Manuel has 18 yards of fabric to make table runners. It takes Three-fourths of a yard to make each runner. The expression that r
1 answer:
Inequality helps in comparison. The possible number of table runners that Manuel could make is 20, 22, and 24.
<h3>What is Inequality?</h3>Inequality helps us to compare two unequal expressions to form an equation.
Given to us
Left over cloth = 18 - (3/4)t
In the given equation, t shows the number of table runners that can be made with 18 yards of fabric.
As the total amount of fabric that is used for making must not be more than 18 yards, we can write the equation as,
solving it for t,
Thus, the number of tables runner that can be made with 18 yards of cloth such that the size of the table runner is must be equal to less than 24.
Hence, the possible number of table runners that Manuel could make is 20, 22, and 24.
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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>
To learn more on derivatives, we kindly invite to check this verified question: brainly.com/question/2788760