Question

A kitchen bench is in the shape of a segment of a circle. The segment is bounded by an arc of length 200 cm and a chord of length 160 cm. The radius of the circle is r сm and the chord subtends an angle at the centre of the circle. 200 cm 160 cm NOT TO SCALE rcm rcm (i) Show that 1602 = 2r2(1 - cos 6). (ii) Hence, or otherwise, show that 802 + 25 cos 0 - 25 = 0. (iii) Taking , = n as a first approximation to the value of e, use one application of Newton's method to find a second approximation to the value of 0. Give your answer correct to two decimal places.

Answer 1

ميريامنا = 9 مع ممو Wehave by Coffare Rules 0 -I) AB= OAMOA_20A. OA CASO, 2 = 2( مرد - و (وما - )د2 = ( ) مN = 200 - وما 10 = 10 ہم = ال : he) 25 Substituting in (W = (0) - 8 (عها - ) كو 8 r r = 252 (I-Loso) 60" = 25 (1 - 6)

Wehave flora sot 25 Coso -25 & 10) = 160-258mo Now bay Newton's Method flo) given 0,2K Oo - T - 84-25-25 164 Culosta-1 Sinkeo) 1642 8950 84 +50 4K725 = 25.32 164 87 0.14TC