(i) Is the binary operation *, defined on set N, given by a * b = for all a,b N, commutative?
(ii) Is the above binary operation * associative?
Let Express A as sum of two matrices such that one is symmetric and the other is skew symmetric.
Show that the rectangle of maximum area that can be inscribed in a circle is a square.
Let a rectangle ABCD be inscribed in a circle with radius r.
Let A be the area of the rectangle ABCD.
Therefore, by the second derivative test, is the point of the local maxima of A.
So, the area of the rectangle ABCD is the maximum at
Now,
Hence, the rectangle of the maximum area that can be inscribed in a circle is a square.
Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height h is