Answer the given questions, showing step by step working outs. Q5.(x+2, if 1≤x≤2f(x)=(x²if 2≤ x ≤3a) Show that f(x) is continuous in the interval [1, 3].b) Determinef(x) dx.Q6.For sin xy + cos y + x² = ex² + Inx, use implicit differentiation to finddydx

Answered: Q5. (x+2, if 1≤x≤2 f(x) = (x² if 2≤ x…

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 human nervous system is extremely sensitive to changes in the environment. Stimuli that remain the same do not demand the same amount of attention as those that are new. You are a human factors psychologist working for a large automobile manufacturer. You have been assigned the task of determining what type of hot-engine warning system will be used on the next generation of small pickup trucks. The designers have given you three alternative systems: (a) a traditional temperature gauge that reads cold to the left, normal in the middle, and hot to the right; (b) a hot- engine warning light that flashes when the engine is about to overheat; and (c) a temperature gauge similar to (a), except that the entire gauge flashes on and off when the engine is about to overheat. You decide to test these three designs by having three separate groups of participants use the various warning systems in a driving simulator. The independent variable in this experiment is the type of warning system,…
Im having trouble on the last part which is Part c. I dont know if its C or B. I think its B but im not sure. The rest dont bother doing because im pretty sure its right so just focus on part c
Sarah was calculating the speeds (mph) of vehicles travelling down Maple Street on two separate days at 9 am for an hour. Below is the data she collected. Wednesday's Speeds: Sunday's Speeds: 34,28,24,17,39,44,64,33,27,21,38,40,60,30,25,37,30,25,35,30 18,27,34,37,49.55,63,61,48,30,27,17,17,15,26,46,25 4) Find the Standard Deviation of each day. Wednesday's Standard Deviation Table X x (x-)²2 n-l Sunday's Standard Deviation Table 7 (x-2)² n-1 2). Sketch Wednesday's Bell Curve with 30 Sketch Sunday's Bell Curve with 30 (x-7)²= x-F (x-7) 2 3. Based on your analysis of the data and standard deviations, which day would you say is the most dangerous day on Maple Street?
Empathy means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16 couples in their midtwenties who were married or had been dating for at least two years. They zapped the man's hand with an electrode while the woman watched, and measured the activity in several parts of the woman's brain that would respond to her own pain. Brain activity was recorded as a fraction of the activity observed when the woman herself was zapped with the electrode. The women also completed a psychological test that measures empathy. Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Empathy Score 43 46 35 59 64 66 58 47 44 49 56 68 28 71 27 108 Brain Activity -0.129 0.389 0.019 0.378 0.016 0.419 0.109 0.515 0.149 0.746 0.245 0.57 0.219 0.716 0.364 0.762 Given that the equation for the regression line is y^=0.00709x−0.04187y^=0.00709x−0.04187, what is the residual (or deviation), yi−y^iyi−y^i, for subject 14?ANSWER: Speak
Name the forecasting methods
A survey looked at how long it takes a typical company to recoup an investment in research. The survey determined that 39% of the corporations took six months or less to recoup their investment. The data table below shows a sample of the time, in months, it might have taken 20 corporations to recoup their investment. Complete parts a and b. 9.0 8.0 4.0 4.0 7.0 8.0 7.0 7.0 9.5 5.5 7.5 12.0 8.5 5.5 10.5 10.0 7.5 4.5 7.0 7.5 a. Determine the number of corporations that recovered their investement in research in six months or less. There were 5 corporations that recovered their investment in research in six months or less. b. Calculate the probability of obtaining at most the number of corporations that you determined in part a if the percent of those recovering their investment is as indicated by the survey. The probability (Round to four decimal places as needed.)
An electronics company makes communications devices for military contracts. The company just completed two contracts. The navy contract was for 2,780 devices and took 29 workers two weeks (40 hours per week) to complete. The army contract was for 6,380 devices that were produced by 39 workers in three weeks (40 hours per week). a. Calculate the productivity for navy and army contracts in units produced per labor hour. Note: Round your answers to 2 decimal places. Contract Navy Army Productivity
You collect data of average annual returns for Amazon Stock and Microsoft Stock and make the following table: (This data can be copied into Excel.) You use this data to answer the research question: are true population Amazon Returns greater than true population Microsoft Returns? What is your point estimate of the difference in Amazon Returns and Microsoft Returns? Enter your answer as a positive number. Round your answer to four decimal places.
An outbreak of the deadly Ebola virus in 2002 and 2003 killed 91 of the 95 gorillas in 7 home ranges in the Congo. To study the spread of the virus, measure " distance" by the number of home ranges separating a group of gorillas from the first group infected. Here are data on distance and number of days until deaths began in each later group: Distance xx 2 5 4 4 4 6 Days yy 4 21 29 40 47 49 Use a calculator or software to find the following values. (a) Find the mean and standard deviation of xx. MEAN: STANDARD DEVIATION: (b) Find the mean and standard deviation of yy. MEAN: STANDARD DEVIATION: (c) Find the correlation rr between xx and yy. r:
A comparative Psychologist tests the amount of time it takes for mice to complete a maze as their dependent variable. What type of data would this be? a. ratio b. interval c. ordinal d. nominal

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Q5. (x+2, if 1≤x≤2 f(x) = (x² if 2≤ x ≤3 a) Show that f(x) is continuous in the interval [1, 3]. b) Determine f(x) dx. Q6. For sin xy + cos y + x² = ex² + Inx, use implicit differentiation to find dy dx