ElectricPavlov

You will get    0= 0 

The work done on an object by a net force equals the change in kinetic energy of the object:

1/2mv^2   originally was    (1/2)  1210 (7.33)^2    = 32505.98 j

                 later was           (1/2)  1210 (1.88)^2   =    2138.31  j   

Work = KEf - KEo  = work done = -30367.67 j

P.S.   a  N-m  IS   a joule    the SI  unit of work.

Potential energy at the top of the slide (mgh) is converted to kinetic enegy at the bottom of the slide (1/2mv^2) ....the difference is the energy lost to friction

mgh = 77(9.81)(42.6 sin42.3)            = 21656.71 j

1/2mv^2 = 1/2(77)(20.3^2)                = 15865.47 j

                                                             ________

DIFFERENCE LOST TO FRICTION = 5791.25 j

Is  '1 and a half ton'   =  1001 lbs   or   3000 lbs?    Wording is unclear......

For compunding QUARTERLY the QUARTERLY (periodic) interest rate would be 17%/4 = 4.25%   (i= .0425)

then    FV = PV (1+i)^n       we want to double PV    ...or  FV = 2

             2 = (1+.0425)^n

           LOG (2) = n LOG (1.0425)

              n= 16.653    PERIODS        Period is 3 months       16.653 x 3 =49.96 months = 4.16 years

For CONTINUOS COMPOUNDING      FV = PV e^(rt)          r= .17  

                                                                 2 = e^(.17 t)

                                                               ln(2) = .17t

                                                                 t= 4.07    years        (it would double about 1 month earlier than the first example)

5x^5 - 80x = 0

5x(x^4-16) = 0      for this to be true,

either    5x= 0        which means  x= 0

or  x^4 - 16 = 0       which means  x^4 = 16    or  x = +- 2           x = 0,2, -2

At   1.92 for 4 apples   each apple costs   1.92/4 = 48 cents

At   4.20 for 10 apples  each apple costs  4.20/10 = 42 cents each

Apples are cheaper if you buy them  10 at a time    .....

You want the line equation   y= mx + b    where m= slope (3/5)

y=3/5 x  + b    to find 'b' , substitute the point you are given (4,-6) to find the value of 'b'

-6 = 3/5 (4) + b

-6 =12/5 +b

-8 2/5 = b

so your equation is    y = 3/5 x -  8 2/5

2 /(2/3) = (2/1) / (2/3) =  2/1 x 3/2 = 6/2 = 3