ElectricPavlov

I come up with 1 out of 40,320   chance.

nPr =

8P7  = 40320

1st digit  8 choices

2nd        7

3rd         6

4th          5

5th          4

6th          3

7th          2        8x7x6x5x4x3x2 = 40320 possible combinations of which ONE will be 654 5222

The value of sin only goes between  -1 and +1    there is no 2.1 of which to take the inverse sine....sorry ...better take a look at that problem again!

I do not know if this is correct, but I will try    y= sqrt (2x+1)    Gives the RADIUS of the object that is to be rotated       pi r^2 = area  so:

Integral (0-3)  pi (sqrt(2x+1)) ^2  =  pi  integral (0-3)  2x+1       =     pi  (0-3)  1/2x^2  + x  + K     K= Constant (which I THINK we can make '0') 

From 0 to 3

pi ( 4.5 + 3 -0) = pi(7.5) = 23.56    ????????????

I will NOT guarantee this result.      Can anyone verify this?.     We had a question like this sometime back .... (and I got it WRONG then!)

Volume of box = 5184 in^3

Total volume of trailer is  5(12)x4(12)x12(12) = 414720 in^3

Number of boxes to fill will be    414720/5184= 80 boxes to fill with no wasted space

L x W x H = 5184          L must divide into 12 (144 inches) evenly   W into 4 (48 inches)evenly  and H into 5(60 inches) evenly

We can just ASSIGN one of these variables to find the other two....let's make  W= 24 inches

then    L x W x H= 5184

           L x H = 5184/24=216

           L x H = 216                     Let's make H= 12 inches   then L=18

L x W X H = 18 x 24 x 12 =   5184   CHECK !          AND  L= 18  goes into 144   evenly at 8 times

                                                                                           H= 12 goes into 60      evenly at 5 times

                                                                                           W=24 goes into 48      evenly at 2 times      8x5x2= 80 boxes CHECK !

THIS is only ONE possible solution out of MANY !!!!!

Volume of box = 5184 in^3

Total volume of trailer is  5x4x12 x (1728)  cubic inches = 414720 in^3

Number of boxes to fill will be    414720/5184= 80 boxes to fill with no wasted space

L x W x H = 5184          L must divide into 12 evenly   W into 4 evenly  and H into 5 evenly

12/L x 4/W x 5/H = 80

OK.....did a little math and drawing pictures and came up with 50 rows of nickles (actually 50.55)  to a side if you offset the rows so the nickles stack more closely

Ignoring the .55  nicklle in the solution

50 x 50 = 2500 nickles   maximum    = $125.00

...as an addendum to EP above..... If you 'overlap'  (more correctly: 'OFFSET') the nickles row by row, you can get more of them on the table top, but STILL not 2832 of them but MORE than 2209 of them....not sure how to calculate this though.....will se if I can come up with a method.....

186

Kinetic Energy   K.E. = 1/2 mv^2   

KE = 1/2  m (70)^2

110 = 1/2 m 4900

m = 2(110)/4900 =  .04489 kg = 44.89 grams  

1 sq meter is 1000mm x 1000 mm

1000 x 1000  / 353 = 2832.86   (if they were SQUARE and not round)

diameter of a nickel  is   353/pi = r^2   r = 10.6mm     Diameter is  21.2    1000/ (21.2) = 47 nickles to a side    47 x 47 = 2209 nickles  ($110.45)