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6. Derive a power balance equation for the RL and RC circuits. (see Problem 5) Discuss the significance of the signs of the three power terms.
5. The power generated or dissipated by a circuit element equals the voltage across the element times the current through the element. Show that the power dissipated by a resistor equals
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Fundamentals of Differential Equations and Boundary Value Problems
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forward3. According to Hooke's law, the force F required to stretch a spring x units beyond its natural length is directly proportional to x. a. Write an equation which expresses the relationship between F and x. b. Suppose that it takes a force of 8 pounds to stretch a spring 8 centimeters long to a new length of 10.5 centimeters. Find the value of the constant of proportionality k, which is known as the spring constant. c. How much weight is needed to stretch the spring described in (b) to a length of 10.8 centimeters?arrow_forward1. If rxty = +1 and rx2y = -1, can you tell what happens to rxy when we combine x1 and x2 into a new variable? Make and provide your own data for your demonstration.arrow_forward
- Analyze the problem and determine what particular gas laws to be applyarrow_forward4. Coffee at temperature 180°F is cooling in a room with constant temperature 75°F. If it takes for the coffee temperature to reach 155°F after 5 minutes, what additional time is needed for the coffee to cool to 130°F?arrow_forward8. It is thought that the period T of a planet's year is related to r, its mean distance from the sun, by an equation of the form T = Kr" where k and n constants. If T is measured in Earth-years and r in astronomical units of distance, the values for the six inner planets are: r T Mercury 0.3871 0.2408 Venus 0.7233 0.6152 Earth 1.000 1.000 Mars 1.524 1.881 Jupiter 5.203 11.86 Saturn 9.539 29.46 Use natural logarithms to plot these values as an approximate straight line. From your graph of In T against In r find the gradient of the graph and hence the values of n and k.arrow_forward
- Eliminate the arbitrary constants on the given equationarrow_forward4. Newton's Law of cooling states that the rate at which a body changes temperature is proportional to the difference between its temperature and that of the surrounding medium. If a body is in air temperature 35° and the body cools from 120° to 60° in 40 minutes, find the body temperature after 100 minutes. 5. There are 100 gal of brine in a tank and the brine contains 70 Ibs of dissolved salt. fresh watr runs into the tank at the rate of 3 gal/min, and the mixture kept uniform by stirring, runs out at the same rate. How many pounds of salt are there in the tank at the end of 1 hr?arrow_forwardf(x) = 2x? + 2x + 4 a) Find f'(x). 4x+2 b) Identify the graph that displays f in blue and f' in red. 10 A. 10 1.0 10 -10 10 F10 10 -10 10 B.arrow_forward
- 17. The amount of germs in a certain culture increases at a rate proportional to the number present. If the amount of germs doubles every year, how many years will the number of germs tripple? ONCS 22. A. 1.952 C. 2.568 B. 4.214 919W zgniblori D. 1.585 18. A surveyor, standing S 65° W of a tower measures the angle of elevation of the top of the tower as 46° 30'. From a position S 67° E from the tower the elevation of the top is 37°15'. Determine the height of the tower if the distance between the two observations is 75 m. A. 32.5 m C. 36.2 m D. 43.5 m 88 B. 39.7 m 19. A spherical balloon is inflated with helium at the rate of 100m ft³/min. How fast is the surface area increasing (in ft2/min) at the instant the radius is 5 ft? A. 30T C. 50T B. 40T D. 45% indi of thearrow_forward2.1 number 22 part a b and c show all the work pleasearrow_forward36. When a cold yam is put into a hot oven to bake, the tem- perature of the yam rises. The rate, R (in degrees per minute), at which the temperature of the yam rises is gov- erned by Newton's Law of Heating, which says that the rate is proportional to the temperature difference between the yam and the oven. If the oven is at 350°F and the tem- perature of the yam is H°F, (a) Write a formula giving R as a function of H. (b) Sketch the graph of R against H.arrow_forward
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