Consider a point with rectangular coordinates (x, y). If x<0 then the polar coordinates of the point are (r,θ) where r≥0 and −π/2≤θ<3 π/2and:

r=

θ=

If x≥0 then the polar coordinates of the point are (r,θ) where r≥0 and −π/2≤θ<3 π/2 and:

r=

θ=​

The weight of an object in a particular scale is 175.2 lbs. the measured weight may vary from the actual weight by at most 0.1 lbs. what is the range of actual weights of the object

The table below shows the angle measurements for triangle abc and triangle xyz. if triangle abc is similar to triangle xyz, what does angle z equal, in degrees?

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?