Aparticle moves on a line away from its initial position so that after t hours it is s = 4t^2 + t miles from its initial position. find the average velocity of the particle over the interval [1, 4]. include units in your answer.

Average velocity is 21 miles/hr

Step-by-step explanation:

Given a particle moving away from its initial position

Position after t hours that is

                    s(t) = 4 + t

We have to find the average velocity of the particle over the interval [1,4]

Average velocity =

             Distance travelled =

                                             = s(4) - s(1)

                                             = 4 + 4 - 4 -1

                                             =  63 miles

                Time elapsed = 4 - 1 = 3

Average velocity =

                             = 21 miles/hr

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct