1. If (1,2),(4,y),(x,6) and (3,5) are the vertices of a parallelogram taken in order, find x and y.

Find the point on the curve y=x^3-3x whose tangent parallel to the chord joining(1,-2)and(2,2)

x(y-x)dy=y(y+x)dx

Solve for x and y:
0
x y
a b
 
ax + by = a2 + b2

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Z=20x+10y,x+2y<28 and 3x+y<24,x>2,x,y>0