A leading medical journal has claimed that 71% of roller coaster rides get extreme anxiety just before the ride begins. A popula
1 answer:
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The correct answers are:
(1) 6, 11, 16, 21, 26 (Option B)
(2);
(Option A)
(3) (Option D)
Explanations:
(1) Given Sequence:
Now in order to find the first 5 terms, we need to put n=1,2,3,4,5 in the above sequence and solve.
For n=1:
For n=2:
For n=3:
For n=4:
For n=5:
Hence, the first five terms are: 6, 11, 16, 21, 26 (Option B)
(2) Given Sequence:
8, 6, 4, 2, …
Now to find the recursive definition, we need to adopt trial-and-error approach.
As, (meaning the first element of the sequence is 8), the second or nth value of the sequence can be found by using the following formula:
--- (1)
Where, n = the index of the number in a sequence
d = difference between two consecutive numbers = 8-6 = 2
Now,
The second number of the sequence has to be 6 by using (1). Put n = 2 and d = 2 in (1):
Since , therefore,
(correct)
Hence the correct answer is ;
(Option A)
(3) Given Sequence:
−2, 1, 4, 7, …
To find the explicit definition, use the following formula:
--- (X)
Where,
Plug in the values in (X):
(X)=> (Option D)
Answer:
The velocity function is .
The acceleration function is .
When t = 44, the velocity is .
When t = 44, the acceleration is .
Step-by-step explanation:
We know that the position function is given by
Velocity is defined as the rate of change of position or the rate of displacement. If you take the derivative of the position function you get the instantaneous velocity function.
Acceleration is defined as the rate of change of velocity. If you take the derivative of the instantaneous velocity function you get the instantaneous acceleration function.
The instantaneous velocity function is given by
The instantaneous acceleration function is given by
To find the velocity and acceleration when t = 44, we substitute this value into the velocity and acceleration functions