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In Exercises 55−60, verify that
55.
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- Explain, in terms of linear approximations, why theΒ approximation is reasonable.Β ln 1.05 = 0.05 (1.01)6=1.06.arrow_forwardFind the linear approximation of f(x)=lnβ‘x at x=7 and use it to approximate lnβ‘(7.05). Β L(x)=? x + ? lnβ‘(7.05) β ?arrow_forwardIn a study of a marine tubeworm, scientists developed a model for the timeΒ TΒ (measured in years) required for the tubeworm to reach a length ofΒ LΒ meters. On the basis of their model, they estimate that 170 toΒ 250 yearsΒ are required for the organism to reach a length ofΒ 2 meters,Β making this tubeworm the longest-lived noncolonial marine invertebrate known. The model is given below. TΒ =Β 20ebLΒ βΒ 28 b Β HereΒ bΒ is a positive constant that requires estimation. What is the value ofΒ bΒ if an estimate ofΒ 175Β yearsΒ to reach a length ofΒ 2 metersΒ is correct? (Round your answer to two decimal places.) bΒ =Β Β What is the value ofΒ bΒ if an estimate ofΒ 230Β yearsΒ to reach a length ofΒ 2 metersΒ is correct? (Round your answer to two decimal places.) bΒ =arrow_forward
- AΒ 631-kg elevator starts from rest and moves upward forΒ 3.30Β s with constant acceleration until it reaches its cruising speed,Β 1.76Β m/s. (a) What is the average power of the elevator motor during this period?Β hp(b) How does this amount of power compare with its power during an upward trip with constant speed? (Give the power during an upward trip with constant speed.)Β hparrow_forwardA tank contains 175 liters of fluid in which 20 grams of salt is dissolved. Brine containing 0.75 gram of salt per liter is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. What is the exponent of e in the integrating factor if qin is the inflow rate? Select one: a. (Inflow rate divided by tank volume) b. (Inflow rate divided by outflow rate) c. (Inflow rate divided by outflow concentration) d. (Outflow rate divided by tank volume) Which of the following statements is TRUE about the mixture model? Select one: a. The solution to the mixture model is obtained using the separation of variables. b. In a steady state system, the inflow is equal to the outflow. c. The value of k is positive. d. In an unsteady state system, the inflow is equal to the outflow. How much salt in grams is in the tank in 30 minutes? Select one: a. 106.70 b. 13.888 c. 165.69 d. 34.781 e. 235.96 f. 64.731 At what time in minutes will the concentration ofβ¦arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage