Numerical Weather Prediction (NWP). Consider the ordinary differential equation= -x for the range t = 0 to t = a withdtthe initial condition that x(0) = 1.Find a solution analytically with a = 5.Solve this numerically with forward difference (Euler) method with At = a/n,n = 100 and t =k At. You can use some tools to do thisSolve this numerically with backward Euler method.Draw three solutions: (i) analytical, (ii) forward Euler, and (iii) backward%3DEuler.

Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Answered: Consider the ordinary differential…

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 researcher studies water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same dates 5 years later. The researcher immerses a weighted disk painted black and white and measures the depth (in inches) at which it is no longer visible. The collected data is given in the table below. Complete parts (a) through (c) below. Observation 1 2 3 4 5 6 3/19 5/30 7/3 9/13 1/25 41.6 72.7 72.4 65.9 49.3 72.1 11/7 64.2 68.6 76.6 69.4 69.8 70.5 Date Initial Depth, X₁ Depth Five Years Later, Y; B. Using the same dates maximizes the difference in water clarity. C. Those are the same dates that all biologists use to take water clarity samples. D. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. b) Does the evidence suggest that the clarity of the lake is improving at the α = 0.05 level of significance? Note that the normal probability plot and boxplot…
DIRECTIONS : Using the data given below answer the questions based on it. Price (Rs.) Quantity ('000 Kg.) Commodity 2004 2005 2004 2005 Rice 9.3 4.5 100 90 Wheat 6.4 3.7 11 10 3 Pulses 5.1 2.7 Also, E P,9, = 504.2; E P,q, = 1025.9; E P,9, = 450.1; £ P,q, = 916.3.
Determine the new equation after rotated parallel to the principal axes for the equation below and also determine the angle of rotation! 2x^2 + 4xy − y^2 = 24
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Write Up Assignment 4: Due March 24th Dt. Parker is a math professor at University Blackwood, home of the fighting corn nuggets. Dr. Parker has been gathering information on his Algebra I class for years. Dr. Parker also serves as a member of the graduate faculty in the Applied Statistics department at UB. You are one of Dr. Parker's graduate assistance (which can be a thankless position at times). Dr. Parker has given you a data set of his Algebra I case. Historically the final exam average for Dr. Parker's Algebra course has been 79.8. For this assignment you will use the data set provided and complete the following data analysis. 1. A correlation analysis For this analysis, you will select the correct variable or variables to be used and you will provide the following information below as a well written, referred document. A research question Variables used for the question The correct null and alternative hypotheses A description and the assumptions for the analysis Relevant SPSS…
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A researcher studies water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same dates 5 years later. The researcher immerses a weighted disk painted black and white and measures the depth (in inches) at which it is no longer visible. The collected data is given in the table below. Complete parts (a) through (c) below. Observation 1 2 3 4 5 6 1/25 3/19 5/30 7/3 9/13 11/7 71.2 35.6 53.8 41.2 57.3 43.4 72.1 35.1 59.0 41.0 61.0 47.0 Date Initial Depth, X, Depth Five Years Later, Y, Click the icon to view the table of critical t-values. (a) Why is it important to take the measurements on the same date? OA. Using the same dates makes it easier to remember to take samples. B. Those are the same dates that all biologists use to take water clarity samples. C. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. D. Using the same dates maximizes…
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