The parabolic motion is an illustration of a quadratic function
The equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31
<h3>How to model the function?</h3>
Given that:
x stands for time and y stands for height in feet
So, we have the following coordinate points
(x,y) = (5,0), (11,0) and (10,80)
A parabolic motion is represented as:
y =ax^2 + bx + c
At (5,0), we have:
25a + 5b + c = 0
c= -25a - 5b
At (11,0), we have:
121a + 11b + c = 0
Substitute c= -25a - 5b
121a + 11b -25a - 5b = 0
Simpify
96a + 6b = 0
At (10,80), we have:
100a + 10b + c = 80
Substitute c= -25a - 5b
100a + 10b - 25a -5b = 80
75a -5b = 80
Divide through by 5
15a -b = 16
Make b the subject
b = 15a + 16
Substitute b = 15a + 16 in 96a + 6b = 0
96a + 6(15a + 16) = 0
Expand
96a + 90a + 96 = 0
This gives
186a = -96
Solve for a
a = -16/31
Recall that:
b = 15a + 16
So, we have:
b = -15 * 16/31 + 16
b =-240/31 + 16
Take LCM
b =(-240 + 31 * 16)/31
[tex]b =256/31
Also, we have:
c= -25a - 5b
This gives
c= 25*16/31 - 5 * 256/31
Take LCM
c= -880/31
Recall that:
y =ax^2 + bx + c
This gives
y = -16/31x^2 + 256/31x - 880/31
Hence, the equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31
Read more about parabolic motion at:
brainly.com/question/1130127
Your answer is going to be B.y-2=-3/8(x+4)
Answer:
-8.8c + 2.2 OR SOLVED c = 0.25
Step-by-step explanation:
<u>Step 1: Combine like terms</u>
- 5.8c + 4.2 - 3.1 + 1.4c − 5.8c + 4.2 − 3.1 + 1.4c
<em>-8.8c + 2.2</em>
<em />
<u>Step 2: If needed solve for c</u>
-8.8c + 2.2 - 2.2 = 0 - 2.2
-8.8c / -8.8 = -2.2 / -8.8
<em>c = 0.25</em>
<em />
Answer: -8.8c + 2.2 OR SOLVED c = 0.25
Answer:
Zero
Step-by-step explanation:
Since the line is a horizontal line, the slope does not change. The slope is zero.
