Answer:
-11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
Step-by-step explanation:
12 and 13 are exempt because the opposite is -11 is 11, and all others above -11 and below 11 are the integers.
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
Answer:
<h3>1. t=10</h3><h3>2. t=4</h3><h3>3. t=40</h3>
Step-by-step explanation:
Isolate the term of t from one side of the equation.
<h3>1. 4t=40</h3>
First, you have to divide by 4 from both sides.
4t/4=40/4
Solve.
Divide the numbers from left to right.
40/4=10
<h3><u>
t=10</u></h3>
<h3>2. 10+t=14</h3>
<u>First, change sides.</u>
t+10=14
<u>Then, subtract by 10 from both sides.</u>
t+10-10=14-10
<u>Solve.</u>
<u>Subtract the numbers from left to right.</u>
14-10=4
<h3><u>
t=4</u></h3>
<h3>3. 70-t=30</h3>
First, subtract by 70 from both sides.
70-t-70=30-70
Solve.
30-70=-40
<u>Rewrite the problem down.</u>
-t=-40
Divide by -1 from both sides.
-t/-1=-40/-1
<u>Solve.</u>
<u />
<u>Divide the numbers from left to right.</u>
-40/-1=40
<h3><u>
t=40</u></h3>
- <u>Therefore, the correct answer is t=10, t=4, and t=40.</u>
I hope this helps! Let me know if you have any questions.
<h2>
Answer: He can make <u><em>
24</em></u>
mats.</h2>
Step-by-step explanation:
10 yards is equal to 360 inches. If you divided 360 inches by 15 inches, the answer will be 24. So the answer is 24 mats.
