That the volume V(t) of water in the pond at time t satisfies the differential equation d y d t = k − α π ( 3 a π h ) 2 3 V 2 3 .

Question

Want to see the full answer?

Answer 1

Question

Chapter 2.5, Problem 18P

(a)

To determine

To show: That the volume V(t) of water in the pond at time t satisfies the differential equation dydt=k−απ(3aπh)23V23.

(b)

To determine

The equilibrium depth of water in the pond.

(c)

To determine

A condition that must be satisfied if the pond is not to overflow.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Module Code: MATH380202 3. (a) Let {} be a white noise process with variance σ2. Define an ARMA(p,q) process {X} in terms of {+} and state (without proof) conditions for {X} to be (i) weakly stationary and (ii) invertible. Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q) process and show how it can also be represented as an ARMA process, giving the AR and MA orders of this representation. (b) The following tables show the first nine sample autocorrelations and partial auto- correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice that the notation in this part has no relationship with the notation in part (a) of this question.) Identify a model for this time series and obtain preliminary estimates for the pa- rameters of your model. X₁ = 15.51, s² = 317.43. k 1 2 3 4 5 6 7 Pk 0.981 0.974 0.968 akk 0.981 0.327 8 9 0.927 0.963 0.957 0.951 0.943 0.935 0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012 Y₁ = VX : y = 0.03, s² = 11.48. k 1…

Let G be a graph with n ≥ 2 vertices x1, x2, . . . , xn, and let A be the adjacency matrixof G. Prove that if G is connected, then every entry in the matrix A^n−1 + A^nis positive.

Module Code: MATH380202 1. (a) Define the terms "strongly stationary" and "weakly stationary". Let {X} be a stochastic process defined for all t € Z. Assuming that {X+} is weakly stationary, define the autocorrelation function (acf) Pk, for lag k. What conditions must a process {X+) satisfy for it to be white noise? (b) Let N(0, 1) for t€ Z, with the {+} being mutually independent. Which of the following processes {X+} are weakly stationary for t> 0? Briefly justify your answers. i. Xt for all > 0. ii. Xo~N(0,) and X₁ = 2X+-1+ &t for t > 0. (c) Provide an expression for estimating the autocovariance function for a sample X1,..., X believed to be from a weakly stationary process. How is the autocor- relation function Pk then estimated, and a correlogram (or acf plot) constructed? (d) Consider the weakly stationary stochastic process ✗+ = + + +-1+ +-2 where {E} is a white noise process with variance 1. Compute the population autocorre- lation function Pk for all k = 0, 1, ....

Answer 2

Question

Chapter 2.5, Problem 18P

(a)

To determine

To show: That the volume V(t) of water in the pond at time t satisfies the differential equation dydt=k−απ(3aπh)23V23.

(b)

To determine

The equilibrium depth of water in the pond.

(c)

To determine

A condition that must be satisfied if the pond is not to overflow.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 2.5, Problem 18P

(a)

To determine

To show: That the volume V(t) of water in the pond at time t satisfies the differential equation dydt=k−απ(3aπh)23V23.

(b)

To determine

The equilibrium depth of water in the pond.

(c)

To determine

A condition that must be satisfied if the pond is not to overflow.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 2.5, Problem 18P

(a)

To determine

To show: That the volume V(t) of water in the pond at time t satisfies the differential equation dydt=k−απ(3aπh)23V23.

(b)

To determine

The equilibrium depth of water in the pond.

(c)

To determine

A condition that must be satisfied if the pond is not to overflow.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 2.5, Problem 18P

(a)

To determine

To show: That the volume V(t) of water in the pond at time t satisfies the differential equation dydt=k−απ(3aπh)23V23.

(b)

To determine

The equilibrium depth of water in the pond.

(c)

To determine

A condition that must be satisfied if the pond is not to overflow.

Answer 6

Chapter 2.5, Problem 18P

(a)

To determine

To show: That the volume V(t) of water in the pond at time t satisfies the differential equation dydt=k−απ(3aπh)23V23.

Answer 7

Chapter 2.5, Problem 18P

(a)

To determine

To show: That the volume V(t) of water in the pond at time t satisfies the differential equation dydt=k−απ(3aπh)23V23.

Answer 8

(b)

To determine

The equilibrium depth of water in the pond.

Answer 9

(b)

To determine

The equilibrium depth of water in the pond.

Answer 10

(c)

To determine

A condition that must be satisfied if the pond is not to overflow.

Answer 11

(c)

To determine

A condition that must be satisfied if the pond is not to overflow.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 15

Ch. 2.1 - In each of Problems 1 through 12: Draw a direction...Ch. 2.1 - In each of Problems 1 through 12: Draw a direction...Ch. 2.1 - Prob. 3P Ch. 2.1 - Prob. 4P Ch. 2.1 - Prob. 5P Ch. 2.1 - Prob. 6P Ch. 2.1 - In each of Problems 1 through 12: Draw a direction...Ch. 2.1 - Prob. 8P Ch. 2.1 - Prob. 9P Ch. 2.1 - Prob. 10P

That the volume V(t) of water in the pond at time t satisfies the differential equation d y d t = k − α π ( 3 a π h ) 2 3 V 2 3 .

To show: That the volume V(t) of water in the pond at time t satisfies the differential equation dydt=k−απ(3aπh)23V23.

The equilibrium depth of water in the pond.

A condition that must be satisfied if the pond is not to overflow.

Want to see the full answer?

Chapter 2 Solutions