Ronin kicks a ball over the gate of the first floor balcony. The function h(t)=-36t^2+288t+9 can be used to model the height of
1 answer:
Answer: 4 seconds
Step-by-step explanation:
Given: The function can be used to model the height of the ball where t is the time in seconds after the ball kicked and h(t) is the height in feet.
Differentiate the given function with respect to t , we get
Put h'(t)=0
Also,
By second derivative test, h(t) is maximum at t=4.
Hence, the time in Devon which the ball reaches it maximum height = 4 seconds
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If r<1 then the series converges, if r>1 the series diverges and if r=1 the test is inconclusive and we can't assure if the series converges or diverges. So let's see the terms in this limit:
Then the limit is:
We can simplify the expressions inside the absolute value:
Since none of the terms inside the absolute value can be negative we can write this with out it:
Now let's re-writte n/(n+1):
Then the limit we have to find is:
Note that the limit of 1/n when n tends to infinite is 0 so we get:
So from the test ratio r=0.4 and the series converges. Then the answer is the second option.