Solve: 5x + y < 100 x + y < 60 x> 0 y > 0?

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By subtracting equation 1 and 2 we get x<10 By 5*second equation and subtracting first we get y<50 so The Solution holds true for all values of 0
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Solving them simultaneously, 4x <40 x<10 y<50
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It is nothing but area of quad with points (0,0), (0,50), (10,0), (10,50).
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|z-3-4i|=7 find the locus of z. sol.we know that in argand plane the complex no. is represented with a pt. compare this equation with |z-q|=r whera q is a complex no. (every real no. is also a complex no.)so Q=(3,4) in argand plane .and z is any point on the argand plane. |z-3-4i| represent the distance of point z from pt.(3,4) in the argand plane or complex plane. this distance is also given in the question =7.so the locus of z is any point from pt.(3,4) which is at a distance 7 from point (3,4).which is represnt a circle.because the circle is a curve traced by a moving point which is moving in such a way that it is at a fixed distance from a fixed pt. while moving.
It can be re written in Cartesian form as (x-3)^2 + (y-4)^2 = 7^2 This is equation of a circle with center at (3,4) and radius equal to 7
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