SECTION II
Only TWO questions should be attempted from this Section.
Mark
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9. (i)lf x = a — b and - = , prove that xy — —ab
y ci b
and that x2 — 2xy = a2 + £2.
If, further, ab — 6 and a2 + 62 = 16, find the values
of x and y. (8)
(ii) From the formula T = 2tt , find T given
^ hg
/* = 16• 5, & = 11 -7, £ = 981, and 77 = 3 • 142. (6)
10. (i) A ball whose diameter is 31 in rests on a horizontal ring
of diameter 2 in. Calculate the distance of the bottom
of the ball below the level of the ring. (7)
(ii) A train is scheduled to travel a 90 mile journey in a
certain time. On a particular day, owing to track
repairs, its average speed was reduced by 4 miles per
hour and it arrived 15 minutes late. How long is the
train scheduled to take for the journey ? (7)
11. (i) Determine the range of values of x between 0° and 180°
for which cos2 x is less than J. (”)
(ii) In carrying out a search, a ship sails from a harbour, H,
north-eastwards to a position, P, and then north¬
westwards to a marker buoy, M, which is situated 1 mile
east and 5 miles north of H.
If HP — x miles, and PM = y miles, prove that
x y = 5 V2.
Obtain a second linear equation for x and y, and hence
or othemise find x and y correct to two decimal places. (°)
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