The position of a particle on the x-axis at time t, t > 0, is s(t) = ln(t) with t measured in seconds and s(t) measured in feet. what is the average velocity of the particle for e ≤ t ≤ 2e? a. ln2 b. the quotient of 1 and the quantity of 3 times c. the quotient of the natural logarithm of 2 and e d. the quotient of the natural logarithm of 2 and 2

Option: C is the correct answer.

C. the quotient of the natural logarithm of 2 and e .

Step-by-step explanation:

We are given a function s(t) that denotes the the position of a particle on the x-axis at time t, t > 0, as:

Now we are asked to find the average velocity of the particle for e ≤ t ≤ 2e.

We know that the average velocity is defined as the ratio of total distance to total time.

Now total distance covered in e ≤ t ≤ 2e is:

( Since, )

Also, total time is:

Hence, average velocity is:

Option: C is the correct answer.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

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step-by-step explanation: