During 3 to 4  secs water balloon's height decreasing the fastest

D)The height of the water balloon at 16 seconds is 0

Step-by-step explanation:

Given : A linear model with ordered pairs at 0, 60 and 2, 80 and 3, 80 and 4, 20 and 6, 0 and 7, 0 and 8, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet.

x            y

0          60

2          80

3          80

4          20

6          0

7          0

8          0

A) During what interval(s) of the domain is the water balloon's height increasing

We can refer the table balloon height increasing from 60 to 80 and then starts decreasing

So, interval = 0 sec to 2 seconds

So, interval(s) of the domain is the water balloon's height increasing  is 0 sec to 2 sec

B) During what interval(s) of the domain is the water balloon's height staying the same

We can see that for 2  to 3  secs the height of the balloon is remaining same 80

So, interval(s) of the domain is the water balloon's height staying the same  is 2 sec - 3 sec.

C)During what interval(s) of the domain is the water balloon's height decreasing the fastest

During 3 to 4  - Decrease = 60 ft/s

During 4 to 6  - Decrease = = 10 ft/sec  

During 3 to 4  secs water balloon's height decreasing the fastest

D: Use the constraints of the real-world situation to predict the height of the water balloon at 16 seconds

After 6 secs balloon has reached ground so it will remain on ground

Hence  the height of the water balloon at 16 seconds is 0

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

is this part of a question or something