Asingle conservative force vector f = (4.0x - 12)i hat n where x is in meters, acts on a particle moving along an x axis. the potential energy u associated with this force is assigned a value of 20 j at x = 0. (a) write an expression for u as a function of x, with u in joules and x in meters.

(4.0x - 12)i . (5/3)i

Step-by-step explanation:

Potential energy = Workdone

Workdone = Force x distance

Force = F = (4.0x - 12)i  N

Workdone = 20J

At  x= 0

F = -12i

/F/= 12

Workdone = Force  x distance

20  =   12 x   distance

Distance =  20/12

               =  5/3

In the vector form  distance is written as (5/3)i

Since Workdone/ Energy is scalar, U can be expressed as a dot product of  the vectors of Force and distance :

(4.0 x - 12)i . (5/3)i

correct answer:

b.(19,-2)

answer: - (a)

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term=

second term=

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula :

b)   let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

∴there are 88 seats in 12 rows.