A region used for agricultural drainage has become contaminated with a mineral. Flushing the region withwater will reduce the amount of the mineral for a while, but it will then begin to build up again. Themodel of the percent of the mineral present in the soil t months after the flushing begins is given byt² + 492t(a) What value(s) of t should be used to test for the minimum amount of mineral?Separate your answers with a comma.M(t)t-After"(b) When will the amount of the mineral be reduced to a minimum?1 ≤ t ≤ 12.%months(c) What is the minimum percent of the mineral?

Given Information:Model for the percent of mineral present is To find:i) The values of in which…

Answered: A region used for agricultural drainage…

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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The deck of a bridge is suspended 285 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y = 285 − 16t2. (a) Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 2 and lasting the following amount of time. (i) 0.1 seconds (ii)0.05 seconds (iii)0.01 seconds (b) Estimate the instantaneous velocity (in ft/s) of the pebble after 2 seconds.
Data about the sound levels from a new speaker are collected at a manufacturing facility and are used to calculate the model ŷ = 62.4(0.915)x, where x represents the distance from the speaker in meters and ŷ represents the predicted sound level in decibels. Interpret the percent rate of change of the model in the context of the problem. For every increase in one meter from the speaker, the sound level is predicted to decrease by about 91.5%. For every increase in one meter from the speaker, the sound level is predicted to decrease by about 8.5%. For every increase in one meter from the speaker, the sound level is predicted to increase by about 91.5%. For every increase in one meter from the speaker, the sound level is predicted to increase by about 8.5%.
The air in a room with volume 180 m³ contains 0.3% carbon dioxide initially. Fresher air with only 0.05% carbon dioxide flows into the room at a rate of 2 m³/min and the mixed air flows out at the same rate. Find the percentage p of carbon dioxide in the room as a function of time t (in minutes). p(t) = 0.5556e % +0.7 X What happens to the percentage of carbon dioxide in the room in the long run? lim p(t) = 0.007 X %
Alcohol-Related Traffic Accidents As a consequence of increasingly rigid rules aimed at decreasing the number of alcohol-related traffic accidents in a particular state, initial data shows that the number of such accidents has changed at a rate of R(t) = -18 - te0.2t accidents/month t months after the rules took effect. There were 2040 alcohol-related accidents for the year prior to the rules' implementation. Choose how many alcohol-related accidents were anticipated in the first year the rules were in effect.
In this model, the period immediately after the stock is issued offers excess returns on the stock—that is, the stock is selling for more than it is really worth. One such model for a class of Internet IPOs predicts the percent overvaluation of a stock as a function of time as R(t)=250(t2/(2.718)3t) where R (t) is the overvaluation in percent and t is the time in months after the initial issue. a. Use the information provided by the first derivative, second derivative, and asymptotes to prepare advice for clients as to when they should expect a signal to prepare to buy or sell (inflection point), the exact time when they should buy or sell (local maximum and minimum), and any false signals prior to a horizontal asymptote. Explain your reasoning. please type answer.
The rabbit population at the city park increases by 16% per year. If there are intially 119 rabbits in the city park. 1. Write a model for the population (y) in terms of years (t). y= 2. Find the rabbit population in 17 years. (Round to the nearest whole rabbit)= 3. [Estimate] When the rabbit population reaches 11033. It will happen between year and year
Rewrite > Σ 4) n(n-1)c,x"-2 + x² 5c,,x" as a single power series with the n=0 n=0 general term containing x*. b) Find the recurrence relation for the power series solution about x = 0 of the differential equation y" – y=0 for k = 0,1,2,... c) Find the first four nonzero terms of a power series solution about x =0 of the differential equation y"+ xy = 0.

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