If an object is projected upward from ground level with an initial velocity of 48ft per sec, then its height in feet after t seconds is given by s(t)= -16t^2+48t. Find the number of seconds it will take to reach its maximum height. What is this maximum height? The object will take __ second(s) to reach its maximum height. (Simplify your answer.) The maximum height reached by the object is __ feet. (Simplify your answer.)

t = 1.5 s and s(t) = 36 feet

Step-by-step explanation:

The height reached by an object as a function of time t is given by :

...(1)

t is in seconds

To find the maximum height, put

It will take 1.5 seconds to reach its maximum height.

Put t = 1.5 s in equation (1), such that,

The maximum height reached by the object is 36 feet.

step-by-step explanation:

107 units

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for