Using dimensional analysis, show that the planets obey Kepler's third law.
To demonstrate that planets obey Kepler's third law using dimensional analysis, we start with the gravitational force between a planet and the Sun, given by Newton’s law of gravitation:
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Television sets for repair arrive at random at an average rate of 4 per day to a single repairman who takes an average of hours to carry out each repair. It being assumed that the repair times have an exponential distribution. What is the average number of television sets in the workshop? What is the probability that an arriving set will find at least 3 sets in front of it? The repairman works for eight hours a day.
Using dimensional analysis, show that the planets obey Kepler's third law.
Suppose that a given population can be divided into parts, those who have a given disease and can infect others and those who do not have it, but are susceptibles. Let x be the proportion of susceptible individuals and y the proportion of infectious individuals, then x + y = 1. Assume that the disease spreads by contact between sick and well members of the population and the rate of spread is proportional to the number of such contacts. If yo is the initial proportion of infectious individuals then
i) Formulate a mathematical model for the given problem and write a differential equation governing it.
ii) Find the equilibrium points of the equation obtained in (i).
iii) Solve the given problem. What happens to the spread of the disease as t→∞?
एक विशेष बत्तु उत्पादित करने वाली N अभिन्न फर्म हैं। प्रत्येक फर्म का q एकक उत्पन्न करने का लागत फलन एकक वन है। प्रत्येक फर्म का आपूर्ति फलन ज्ञात कीजिए। मांग फलन
है। संतुलन मूल्य भी प्राप्त कीजिए।
एक कप कॉफी जिसका तापमान 95°C क है, को एक कमरे में, जिसका तापमान 25°C क है, रखा गया है। दो मिनट बाद कॉफी का तापमान 70°Cसी हो जाता है। बताइए कि कॉफी का तापमान 50°C क कब होगा?
A spherical cell of radius a is taking in a nutrient from its surroundings and metabolizing it. Assume that the concentration of nutrient in the cell at r = a is zero, for t > 0, and the initial concentration is Co for r
Find the concentration C(r,t) at any instant of time. Also write the steady-state solution.
Return distribution of the two securities are as given in the table below:
Find the correlation coefficient of the two securities. What does this value of
suggest about the shape of the curve representing the set of portfolios of the two securities?