There is a famous puzzle called the Towers of Hanoi that consists of three pegs and n circular disks, all of different sizes. The disks start on the leftmost peg, with the largest disk on the bottom, the second largest on top of it, and so on, up to the smallest disk on top. The goal is to move the disks so that they are stacked in this same order on the rightmost peg. However, you are allowed to move only one disk at a time, and you are never able to place a larger disk on top of a smaller disk. Let tn denote the fewest moves (a move being taking a disk from one peg and placing it onto another) in which you can accomplish the goal. Determine an explicit formula for tn.

  5.   y=6; de=7; fg=8

  6.   x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

  y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

  y = 6

of course, the total chord length is the sum of the lengths of its segments.

  de = dh +eh = 3+4 = 7

  fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

  x = lk = mk×nk/jk = 6×7/10 = 4.2

  jl = jk +lk = 10 +4.2 = 14.2

  mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.

2 5/8 is the final answer! : )

hi! i think the answer is 1/2 : )

he can buy 4lbs. of live bait and 1lbs of natural bait

step-by-step explanation: