(a) The Celsius scale is devised so that is the freezing point of water (at 1 atmosphere of pressure) and is the boiling point of water (at 1 atmosphere of pressure). If you are more familiar with the Fahrenheit scale, then you know that water freezes at and boils at Find a linear equation that relates temperature measured in degrees Celsius and temperature measured in degrees Fahrenheit. (b) The normal body temperature in humans ranges from to Convert this temperature range into degrees Celsius.
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Suppose the number of phone calls arriving at a switchboard per hour is Poisson distributed with mean 3 calls per hour. (a) Find the probability that at least one phone call arrives between noon and 1 P.M. (b) Assuming that phone calls in different hours are independent of each other, find the probability that no phone calls arrive between noon and 2 P.M.
In Problems we consider communities composed of two species. The abundance of species 1 at time t is given by N1(t), the abundance of species 2 at time t by N2(t). Their dynamics are described by Assume that when both species are at low abundances their abundances increase and that f1 and f2 change sign when crossing their zero isoclines. In each problem, determine the sign structure of the community matrix at the nontrivial equilibrium (indicated by a dot) on the basis of the graph of the zero isoclines. Determine the stability of the equilibria if possible. See Figure 11.66.
In Problems use Lagrange multipliers to find the answers to the indicated problems in Section 5.4. Problem 9 (REFERENCE PROBLEM 9) A rectangle has its base on the x-axis, its lower left corner at (0, 0), and its upper right corner on the curve y = 1/x. What is the smallest perimeter the rectangle can have?