Answer:
Recursive form of sequence is given by f(n) = f(n-1) - 3
Step-by-step explanation:
The explicit form of sequence is given as
f(n) = −3n + 2
So nth term is given by
f(n) = −3n + 2
(n-1)th term is given by
f(n-1) = −3(n-1) + 2
We have
f(n) - f(n-1) = −3n + 2 - (−3(n-1) + 2)
f(n) - f(n-1) = −3n + 2 +3(n-1) - 2
f(n) - f(n-1) = −3n + 2 +3n -3 - 2
f(n) - f(n-1) = -3
f(n) = f(n-1) - 3
Recursive form of sequence is given by f(n) = f(n-1) - 3
The rocket will take 9.25 seconds to return to ground
<em><u>Solution:</u></em>
Given that toy rocket is launched vertically upward from ground level with an initial velocity of 148 ft per second
<em><u>Height "h" after "t" seconds is given by equation:</u></em>
![h(t) = -16t^2 + 148t](https://tex.z-dn.net/?f=h%28t%29%20%3D%20-16t%5E2%20%2B%20148t)
To find: time taken by rocket to return to ground
The time taken by rocket to return to ground is found by substituting h(t) = 0 in above equation
![0 = -16t^2 + 148t](https://tex.z-dn.net/?f=0%20%3D%20-16t%5E2%20%2B%20148t)
First take "t" as common term
![t(-16t + 148) = 0](https://tex.z-dn.net/?f=t%28-16t%20%2B%20148%29%20%3D%200)
Zero product property. The zero product property states that if a⋅b = 0 then either a or b equal zero. This basic property helps us solve equations like (x+2)(x-5) = 0
So for above equation we get,
![t = 0 \text{ or } -16t + 148 = 0](https://tex.z-dn.net/?f=t%20%3D%200%20%5Ctext%7B%20or%20%7D%20-16t%20%2B%20148%20%3D%200)
-16t + 148 = 0
-16t = -148
t = 9.25
When t = 0 , the rocket would not left the ground. So ignore t = 0
So t = 9.25
So the rocket will take 9.25 seconds to return to ground
Answer:
The answer is D- 20/12
Step-by-step explanation: