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Answers by Dr Gulshan S.

25 Cos 2t +12 Sin (t+pi/2) + 2 Cos2 t = 25 Cos2 t - 25 Sin2 t  + 12 Cos t + 2 Cos2 t  = 27 Cos 2 t  -25 Sin2 t + 12 Cos  t = 52 Cos2 t -25 + 12 Cos t 

Let X = Normal selling price Price after discount = X - 0.2X =0.8 X Ley Y be the buying price of trader  The profit originally was X-Y New Profit = 0.8X- Y =0.04 (X-Y) 0.76X = 0.96Y X/Y = 1.263 (X-Y)/ Y is fractional profit multiplied by 100 will give original percent...

tan(theta)  =8/6 = 4/3 Where theta is the angle with horizontal when x = 6m = y/x(as y= 8m when x= 6 m) y=4/3(x)     dy/dt =( 4/3) dx/dt  Speed on wall =( 4/3 ) speed on ground = (4/3) 0.5 =2/3 m/s = Speed on the wall  

Word Problem (answer)

Let R1 = rate of flow of water from pipe 1 ( Volume flowing per hour) and V = volume of tank  R1 = V/t1 = V /4 For pipe 2 R2 =  V/ 6   T = time when both pipes are used  T = V / (R1 + R2) T = V/ ( V/4 + V/6 ) Time taken = 2.4 hrs...

6x(2y-3) -(2y-3) =12xy-18x -2y+3  =6x(2y -3) - 1* (2y-3) Taking (2y-3) as common   it is = (6x-1)(2y-3)