Problem 1The velocity of any object, v gliding into atmosphere can be approximated as:mgV =- m² (1 - e-m²)CIf the object is a space shuttle with a mass of 90,000 kg glides into theatmosphere, at time = 500 second, its velocity is 5 times speed of sound at sealevel. Using the Newton-Raphson method, determine its drag, c. Usegravitational acceleration, g = 9.81 m/s².

The velocity of sound at sea level is about 340 m/s. Newton-Raphson method uses the formula:…

Answered: The velocity of any object, vgliding…

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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Problem 4 A circular swimming pool has a diameter of 18 meters, the sides are 4 meters high, and the depth of the water is 2.5 meters. The acceleration due to gravity is 9.8 m/s^2 and the density of water is 1000 kg/m^3. How much work is required to:(a) pump all of the water over the side? _________________ (b) pump all of the water out of an outlet 2 m over the side?______________ Note: The answers are neither 556875pi J and 961875pi J nor 1748588 J and 222547 J.
Problem 19 The velocity function is v(t)=(-t^2)+3t-2 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-2,5]. Displacement= Distance Traveled=
Problem 1: You are the manager of a forest product company with land recently replanted with a fast-growing species of pine. The merchantable volume of timber at time t is given by Q(t) = at + bt2 − dt3, where a = 10, b = 1, d = 0.01. a) What is the rotation length that maximizes the mean annual increment (Q(T)/T) and what is the associated volume? b) If the net price per unit volume is p = 1 and the discount rate is δ = 0.05, what is the optimal length, volume at harvest, and present value of profits (πS(TS)) for a single rotation? Does your answer satisfy the FOC, [Q′(T)/Q(T)]= δ ?
Problem 16 If the work required to stretch a spring 4 feet beyond its natural length is 12 foot-pounds, how much work is needed to stretch it 30 inches beyond its natural length?
Solve the following situational problems involving circular functions. 3.The diameter of a bicycle is 26 inches .If you are traveling at a speed of 35 miles per hour n the bicycle ,through how many lutions per minute are the wheel turning? 4.In the the classic novel Din Quixote,the character famously battles a windmill .Suppose the center of the windmill is 20 feet off the ground,and the sails are 15 feet long .Din Quixote is at the tip of one of the sails . The sails are turning at the rate of one counterclockwise rotation every 60 seconds .After 1 minute and 40 seconds ,Din Quixote fell of the sail and straight down to the ground .How far did he fall?
In each of Problems 33 through 36, try to transform the given equation into one with constant coefficients by the method of Problem 32. If this is possible, find the general solution of the given equation. 33.y′′+ty′+e−t2y=0,−∞<t<∞
Problem 2: (Reference only) x(t)=xo+(vo/k)(1-e^-kt) Need the answer for #4
In each of Problems 26 through 31, use the method of Problem 25 to solve the given equation for t > 0. 26.t2y″ + ty′ + y = 0
QUESTION 4 A simple random sample of 900 students from a college with student population 10,000 is taken to estimate the percentage of commuters. The result is 378 students commute. Thus, we can infer that about % of the student population commute. This is inferential statistics where we infer some parameter of the population from the statistics of the population. Using the bootstrap method, the SD of the box is estimated to be 0.5 by using the short-cut formula. The SE for percentage is 1.7%. Double check this number to make sure you know how to calculate it. Thus, the 95% confidence interval is between % and %. Round each answer to the nearest tenth. Thus, the 68% confidence interval is between % and %. Round each answer to the nearest tenth.

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