3. Use Euler's method to approximate the value of = -2x3 + 12x2 - 20x + 8.5 from x =0 to x = 4. The initial condition is y(0) = 1. Use the following step size:a. h= 0.5dxb. h 0.25C. h 0.1d. Compute for the true error and relative percentage error using the true value of y = -0.5x* +4x3 + 8.5x + 1 at x-4 for each given steps.1. Ka Ping has decided to save money roughly P100 per week. Suppose he makes a bi-monthlydeposits of this money into a bank account that pays annual interest of 10%, compoundedcontinuously. Use annuity formula: = rS + d; S(0) = Sods%3Ddta. Use Euler's method and approximate the balance after 4 years.b. Solve the general solution of the given annuity formula and solve for the exact value.3 dy2. 32+5y = sin x, y(0.3)= 5 and using a step size of h = 0.3, Approximate the value of y(0.9)dxusing Euler's method.

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Answered: 3. Use Euler's method to approximate…

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 snow plower recorded inches of snow fall and the yield by measure of square acreage over the previous 5 seasons. The regression equation is determined to be y=38.4+6.3x where x represents the inches of snowfall and y the measure of yield. 1. use the best fitting line to predict yield for 6 inches of snow 2. one of the records is (6,75) what is teh residual if x is 6
The point (9.1,71) is a point on the scatterplot. Draw the graph of the regression line on the scatterplot on the back of this paper using the y-intercept and the point(I = 3,y = 191). Indicate the residual for z = 9.1 by drawing the vertical line between(9.1, 71) and the corresponding point on the regression line. Will the residual be a positive or negative value?(f) Find the value of the residual for x = 9.1.
Let f(x)f(x) be the height of a maple tree in inches and xx the number of years since 2000. A linear model for the data is f(x)=9.44x+84.182f(x)=9.44x+84.182.36912155060708090100110120130140150160170180190200210220A) To the nearest inch, estimate the height of the maple tree in 2011. inchesB) Use the equation to find the year in which the tree will be 237 inches tall.
While collecting data on shoe sizes (y) compared to heights in inches (x) of male students in the class a student found that the shoe sizes ranged from size 7 to size 11 and the heights of the students ranged from 60 to 72 inches. The student ran a linear regression to get the function = 1 -x- 3 13 where y is the shoe size and is the height of the person in inches. What would be the shoe size for a student who was 73 inches tall? Shoe sizes only show up in incriments of 0.5 (ie. 7, 7.5, 8, 8.5, 9, 9.5, ....) so round to the nearest 1/2 shoe size. Show all your work.
Let f(x)f(x) be the height of a maple tree in inches and xx the number of years since 2000. A linear model for the data is f(x)=9.44x+84.182f(x)=9.44x+84.182.36912155060708090100110120130140150160170180190200210220A) To the nearest inch, estimate the height of the maple tree in 2015. inchesB) Use the equation to find the year in which the tree will be 239 inches tall.
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were: y=ax+b a=-1.383 b=24.599 r2=0.962361 r=-0.981 Use this to predict the number of situps a person who watches 5.5 hours of TV can do (to one decimal place)
There is a relationship between perceived corruption and human development in a country that can be modeled by H(x) = 0.3 +0.28 In x. In this formula, x represents the Corruption Perception Index, where 1 is very corrupt and 10 is least corrupt. The output gives the Human Development Index, which is between 0.1 and 1 with 1 being the best for human development. (a) For country A, x = 5. Evaluate H(5) and interpret the result. (b) The Human Development Index is 0.69 for country B. Find the Corruption Perception Index for country B. (a) H(5)~ (Simplify your answer. Round to two decimal places as needed.)
Jane collects data from 40 elementary school students and finds that the relationship between age (x) and score on a certain test (y) is given by y=3.2x+45. What can she extrapolate about the score a 16-year old will get on the test?
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were y=ax+b a=-1.324 b=23.586 r2=0.887364 r=-0.942 Use this to predict the number of situps a person who watches 11.5 hours of TV can do (to one decimal place)
The population of a town can be modelled by the function P(t)= 20 (4t+3)/(2t+5), where P is the population, in thousands, and t is the time, in years, after the year 2000 (t > 0). Clearly label all cases (a, b, c,…). Answers must be clear to read and show all steps. Use appropriate units for your answers. What is the difference between an average rate of change and an instantaneous rate of change?
For 50 students of a class the regression equation of marks in Statistics (X) on the marks in Accountancy (Y) is 3Y – 5 X + 180 = 0. The mean marks of Accountancy is 44 and variance of marks in Statistics is 9/16th of the variance of marks in Accountancy. Find the mean marks of Statistics and the coefficient of correlation between marks in two subjects.
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were:y=ax+b a=-1.075 b=27.958 r2=0.919681 r=-0.959 Use this to predict the number of situps a person who watches 12 hours of TV can do (to one decimal place)

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