Find the expressions for the unit vectors in cylindrical coordinate system, p, φ,2. in terms of x, ý, 2. find the time-derivative of each. hints: unit vector p is defined in (x, y) plane. remember that α -φ is perpendicular to a the easiest way to find φ is to express rho through φ and add 90 degrees

Researchers conducted an experiment to identify the effects of three different hand sanitizers on the growth of bacteria. the researchers grew one type of bacteria in twenty-four identical covered petri dishes. then, they opened eighteen petri dishes and applied the three hand sanitizers to six petri dishes each. they left the remaining six petri dishes closed as a control group. when the researchers measured the growth of bacteria two days later, the six dishes that had no hand sanitizer showed the least amount of bacterial growth. the researchers concluded that not using any hand sanitizer would lead to the least bacterial growth. which statement best explains why the researchers’ conclusion was not justified? the experiment tested too many variables. the control group was not treated the same as the experimental group. the sample size of twenty-four petri dishes is not large enough. the single type of bacteria is not adequate to make any conclusions.