CPhill

6,9,9,4,7 to make 544

9!/6!  +  4! + 9 + 7   =

504 + 24 + 16  =

504  + 40  =

544

Here's the Calculus approach.........first, solve the volume in terms of h

300 = pi*r^2 *h

h = [300] /[pi*r^2]  .......now....substitute this into the surface area "formula"

S_area  =  2pi*r^2  +  2pi*r*h

S_area  = 2pi*r^2 + 2pi*r* [300]/[pi*r^2]

S_area = 2pi*r^2  + 600r^(-1)      ....take the derivative with respect to r......

S' _area =  4pi*r - 600r^(-2)    .....set this to 0

4pi*r - 600r^(-2) = 0

4pi*r  = 600r^(-2)

pi*r  = 150r^(-2)

r^3   = 150/pi

r = (150/pi)^(1/3)   = about 3.628     .....as Solveit found .......

And h = 300/ [pi * 3.628^2]  = about 7.255

And the minimum surface area would be just as Solveit found......

|-5(5)+12| =

|-25 + 12|  =

|-13 |  =

13

25 + 2*15 [ 1 - .6^7] / [ 1 - .6 ]  = 97.9 m

74 = a₁ + d(5 - 1)  →    74 = a₁ + 4d    (1)

1460 = a₁ + d(71 - 1) →   1460  = a₁ + 70d   (2)

Subtract (1) from (2)

1386  = 66d  divide both sides by 66

21 = d

Using (1)

74  = a₁ + 21(4)

74  = a₁ + 84      subtract 84 from both sides

-10  = a₁

The general formula is :

a_n  = -10 + 21(n - 1)

13th term   =

-10 + 21 (13 - 1)

-10 + 21 (12)  =

242

592 is the greatest integer divisible by 4 that is less than 595

28  is the next integer after 27 that is divisible by 4

So......the number of multiples is given by :  592/4 + 28/4  + 1   =  148 - 7 + 1  =  142

x^3   = 125      take the cube-root of both sides

x  = 5  

36   =  a₁ + d ( 6 -1)      →  36 = a₁ + 5d       (1)

113 =  a₁  + d ( 17 -1)  →  113  = a₁ + 16d   (2)

Subtract (1) from (2)

77  = 11d     divide both sides by 11

7 = d

And using (1)  to find a₁, we have

36 = a₁+ 5(7)

36 =  a₁  + 35         so........a₁ must = 1

And

a₂₃  = 1 + 7(23 -1)

a₂₃  = 1 + 7(22)

a₂₃  = 155

( [80000 - 76000] / 80000) x 100%  =    5%  reduction

16x^2 + 24x + 9  =     take the square root of the first and last terms and separate them with a plus..........enclose this in parentheses and exponentiate it to the second power

 square root of 16x^2  = 4x

square root of 9  = 3    

(4x + 3) ^2       .....and that's it........