3. The survival of two species depends on their mutual cooperation. For instance, a speciesof bee that feeds primarily on the nectar of one plant species and simultaneously pollinatesthe plant. One simple model of mutualism is given bydr= -ax + bxyxtdy= -my + nxydtwhere a, b, m, and n are all positive constants.(a) What assumptions are implicitly being made about the growth of each species in theabsence of cooperation?

Answered: Image /qna-images/answer/4fb7b3b0-13f5-407b-a85d-8f0f833df9bd.jpg

Answered: 3. The survival of two species depends…

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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A second-order chemical reaction involves the interaction of onc molccule of a substance P with one molecule of another substance Q to produce one molecule of another substance X. Suppose that p and q are the initial concentrations of P and Q and let r(t) be the concentration of X at time t. Then p- I(t) and q -r(t) are the concentrations of P and Q at time t, and the rate at which the reaction occurs is given by the equation dr *(I - b)(I – d)o= dt where a is a positive constant. Solve the initial value problem with r(0) = 0 assuming p # q. Answ: r(t) = Pq(e®(q-p)t _1 qea(q-p)t-p , you may nced to manipulate your answer to get this.
2 Problem 2. Sketch a proof of these formulas for linear regression, described on the following page. P;(x1, y1) y = mx + b P2(x2, y2) w = (mx + b – y)² + ... + (mxr, + b – (1) (See the accompanying figure.) Show that the values of m and b that do this are (E»)(E») - »>»» (E.) - »>«? т (2) b= Σχ (3) - m
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Clean Fossil Fuels. In the article, “Squeaky Clean Fossil Fuels” (New Scientist, Vol. 186, No. 2497, p. 26), F. Pearce reported on the benefits of using clean fossil fuels that release no carbon dioxide (CO2), helping to reduce the threat of global warming. One technique of slowing down global warming caused by CO2 is to bury the CO2 underground in old oil or gas wells, coal mines, or porous rocks filled with salt water. Global estimates are that 11,000 billion tonnes of CO2 could be disposed of underground, several times more than the likely emissions of CO2 from burning fossil fuels in the coming century. This could give the world extra time to give up its reliance on fossil fuels. The following bar chart shows the distribution of space available to bury CO2 gas underground. a. Explain why the break is found in the third bar. b. Why was the graph constructed with a broken bar?
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2. The DTDS given by P+1 = 3(P; + 18) describes a population in which 18 individuals are added to the population at the beginning of each generation and of that population survives. (a) Starting from a population of Po = 8 individuals, calculate the next three terms, that is, find P1, P2, and P3. (b) Calculate the equilibrium point of the model above. Show necessary algebra!
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