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.

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.

answer is x<