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Consider the equation z^{11} = (1 + \sqrt{3}\, i). Find the value of z which satisfies this equation and which has the second smallest positive argument \theta, 0 < \theta < 2\pi. Express...

A pack of cards has a 10% chance of containing a rare card. You buy 10 packs of cards. What is the probability that you end up with at least 2 rare cards?

A block of ice in the form of a cube with sides x cm, melts at the rate of 6.45 cm3 per minute. Find the rate of change of x at the instant when x = 10 cm.

The volume of a sphere is increasing at a constant rate of 19.2 pi cm3s-1. Find the radius of the sphere at the instant when the radius is increasing at a rate of 0.3 cm s-1 .

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