A farmer needs to enclose three sides. of a pasture with a fence (the fourth side is a cliff wall). The farmer has 95 meters of fence and wants the pasture to have an area of 1125 sq-meters. What should the dimensions of
the pasture be? (For the purpose of this problem, the width will be the smaller dimension (needing two sides);
and the length should be as long as possible.)

Evaluate the discriminant of each equation. tell how many solutions each equation has and whether the solutions are real or imaginary. x^2 + 4x + 5 = 0

Jody bought 20 shares of amazon at the close price of $121.00. she bought 20 more shares a year later at the price of $127.00. two years later, she sold all of her shares at the price of $133.00. her broker charges $50 for each transaction. after all of these transactions, how much money did jody make?

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?