Tutor profile: Eugene H.

A balloon under compression, is loosing volume at the rate of 10 Liters/second. Its initial volume 10000 Liters. How long until the volume of the balloon is equal to 0 Liters.

The rate at which the compressed balloon is loosing volume is 10 Liters/second. The initial volume of the balloon is 10000 liters. The desired value is the time it would take for the volume of the compressed balloon to be equal to 0 Liters. The answer is dividing the initial volume by the rate with respect to time of volume loss which is 10 liters/second. The answer is 1000 seconds.

Explain the concept of getting the complex root(s) of a polynomial equation of degree 2.

Roots of polynomials of degree 2 occur with the term under the square root, gives a negative number. This occurs when b^2-4ac<0 for a polynomial of a*x^2+b*x+c^2. Note: The resultant root would be complex and wouldn't have a corresponding value on a Y-X graph.

Explain the Concept of using the 1st derivative of a function to find possible maxima/minima(s) within a certain interval of the domain of a function?

The 1st derivative can give the possible point within an interval of a domain of a function because it gives where the instantaneous slope of the function goes to zero, where the slope stops changing with respect to the range (dependent variable) within an interval of the domain.