Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y = 6x + 7 and the parabola y = x^2 about the following lines:

Problem 1: x axis

Problem 2: the line y = 49.

Which logarithmic equation is equivalent to the exponential equation below? e^a=55(you will receive 34 points)

Adaylily farm sells a portion of their daylilies and allows a portion to grow and divide. the recursive formula an=1.5(an-1)-100 represents the number of daylilies, a, after n years. after the fifth year, the farmers estimate they have 2225 daylilies. how many daylilies were on the farm after the first year?

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?