A right-angled triangle has shorter side lengths exactly c2−b2c2−b2 and 2bc2bc units respectively, where bb and cc are positive real numbers such that cc is greater than bb. Find an exact expression for the length of the hypotenuse (in appropriate units).

A motor boat is set to head north-east from the mainland to the near island, lying approximately 15 km away. The journey should take 25 minutes.If a tide of 2 km/h flows from a north-north-west direction and the wind blows from the south-east at 30 km/h, determine, using complex numbers, the maximum speed and the direction the boat should be headed.

Find the dimensions of the rectangular dog park producing the greatest enclosed area given 260 feet of fencing. The dimensions of each pen will be feet by feet Enter an integer or decimal number [more..]