CHAPTER 2 Derivatives 114 14. If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters) after t seconds is given by H = 10t - 1.86t2. (a) Find the velocity of the rock after one second. (b) Find the velocity of the rock when t = a. (c) When will the rock hit the surface? %3D (d) With what velocity will the rock hit the surface? 15. The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = where t is measured in seconds. Find the velocity of the particle at times t = a, t = 1, t = 2, and t = 3. 1/t², %3D 16. The displacement (in feet) of a particle moving in a straight line is given by s =t- 6t + 23, wheret is measured in seconds. (a) Find the average velocity over each time interval: (i) [4, 8] (iii) [8, 10] (b) Find the instantaneous velocity whent=8. (c) Draw the graph of s as a function of t and draw the secant lines whose slopes are the average velocities in part (a). Then draw the tangent line whose slope is the instanta- neous velocity in part (b). (ii) [6, 8] (iv) [8, 12] %3D 17. For the function g whose graph is given, arrange the following numbers in increasing order and explain your reasoning: 0. g'(-2) g'(0) g'(2) g'(4)
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Question 14
![CHAPTER 2 Derivatives
114
14. If a rock is thrown upward on the planet Mars with a velocity
of 10 m/s, its height (in meters) after t seconds is given by
H = 10t - 1.86t2.
(a) Find the velocity of the rock after one second.
(b) Find the velocity of the rock when t = a.
(c) When will the rock hit the surface?
%3D
(d) With what velocity will the rock hit the surface?
15. The displacement (in meters) of a particle moving in a
straight line is given by the equation of motion s =
where t is measured in seconds. Find the velocity of the
particle at times t = a, t = 1, t = 2, and t = 3.
1/t²,
%3D
16. The displacement (in feet) of a particle moving in a straight
line is given by s =t- 6t + 23, wheret is measured in
seconds.
(a) Find the average velocity over each time interval:
(i) [4, 8]
(iii) [8, 10]
(b) Find the instantaneous velocity whent=8.
(c) Draw the graph of s as a function of t and draw the secant
lines whose slopes are the average velocities in part (a).
Then draw the tangent line whose slope is the instanta-
neous velocity in part (b).
(ii) [6, 8]
(iv) [8, 12]
%3D
17. For the function g whose graph is given, arrange the
following numbers in increasing order and explain your
reasoning:
0.
g'(-2)
g'(0)
g'(2)
g'(4)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F811d810c-f7c9-4ab4-8127-0a3c29b20bba%2F60983d56-0cfa-4a08-ac71-b307d6940f4f%2Fg75de7.jpeg&w=3840&q=75)
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