PLZZ HELP 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:

A linear model with ordered pairs at 0, 26 and 2, 34 and 4, 34 and 8, 30 and 10, 0 and 12, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet.

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 14 seconds. Use complete sentences to support your answer. (3 points)

Given : 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:

To Find : During what interval(s) of the domain is the water balloon's height increasing

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

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

Solution:

Time  height

0 26

2 34

4 34

8 30

10 0

12 0

from 0 to 2 sec  - the water balloon's height increasing

from 2 to 4 sec  and  10  to 12 sec  water balloon's height staying the same

from 4 to 8 sec decreasing speed =   (34 - 30)/( 8-4)  =  1 ft /sec

from 8 to 10 sec decreasing speed =   (30 - 0)/( 10-8)  =  15 ft /sec

Hence 8 to 10 sec  ,   the water balloon's height decreasing the fastest

the height of the water balloon at 14 seconds.  = 0

as at 10 sec balloon reached ground and will stay on ground only  

Step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

answer: it is a.,b.,d.

step-by-step explanation: