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Answer:
The motion of the particle describes an ellipse.
Step-by-step explanation:
The characteristics of the motion of the particle is derived by eliminating in the parametric expressions. Since both expressions are based on trigonometric functions, we proceed to use the following trigonometric identity:
(1)
Where:
(2)
(3)
By (2) and (3) in (1):
(4)
The motion of the particle describes an ellipse.
Answer:
N(1)=50 is a minimum
N(15)=4391.7 is a maximum
Step-by-step explanation:
<u>Extrema values of functions </u>
If the first and second derivative of a function f exists, then f'(a)=0 will produce values for a called critical points. If a is a critical point and f''(a) is negative, then x=a is a local maximum, if f''(a) is positive, then x=a is a local minimum.
We are given a function (corrected)
(a)
First, we take its derivative
Solve N'(t)=0
Simplifying
Solving for t
Only t=1 belongs to the valid interval
Taking the second derivative
Which is always positive, so t=1 is a minimum
(b)
N(1)=50 is a minimum
(c) Since no local maximum can be found, we test for the endpoints. t=1 was already determined as a minimum, we take t=15
(d)
N(15)=4391.7 is a maximum