. A 230 V generator supplies three phase power to a balanced load at rated current of 18 A and power factor of 85%. What is the power delivered by the generator?
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- 1. A cement grinding mill “A” with a capacity of 50 tons/hr utilizes forged steel grinding balls costing P12,000/ton, which have a wear rate of 100 grams/ton cement milled. Another cement mill “B” of the same capacity uses high chrome steel grinding balls costing P50,000/ton with wear rate of 20 grams/ton cement milled. Determine the more economical grinding mill, considering other factors to be the same.(1) A certain appliance is designed to operate at no less than 9/2% below its nameplate voltage and at no more than 6% above its nameplate voltage. If the nameplate voltage is 120 v, what are the minimum and maximum voltages at which this appliance can operate?The radiator in a car is filled with a solution of 55% antifreeze and 45% water. The manufacturer of the antifreeze suggests that for summer driving, optimal cooling of the engine is obtained with only 50% antifreeze. If the capacity of the radiator is 3.3 L, how much coolant should be drained and replaced with water to reduce the antifreeze concentration to the recommended level?
- 2.) Consider an M/M/2 system with an arrival rate of 9 per minute and a service rate of 8 per minute. What is the average time a customer spends in the system? Take your answer to three decimal places. Omit the units in your answer.Consider the following tank-water system. Tank A holds 200 liters of water, initially pure. Brine with a concentration of 3 grams of salt per liter flows into tank A at 5 liters per minute. The solution flows out of tank A into tank B at a rate of 5 liters per minute. Tank B is a 125 liter tank of initially pure water which receives the outflow from tank A, and the well-mixed solution flows out of tank B at 5 liters per minute. Write down a system of differential equations that models the scenario.∫ 3e^(5t) dt
- According to one hypothesis, the growth rate dV/dt of a cell’s volume V is proportional to its surface area A. Since V has cubic units such as cm3 and A has square units such as cm2, we may assume roughly that A ∝ V 2/3, and hence dV/dt = kV 2/3 for some constant k. If this hypothesis is correct, which dependence of volume on time would we expect to see (again, roughly speaking) in the laboratory? (a) Linear (b) Quadratic (c) CubicSuppose that a healthy population of some species is growing in a limited environment and that the current population P0 is fairly close to the carrying capacity M0. You might imagine a population of fish living in a freshwater lake in a wilderness area. Suddenly a catastrophe such as the Mount St. Helens volcanic eruption contaminates the lake and destroys a significant part of the food and oxygen on which the fish depend. The result is a new environment with a carrying capacity M1 considerably less than M0 and, in fact, less than the current population P0. Starting at some time before the catastrophe, sketch a “before-and-after” curve that shows how the fish population responds to the change in environment.2.21 The manufacturing company in Problem 2.20 also produces electric insulators. If the insulators break when in use, a short circuit is likely to occur. To test the strength of the insulators, destructive testing in high-powered labs is carried out to determine how much force is required to break the insulators. Force is mea- sured by observing how many pounds must be applied to the insu- lator before it breaks. The force measurements, collected from a sample of 30 insulators and stored in Force , are:1,870 1,728 1,656 1,610 1,634 1,784 1,592 1,662 1,866 1,764 1,734 1,662 1,550 1,756 1,762 1,866 1,820 1,744 1,810 1,752 1,680 1,810 1,652 1,7361,522 1,696 1,734 1,774 1,788 1,688a. Constructafrequencydistributionandapercentagedistribution. b. Construct a cumulative percentage distribution. c. What can you conclude about the strength of the insulators ifthe company requires a force measurement of at least 1,500 pounds before the insulator breaks?