The complex number 16 has the following roots calculated. 1st root (k = 0): 2 left-bracket cosine (StartFraction 0 pi Over 4 EndFraction) + I sine (StartFraction 0 pi Over 4 EndFraction right-bracket 2nd root (k = 1): 2 left-bracket cosine (StartFraction 2 pi Over 4 EndFraction) + I sine (StartFraction 2 pi Over 4 EndFraction right-bracket 3rd root (k = 2): 2 left-bracket cosine (StartFraction 4 pi Over 4 EndFraction) + I sine (StartFraction 4 pi Over 4 EndFraction right-bracket

  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.

the first question mark is 6 and the second question mark is 26 (the square root)

step-by-step explanation:

30

step-by-step explanation:

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i hope i

i am unable to solve this problem

step-by-step explanation: