Calculate effective noise temperature of the system.
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- Lake Ontario has a volume of approximately V =1600 km3. It is heavily polluted by a certain pollutant with a concentration of co = 0.1%.As a part pollution control, the pollutant concentration of the inflow is reduced to cin = 0.02%. The inflow and outflow rates Qin = Qout = Q = 500 km3 per year. Suppose that pollutant from the inflow is well mixed with the lake water before leaving the lake. How long will it take for the pollutant concentration in the lake to reduce to 0.05%?Differentiate: y = v 6x 8x3 - O y' = (3 – 12x²) /6x – 8x3 %3D - 6-2472 O y' = V6z-873 3-122 O y' = V6z-8z3 O y' = (6– 2422) v6x – 8a3 %3D -In an (M/M/1): (/FIFO) queueing model, the arrival and service rates are 2 = 12/hour and μ = 24/hour. Find the average number of customers in the system and in the queue.
- Let us consider a bacterial cell that depends on chemical reactions using oxygen to produce energy. The cell needs to obtain molecular oxygen from the extra-cellular medium by diffusion through the cell membrane. We model the cell as a water-filled sphere of radius 1 µm. This means that we neglect the presence of the internal structures of the cell: nucleus, nutrients, etc. The oxygen diffusion coefficient (O2) in water at 25°C is 1.0x10-5 cm².s'. Figure 1: Transmission electron microscope Reminder: The distance travelled by diffusion can be picture of a bacterium. [from Wikipedia: written as L(t) = v6Dt, where D is the diffusion “Transmission Electron Microscopy"] coefficient and t the diffusion time. People have measured the distance travelled by the oxygen molecule in water as a function of time. The results are given in the table below. 0.05 17.3 0.001 t(s) L (x10“m) log1o(t) log10(L) 0.005 0.01 0.1 2.45 5.4 7.7 25.5 3. Determination of the diffusion coefficient We would like to…x²t Vt3+1 dt dx 1 Select one: a. 2 xt Vt3 +1 dt + x² e2x Ve3x + 1 1. b. e3x /e3x + 1 C. e4x Je3x + 1 d. xt Vt3 +1 dt + x² e* /e3x + 1 Ve3x+ 1 1A ball at 1200K is allowed to cool down in air at an ambient temperature of 300K. Assuming heat is lost only due to radiation, the diferential equation for the temperature of the ball is given by de =-2.2067x10 "(e-81x10), 0) =1200K dt Find the temperature at t=480 geconds using Runge-Kutta 4 order method Assume a step size of =240 seconds.
- A tank initially holds 100 gallons of salt solution in which 50 lbs of salt has been dissolved. A pipe fills the tank with brine at the rate of 3 gpm, containing 2 Ibs of dissolved salt per gallon. Assuming that the mixture is kept uniform by stirring, a drain pipe draws out of the tank the mixture at 2gpm. Find the amount of salt in the tank at the end of 30 minutes. Integrating Factor = Amount of salt in the tank at the end of 30 minutes =larmony Up to 12-hour battery life 14" FHD IPS display Week 14: Chapter 12 - Linear Re X //nightingale.instructure.com/courses/3057255/assignments/28988705?module_item_id%3D62437114 ntable Flash. Question 3 > A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below. Seeds Produced 51 57 51 50 70 70 55 50 Sprout Percent 49.5 54.5 47.5 47 38 41 54.5 47.5 54 a. Find the correlation coefficient: r= Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? v H1: ? 手0 The p-value is: (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically insignificant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the use of the regression line is not…Some of the highest tides in the world occur in the Bay ofFundy on the Atlantic Coast of Canada. At Hopewell Capethe water depth at low tide is about 2.0 m and at high tideit is about 12.0 m. The natural period of oscillation is alittle more than 12 hours and on June 30, 2009, high tideoccurred at 6:45 AM. This helps explain the following modelfor the water depth D (in meters) as a function of the time(in hours after midnight) on that day: D(t) = 7+ 5cos [0.503(t -6.75)])How fast was the tide rising (or falling) at the followingtimes?(a) 3:00 AM (b) 6:00 AM(c) 9:00 AM (d) Noon