In Fig.23, `O A\ a n d\ O B` are opposite rays: (i) If `( i i ) (iii) x=( i v ) (v) 25^(( v i )0( v i i ))( v i i i ) , (ix)` (x) what is the value of `( x i ) (xii) y ? (xiii)` (xiv) (xv) If `( x v i ) (xvii) y=( x v i i i ) (xix) 35^(( x x )0( x x i ))( x x i i ) , (xxiii)` (xxiv) what is the value of `( x x v ) (xxvi) x ? (xxvii)` (xxviii)

Convert the following polar coordinates to its equivalent Cartesian coordinates. (i) ( i i ) (iii)2,pi)( i v ) (v) (ii) ( v i ) (vii)(( v i i i ) (ix)sqrt(( x )2( x i ))( x i i ) , (xiii)pi/( x i v )6( x v ) (xvi) (xvii))( x v i i i ) (xix) (iii) ( x x ) (xxi)(( x x i i ) (xxiii)-3,-( x x i v )pi/( x x v )6( x x v i ) (xxvii) (xxviii))( x x i x ) (xxx)

Convert the following points from polar coordinates to the corresponding Cartesian coordinates. (i) ( i i ) (iii)(( i v ) (v)2, (vi)pi/( v i i )3( v i i i ) (ix) (x))( x i ) (xii) (ii) ( x i i i ) (xiv)(( x v ) (xvi)0, (xvii)pi/( x v i i i )2( x i x ) (xx) (xxi))( x x i i ) (xxiii) (iii) ( x x i v ) (xxv)(( x x v i ) (xxvii)-sqrt(( x x v i i i )2( x x i x ))( x x x ) , (xxxi)pi/( x x x i i )4( x x x i i i ) (xxxiv) (xxxv))( x x x v i ) (xxxvii)

In Fig.78, we have (i) ( i i ) (iii)/_M L Y=2/_L M Q , (iv) (v) find ( v i ) (vii)/_L M Q (viii) (ix) (x) ( x i ) (xii)/_X L M=( x i i i ) (xiv)(( x v ) (xvi)2x-10 (xvii))^(( x v i i i )0( x i x ))( x x ) (xxi) (xxii) and ( x x i i i ) (xxiv)/_L M Q=x+( x x v ) (xxvi) 30^(( x x v i i )0( x x v i i i ))( x x i x ) , (xxx) (xxxi) find ( x x x i i ) (xxxiii) xdot( x x x i v ) (xxxv) (xxxvi) ( x x x v i i ) (xxxviii)/_X L M=/_P M L ,\ ( x x x i x ) (xl) find ( x l i ) (xlii)/_A L Y (xliii) (xliv) (xlv) ( x l v i ) (xlvii)/_A L Y=( x l v i i i ) (xlix)(( l ) (li)2x-15 (lii))^(( l i i i )0( l i v ))( l v ) ,\ /_L M Q=( l v i ) (lvii)(( l v i i i ) (lix) x+40 (lx))^(( l x i )0( l x i i ))( l x i i i ) , (lxiv) (lxv) find ( l x v i ) (lxvii) xdot( l x v i i i ) (lxix)

Given points P(2,3),Q(4,-2),a n dR(alpha,0) (i) Find the value of ( i i )alpha( i i i ) (iv) if ( v ) (vi) P R+r Q (vii) (viii) is minimum (ix) Find the value of ( x )alpha( x i ) (xii) if ( x i i i ) (xiv)|( x v ) P R-R Q|( x v i ) (xvii) is maximum

(v) (1-i) ^ (2) (1 + i) - (3-4i) ^ (2)

Convert the following Cartesian coordinates to the corresponding polar coordinates using positive r and negative rdot (i) ( i i ) (iii)(( i v ) (v)-1,1( v i ))( v i i ) (viii) (ii) ( i x ) (x)(( x i ) (xii)2,-3( x i i i ))( x i v ) (xv)

Convert the following Cartesian coordinates to the corresponding polar coordinates using positive r and negative rdot (i) ( i i ) (iii)(( i v ) (v)-1,1( v i ))( v i i ) (viii) (ii) ( i x ) (x)(( x i ) (xii)2,-3( x i i i ))( x i v ) (xv)

In Fig. 7.8, O A" "=" "O B a n d" "O D" "=" "O C . Show that (i) ( i i ) (iii)DeltaA O D~=DeltaB O C (iv) (v) and (ii) ( v i ) (vii) A D" "||" "B C (viii) (ix)

Number of four-digit numbers of the form N=a b c d which satisfy following three conditions (i) ( i i ) (iii) 4000lt=N<6000 (iv) (v) (vi) ( v i i ) N (viii) (ix) is a multiple of 5 (x) ( x i ) (xii)3lt=b