Given the position function, s of t equals t cubed divided by 3 minus 12 times t squared divided by 2 plus 36 times t , between t = 0 and t = 15, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle is moving to the right. (5 points) 0 < t < 6 5 < t < 15 t > 15 the particle always moves to the right.

Option D is correct.

as the particle always moves to the right

Step-by-step explanation:

Given the function:   , 0<t<15;

where

s(t) represent the distance in feet.

t represents the time in second.

Since, when the particle is moving to the right,

⇒ s(t) is increasing.

so,

Find the derivative of s(t) with respect to t;

Use derivative formula:

Simplify:

As

⇒

              [ ]

⇒ this is always true because square of any number is always positive

Therefore, it means that the particle always moves to the right.

- 70

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i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

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