The position function of a particle is given by:
The velocity function is the derivative of the position:
The particle will be at rest when the velocity is 0, thus we solve the equation:
The coefficients of this equation are: a = 2, b = -9, c = -18
Solve by using the formula:
Substituting:
We have two possible answers:
We only accept the positive answer because the time cannot be negative.
Now calculate the position for t = 6:
By the polynomial remainder theorem, because <em>x</em> = 2<em>i</em> is a zero of <em>f(x)</em>, we have no remainder upon dividing <em>f(x)</em> by <em>x</em> - 2<em>i</em>.
Computing the quotient yields
Then if the remainder term is 0, follows that <em>a</em> = -12.
Answer:
The correct answer is .
Step-by-step explanation:
There are 135 people in a sport centre.
Let the experiment be to pick a person from the sport centre who only uses exactly one of the facilities.
Total number of possible outcomes = 135
For the gym:
77 people use the gym.
27 people use the gym and the pool.
31 people use the gym and the track.
4 people use all three facilities.
Total number of people using only the gym are 77 - ( 27 + 31 + 4) = 15
For the swimming pool:
62 people use the swimming pool.
27 people use the gym and the pool.
23 people use the pool and the track.
4 people use all three facilities.
Total number of people using only the swimming pool are 62 - ( 27 + 23 + 4) = 8
For the tracks:
65 people use the track.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
Total number of people using only the tracks are 65 - ( 23 + 31 + 4) = 7
A person is selected at random.
Favorable outcomes = 7 + 8 + 15 = 30
Probability that the person uses exactly one of the facilities = =
.