ElectricPavlov

.....but the question states he cannot get anyone to do it !    So  no combos ?

I thought the original answer was correct.....since no other one would do it and Tim had to do it himself.....there are no other combos ????/

6 + thirteen d's = 32

13d = 26

d = 2         

3rd term is 6   next is  8     10    12   14  16  18 20  22 24 26  28 30 32=16th term

1st term is   6 - 2 -2 = 2

Sum_n = n/2 (a₁ + a_n)

          = 20/2 (2 + 40) = 420

For the average length of the two pieces of string.... add them together and divide by 2

(1.5 + 4.5) / 2=

6/2 = 3 inches average

If you are not in calculus, you may not know how to do the deriviative of the function.

This is a bowl shaped parabola (because the leading coefficient is positive)

   the minumum value of the fiunction will occur at an 'x' value of   - b/2a  

        where  b =  -12    and   a = 5

    Use THIS 'x' value in the equation to calculate the minumum value ('y') of the function.....

Put the equations into    y = mx + b     form     m = slope    if  m is the same in both equations, they are parallel

First one

2x + 3y = 4k

3y = -2x + 4k

y = -2/3 x + 4/3 k

Second one

x - 2ky=7

2ky = x-7

y = 1/(2k) x  - 1/(2k) *7

Now for the lines to be parallel     -2/3 = 1/(2k)      solve for 'k'

Use the first point ,  0,5     to find the value of  'c'

    then use the second set of points to find an equation with 'a' and 'b'  in it

       use the third set of points to find ANOTHER equation with 'a' and 'b' in it

                then use the two equations to solve for 'a' and 'b' via elimination or substitution. 

                        Re-post if you need more help....     Go !  

Allen finishes in 12 seconds

    Bruce still has 3 seconds to go to reach the finish his 15 second run

          so Bruce still has  3/15 of the race to go    3/15 x 100 = 20 m left to run

rise / run = 3% = .03

x/ 1800 = .03

x = 54 m

COmmon ratio    r      1st term 6    multiplied by common ratio yields second term

                                        so   r = -1

this sequence just bounces back and forth between  6    and  -6  

    even numbered terms are negative  (like the second term above)

       odd numbered terms are positive

205 th term would be   +6