Ajeweler is dividing 3/8 of a pound of rubies among 4 lots. what part of a pound will each lot weigh?
annual rate = 6 %/yr
monthly rate = ¹/₁₂ × 6 = 0.5 %/mo
if you invested $100 at 6 % annual simple interest, you would have $106 at the end of the year.
simple interest is calculated only on the principal.
if the interest were calculated at 0.5 % monthly simple interest, you would get $0.50 at the end of each month. at the end of 12 mo, you would have $106.
5. y=6; de=7; fg=8
6. x=4.2; jl=14.2; mn=13
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.
4(x+3) is 4x+12
-2x from both sides
-12 from both sides
divide by 2 to both sides
simplify equation to get (1/3)y + 11= -1 then solve for
(1/3)y = -12