q8 24A F(s) =(s - 3)4 + 112B F(s) =(s - 3)56O F(s) =(s - 4)424O F(s) -(s - 3)512E F(s) =(s - 4)34F(s) =%3D(s - 3)5 Given the functionf(1) = 14 e31Use the Laplace Transform table to convert this function into F(S).f(t)F(S)11SS - AN!SN + 1Вsin(B t)s2 + B2Scos(B t)s2 + B2N!(s - A)N + 1ВeA! sin(B t)(s - A)2 + B2S - AeA cos(B t)(s - A)2 + B2

Consider the function f(t)=t4e3t

Answered: Given the function f(t) = 4 e3 Use the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled as p(x) = −0.00022x3 + 0.014x2 − 0.0033x + 12.236 percent where x is the number of years since 2000, data from 0 ≤ x ≤ 50. 1. Determine the value of x in the domain 0 ≤ x ≤ 50 for which the percentage is predicted to be increasing most rapidly (Round your answer to three decimal places). 2. Thus, in which year is the percentage is predicted to be increasing most rapidly? 3. Calculate the percentage at that time. (Round your answer to two decimal places.) 4. Calculate the rate of change of the percentage at that time. (Round your answer to three decimal places.)
Suppose that a political campaign by Loki estimates that the candidate’s polling percentage yand the amount x (in hundred thousands of pesos) that is spent on television advertising arerelated by y = e^0.3x + (5lnx)^2 while the amount that is spent on social media advertising are related by (x −3)^4 + 3y = x. (a) If P300,000 has been spent on television advertising by Loki’s campaign, determine therate of spending that will increase his polling percentage by 2 percentage points per week. (b) Suppose that Loki’s political adversary, Thor, is slowly ramping up his presence on socialmedia. If Loki’s team plans on spending P400,000 on social media advertising and the rateof spending is at P100,000 per week, at what rate will the polling percentage increase?
A small manufacturer has determined that the daily cost in dollars of producing n injected molded parts is given by the formula: C(n) = 0.01n3 - 1.5n2 + 0.25n + 500 Each part can be sold for $1.50 each. How many units must be produced and sold to maximize profit?
The function f(x)=2x^3−33x^2+108x-4 has two critical numbers. The smaller one is x =? and the larger one is x =?
4. If the secant method is used on f(x) = x^5 +x^3 +3 and if x_(n-2) = 0 and x_(n-1) = 1, what is x_n?
A company has two plants that produce the same lawn mower. If x1 and x2 are the numbers of units produced at plant 1 and plant 2, respectively, then the total revenue for the product is given by R = 300x1 + 300x2 − 5x21 − 10x1x2 − 5x22 . When x1 = 5 and x2 = 8, find (a) the marginal revenue for plant 1, ∂R/∂x1, and (b) the marginal revenue for plant 2, ∂R/∂x2.
So, to find a critical point, you would use f(x) and not f'(x)?
The function f(x) = 2x^3 - 27x^2 + 108x - 4 has two critical numbers. The smaller one is x = ? And the larger one is x = ?
Suppose a person's utility function for items x and y is u = ln(x) + ln(y), and he currently has $200 in his pocket, and the price of x is $10 per item and the price of y is $20 per item, find the combination that maximises his utility.
In a hypothetical city, there is a population of 200,000 people. During the year 2000, there were 1,000 deaths from all causes. All new cases of disease “X” have been accounted for and they total 600 (400 males and 200 females). During the year 2000 there were 120 deaths from disease “X”, 100 of them in males. What is the crude death rate for all causes per 1,000 population?
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Given the function f(t) = 4 e3 Use the Laplace Transform table to convert this function into F(s). f(t) F(S) S S - A N! SN +1 B sin(B t) s2 + B2 S cos(B 1) s2 + B2 N! (s - A)N + 1 B eAl sin Bt) (s - A)2 + B2 S - A eA' cos(B t) (s - A)2 + B2 COS - 15