This new table is 39 inches tall. The ant is looking down at his ant friend with an angle of depression of 21 degrees. What is the straight line distance (hypotenuse) between the ant and his friend?

Abag contains 10 white golf balls and 6 striped golf balls. a golfer wants to add 112 golf balls to the bag. he wants the ratio of white to striped gold balls to remain the same. how many of each should he add?

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?

Let f of x equals the integral from 1 to 3 times x of the natural logarithm of t squared. use your calculator to find f″(1).