PS5: Problem 6 Previous Problem Problem List Next Problem (1 point) The pressure P and volume V of an expanding gas are related by the formula PV* = C, where b and Care constants (this holds in adiabatic expansion, without heat gain or loss). Find " if b = 1.4, P = 10kPa, V = 130cm, and = 20cm /min. dP kPa/minPS5: Problem 7 Previous Problem Problem List Next Problem (1 point) In the study of ecosystems, predator-prey models are often used to study the interaction between species. Consider populations of tundra wolves, given by W(t), and caribou, given by C(t), in northern Canada. The interaction has been modeled by MP the equations - do it = aC - bCW, dt -cW + dCW. (a) What values of dC/dt and dW / dt correspond to stable populations? (b) Suppose a = .05, b = .01, c = .05, d = .0001. After finding population pairs (W, () that lead to stable populations, is it possible for the species to live in balance or both species become extinct? Answer "b" for balance and "e" for extinction. (a (bPS5: Problem 8 Previous Problem Problem List Next Problem (1 point) The price (in dollars) p and the quantity demanded q are related by the equation: p- + 2q- = 1100. If R is revenue, dR can be expressed by the following equation: an = dp it dit where A is a function of just q. A Find when q = 5 and = 5. dR Request a HintPS5: Problem 9 Previous Problem Problem List Next Problem (1 point) Evaluate the integral using an appropriate substitution. + 0PS5: Problem 10 Previous Problem Problem List Next Problem (1 point) Find the following integral. Note that you can check your answer by differentiation. (t + 4)2 dt =