Problem_116_Solutio.htm

Hi, would like to know if maple commands can replicate/automate this solution.

rsolve({a(n)=9/19*a(n+1)+10/19*a(n-1),a(0)=0},a)

=-9a(1)+9a(1)(10/9)^n

.......?

Question.doc

Can you make geometric figures that hold a particular area within a given perimeter of 12 matches

My attempt was to start at origin 0,0 and move up 1 unit (a,b) and then 1 unit up or to the right (c,d) etc ... until you enclose the required area (defined by linear spline) s.t. perimeter =12. but it doesn't really work

can someone assist me to animate the following:

 A ladder is leaning against a wall. The base of the ladder starts sliding away from the wall, with the top of the ladder sliding down the wall. As the ladder slides, you watch the red point in the middle of the ladder. What figure does the red point trace? (a circle)

does anyone see what i'm doing wrong, trying to solve for n

add(length(i), i = 1 .. n) = 2893;

o/p: Error, unable to execute add

fsolve(sum(length(i), i = 1 .. n) = 2893,n=500..2000);

o/p: n=2893

but if i do a procedure i get the right answer: 

s := 0; for i to 5000 do t := length(i); s := s+t; if s <> 2893 then next else print(i) end if end do;

1000

Start with the numbers 1, 1/2, 1/3, ... , 1/100. Choose any two numbers M and N from this list and replace them by the single number M + N + M x N. Repeat the process until only one number is left.

eq, take pair (1,1/2)-->1+1/2+1*1/2=2

then (2,1/3)-->3 and so on .... and you obtain 100.

Can someone show me procedure to accomplish this, because when i try to do it i get into a tiz