I. In a thermodynamic system [like the rocket engine] we have the relationship log(P) = nlog (V) + log(C) where P represents pressure, V represents volume, C is a constant and n is an index Show that: C" = P J. If in the previous question, n= 2, find the dimensions of the constant C.

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A: The differential equation given is as follows: Q't=0.0225Qt-0.0003Qt2=ft, Q Given that initially at…

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Q: The logistic equation for the population p (in thousands) at time t of a certain species is given by…

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Q: Suppose that dP/dt- 0.14P(t) represents a mathematical model for the growth of a certain cell…

A: Given:the growth of a culture at time t is dPdt = 0.14P(t)P = 2 million cells

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A: pv1.2=kdifferentiating both side with respect to t∂p∂tv1.2+1.2v0.2∂v∂tp=0∂p∂tv1.2=-1.2v0.2∂v∂tp

Q: The logistic equation for the population p (in thousands) at time t of a certain species is given by…

A: 1st find equilibrium  solution and then find sign of dpdt to draw direction field and then conclude…

Q: Question 3. Prove that L(e^)(«) = * & dt.

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Q: An equation that considers both the above assumptions is dP P kP(1 M - dt

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Q: Given y implicitly by (xy) +e" = log(x+y)+1. Compute y'at the point (0,1).

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Q: Find the Bolution to Hhe initial value problem - Please Write the folution with the computer.

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Q: Derive the solution P(t) = MPo Ро + (М — Роје- of the logistic initial value problem P' = kP(M – P),…

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Q: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

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Q: Suppose the logistic curve y(t) = satisfies that y(0) = 6. What is the 1+6e-7t carrying capacity?

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Q: The solution of the following logistic equation is dy - ry (7 –);y(0) k dt 15 1 -e7rt 105 y – 7k 1…

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Q: 4. Use variation of parameters to find a general solution of r'y" + 5a?y" + 2:ry/ – 2y = x³ log(x)

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Q: Suppose that dP/dt - 0.18P(t) represents a mathematical model for the growth of a certain cell…

A: Given that dP/dt = 0.18 P(t)  Where P(t) is the size of culture at time t.

Q: In a natural habitat, the population of a certain species of snails is given by P= 0.8(Ae* +500),…

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Q: 9. If y= ax for some constants a>0 and b, which of the following graphs is a straight line? (A) y…

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Q: Suppose that y = P(t) represents the population of a city at time t. What does represent? At ΔΡ

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Q: which 20 grams of salt is dissolved. Pure water is being pumped into the tank at a rate of 5…

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Q: A 50-gal barrel is filled completely with pure water. Saltwater with a concentration of 0.3 Ib/ga…

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Q: Suppose that the equation dr = kr(M – x) – Er dt models the population of fish in a lake, where…

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Q: dy - r (11 - 2) : v(0) = ; k (11–);y (0) dt 9

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Q: 1) Find dy/dt for if : y = log2 (81n 2)

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Q: An observation indicates that the frog population Q(t) in a small pond is 25 initially and satisfies…

A: We have to solve given differential equation to find population after t years and then find…