3. Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction isproportional to the product of the instantaneous amounts of A and B not converted to chemical C.Initially, there are 100 grams of A and 50 grams of B, and for each gram of B, 2 grams of A is used. Itis observed that 15 grams of C is formed in 5 minutes. Find an equation for the amount of C, x(1), intime /[ Provide a formula with the only variables x and 1- not necessary to solve for x()]

Answered: Image /qna-images/answer/6d593331-3ec1-4494-afc3-1705c9ba8e9d.jpg

Answered: Two chemicals A and B are combined to…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Newton's law of cooling says that the rate at which a body cools is proportional to the difference in temperature between the body and an environment into which it is introduced. This leads to an equation where the temperature f(t) of the body at time t after being introduced into an environment having constant temperature To is where C and k are constants. Find the temperature of an object when t=9 if To = 17, C = 7 and f(t)= To + Ce k=0.6. - kt The temperature of the object is (Round to two decimal places as needed.)
b The number of liters of blood pumped through the lungs in one minute is given by C = where b is quantity of oxygen used by the body in one minute, a is the quantity of oxygen per liter of a-v blood that has just gone through the lungs, and v is the quantity of oxygen per liter of blood that is about to enter the lungs. Suppose a = 160, b=205, and v= 125. Estimate the change in C if a becomes 150, b becomes 200, and v changes to 125. Find the equation for the total differential of C to estimate the change in C. dC=da+db + dv
In a hybrid-engine vehicle, energy from battery (“b" in Amperes) and from 95 octane unleaded gasoline ("g" in liters) are used intermittently to maximize the distance to be travelled (mileage) between fill- ups and charge-ups. If mileage (M) in kilometers is found out to be: M= 90 b+ 100 g - 3 b' - 5 g? - 2 b g find the values of “b" and “g" that will maximize mileage M, find the maximum mileage and prove that this is a maximum.
While the rate at which ethanol can be produced is important, the total quantity of ethanol that can be produced from a given crop is also important. Use the information listed below to calculate the theoretical yield of ethanol from a 1 hectare plot of corn and a 1 hectare plot of sugarcane in the U.S. (1 hectare = 2 football fields). Show your calculations. Corn Yield: 138 bushels of seed per hectare 1 bushel seed = 2.8 gallons ethanol Sugarcane Yield: 89 tons sugarcane per hectare 1 ton sugarcane = 19.5 gallons ethanol
A certain type of bacteria is known to grow at the rate proportional to the amount that is present. If you start with 2 grams of the bacteria and in two hours there are 2.1 grams, how much you will have after 5 hours ?
A virus spreads by contact and if you get infected you stay contagious. In an isolated population with P persons (no-one dies or are born) the rate of infection at time t (in months after 1/1 2020) is proportional to the product of 1. the number y(t) that are infected, 2. the number that are not infected 3. eat where a is a negative number depending on disease preventive measures. One tenth of the population is infected 1/1-2020. (a) Write out the differential equation y(t) must satisfy and solve it (call the proportionality constant k and remember to explain each step of your solution carefully. Are there for instance any constant solutions?). (b) Find a relation between L = lim->00 y(t), a, Pand k. What can you say about L when a is very small? What can you say about L when a is very big?
A swimming pool whose volume is 10,000 gal contains water that is 0.01% chlorine. Starting at t=0, city water containing 0.002% chlorine is pumped into the pool at a rate of 6 gal/min. The pool water flows out at the same rate. What is the percentage of chlorine in the pool after 1 hour? When will the pool water be 0.004% chlorine? What is the percentage of chlorine in the pool after 1 hour? After 1 hour the pool will be % chlorine. (Round to four decimal places as needed.)
Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially, there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A is used. It is observed that 20 grams of C is formed in 6 minutes. How much (in grams) is formed in 12 minutes? (Round your answer to one decimal place.) grams What is the limiting amount (in grams) of C after a long time? grams How much (in grams) of chemicals A and B remains after a long time? A B Need Help? grams grams Read It Watch It Master
Near the surface of the earth, a ball (with p = 0.1) is released from rest and its flight through the air offers resistance that is proportional to its velocity. How long will it take the ball to reach one-half of its terminal velocity? How far will it travel during this time?

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