If X and Y are independent and identically distributed exponential variables with parameter X = 4, compute each of the following joint densities. (a) U = 3X, V = 5X/Y. O= (a 'n)a'nf (b) U = 5X + Y,V = 3X/(X+Y). D= (a 'n)A'nf

Q: A bacteria colony begins with a population of 120 and quadruples in size every 1.5 days.   If the…

A: Given initial population = 120  So, for t=0, P=120  Using that we get: Quadruples in size every 1.5…

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A: Given- There is considerable evidence to support the theory that for some species there is minimum…

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Q: 3. Show that the differential equation dx is homogenous. Zxy

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A: dA/dt=kA

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A: Consider the given information:

Q: 2. Suppose that a certain population obeys the logistic equation dy dt ry (1 - *) k (a) If the…

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Q: If the function f(x,y) is continuous near the point (a,b), then at least one solution of the…

A: Solution:-

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A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Given Concentration=8g/m3flow rate=24m3/dayVolume=1800m3Initial insecticide concentration in the…

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A:

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A: Equation of normal at the point P(x,y) to the curve is Y-y=-dxdy(X-x). ⇒X=x+ydydx Thus,…

Q: in differentials of functions, if x change by a small amount dx then, what will happen to y?

A: Let a function be y=fx then here y is the dependent variable and x is the independent variable. The…

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A: Given Data: A city has a fixed population is P. Also given, the rate of change (with respect to…

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Q: Suppose a student carrying a flu virus returns to an isolated college campus of 3000 students.…

A: Total no. Of students=3000 And x is the no. Of students interacted with the flu.

Q: 4. A thin homogeneous bar of thermal diffusivity 9, length 2 cms and its left end maintained at…

A: Given that a thin homogeneous bar of thermal diffusivity 9, length 2cms and its left end maintained…

Q: 1. What is the integrating factor of the differential equation ydx – xdy = 0 using case 1?

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Q: 6. Why is it very easy to conclude that x2 dx diverges without making any integration calculations?

A: This question is taken from the calculus and sub-topic is improper integral in which we have to give…

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A: Given Half of the original number of radioactivenuclei have undergone disintegration in a period of…

Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

A: Given:    mg = 2    s = 1.5 inches = 1.5/12 = 1/8 feet     g = 32

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Q: A normal is drawn at a point P (x, y) of a curve, it meets the x-axis at Q. If PQ is of constant…

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Q: If the family of curve has 3 arbitrary constants then the corresponding differential equation is a)…

A: See solution below

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A: Given, the population of a community is known to increase at a rate proportional to the number at…

Q: Without solving explicitly, classify the critical points of the autonomous differential equation dx…

A: See the solution and follow the steps. You will understand easily.

Q: 17. Show that V10x + 1 and Vx + 1 grow at the same rate_ as x→o by showing that they both grow at…

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Q: Suppose a population P(t) satisfies logistic differential equation dP/dt=0.1P(1-(P/2000))…

A: SOLUTION-

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Q: From the differential equation by elimanating arbitary constants  y=ax3+bx2

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Q: Consider a minimal threshold value for a species to survive, T. One way to add in this factor to the…

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Q: If the family of curve has 4 arbitrary constants then the corresponding differential equation is c)…

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Q: Find critical points of ƒ(x) = x² ln(x) — 1⁄x² on the interval (0, ∞).

A: Given; fx=x2lnx-12x2 ; x∈0,∞    As we know that; The critical points of the function, y=fx can be…

Q: In the Four-Step Rule, which among the steps is the most important, upon which the foundation of…

A: We need to eliminate ∆x from the denominator else the limit does not exist.

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Q: Suppose the motion of a mass-spring system is described by the differential equation x"+By'+1y=0.…

A: We will use knowledge of basic differential calculus to solve this problem.   It should be noted…