Determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial).
1 answer:
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a) The limit of the position of particle when time approaches 2 is
.
b) The velocity of particle is
for all
.
c) The rate of change of the distance between particle and particle
at time
is
.
a) To determine the limit for , we need to apply the following two <em>algebraic</em> substitutions:
(1)
(2)
Then, the limit is written as follows:
The limit of the position of particle when time approaches 2 is
.
b) The function velocity of particle is determined by the <em>derivative</em> formula for the division between two functions, that is:
(3)
Where:
- Function numerator.
- Function denominator.
- First derivative of the function numerator.
- First derivative of the function denominator.
If we know that ,
,
and
, then the function velocity of the particle is:
The velocity of particle is
for all
.
c) The vector <em>rate of change</em> of the distance between particle P and particle Q () is equal to the <em>vectorial</em> difference between respective vectors <em>velocity</em>:
(4)
Where is the vector <em>velocity</em> of particle P.
If we know that ,
and
, then the vector rate of change of the distance between the two particles:
The magnitude of the vector <em>rate of change</em> is determined by Pythagorean theorem:
The rate of change of the distance between particle and particle
at time
is
.
<h3>Remark</h3>
The statement is incomplete and poorly formatted. Correct form is shown below:
<em>Particle </em><em> moves along the y-axis so that its position at time </em>
<em> is given by </em>
<em> for all times </em>
<em>. A second particle, </em>
<em>, moves along the x-axis so that its position at time </em>
<em> is given by </em>
<em> for all times </em>
<em>. </em>
<em />
<em>a)</em><em> As times approaches 2, what is the limit of the position of particle </em><em> Show the work that leads to your answer. </em>
<em />
<em>b) </em><em>Show that the velocity of particle </em><em> is given by </em>
<em>.</em>
<em />
<em>c)</em><em> Find the rate of change of the distance between particle </em><em> and particle </em>
<em> at time </em>
<em>. Show the work that leads to your answer.</em>
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Answer: a) Number of nickels, dimes, and quarters are 80, 120, 300 respectively.
b) The coins are worth of 91 dollars i.e. $91 in the piggy bank.
Explanation:
Since we have given that
For every 2 nickels there are 3 dimes ,
So, their ratio will be 2:3
and for every 2 dimes there are 5 quarters.\,
So, their ratio will be 2:5
Now, we'll first find the ratio of nickles to dimes to quarters i.e.
Nickle Dimes Quarters
2 3
2 5
So, it becomes ,
Nickle : Dimes : Quarters
2×2 : 3×2 : 3×5
4 : 6 : 15
Now, let the number of nickle be 4x
Let the number of dimes be 6x
Let the number of quarters be 15x
According to question,
So, number of nickels is given by
Number of dimes is given by
Number of quarters is given by
As we know that
So, According to our question, we get
Hence,
a) Number of nickels, dimes, and quarters are 80, 120, 300 respectively.
b) the coins are worth of 91 dollars i.e. $91 in the piggy bank.