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.
We have been given that Tim spends about 1/3 of each weekday sleeping and about 7/24 of each weekday in school. And we need to find what fraction of the weekday does Tim spend either sleeping or in school.
This means that we need to find the time he spends in sleeping when he is in the school.
Therefore, we have to add the time he spends in sleeping and the time he spends in school.
Therefore, required fraction is given by
Now in order to add the fractions, we have to make the denominator same.
Multiply the numerator and denominator of first fraction by 8 to make the same denominator.
Now, we have the same denominator hence, we can add the numerator
Therefore, Tim spends 15/24 hours each weekday sleeping in the school.