If two parallel lines are intersected by a transversal, prove that the bisectors of the two pairs of interior angles enclose a rectangle.

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Solve : x + y = 18; y + z = 12; z + x = 16
Let x+y=18---(1), y+z=12---(2),z+x=16---(3) Solving (2)-(3) we get y+z-z-x=12-16 y-x=-4--(4) Solving (4)+(5) we get x+y+y-x=18-4 2y=14 y=14/2=7 Substitute y value in (1) x+7=18 x=18-7=11 Substitute x value in (3) z+11=16 z=16-11=5 x=11, y=7, z=5
Deepak
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The radius of a hemisphere is r. What is its volume?

 

Volume of hemisphere of radius r=(2πr³)/3 =Half of the volume of full sphere ((4πr³)/3) = 2π/3 times of volume of cube of side r.
Shradha
Solve : 55x + 52y = 217; 52x + 55y = 217
subtract two equations from each other, we get x=y and then substitute x=y in any of the equation we get values for x and y . x=1.972 ,y= 1.972
Deepak
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