15. Sketch the graph of the relevant function manually (without the aid of a graphing calculator) and show how you obtained the graph. The expression shown is a definite integral, written as:\[\int_{3}^{6} (2 - |x + 4|) \, dx\]This integral represents the area under the curve of the function \( f(x) = 2 - |x + 4| \) from \( x = 3 \) to \( x = 6 \). Here, \( |x + 4| \) denotes the absolute value of \( x + 4 \). To evaluate the integral, one would need to consider the behavior of the absolute value function and possibly split the integral into different intervals where \( x + 4 \) is positive and negative, respectively.

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Answered: 15. Sketch the graph of the relevant…

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 U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)
Getting going in the morning was probably hard for folks on the Overland Trail (just as it may be for you today), so coffee was a highly valued commodity. The Cazneau family starts their journey with a supply of 30 pounds of coffee. When they arrive at Sutter's Fort in California, 188 days later, they have only 3 pounds left. 1. Draw a graph showing the amount of coffee remaining as a function of the time elapsed since the start of the journey. For simplicity, assume the Cazneaus consume coffee at a constant rate. 2. Find the average amount of coffee consumed per day. 3. Develop an equation for the function represented by your graph. Find the slope of your graph. 4. 5. Suppose that at the beginning of their 188-day journey, the Cazneaus are 1600 miles from Sutter's Fort. a. How many miles per day do they travel? For simplicity, assume they travel the same distance each day. b. Of course, as the Cazneaus travel, their distance from Sutter's Fort decreases. Write a formula expressing the…
Before the advent of antibiotics an outbreak of cholera might spread through a city so that the number of cases doubled every 6 days. a. Twenty-six cases were discovered on July 5. Write a function for the number of cases of cholera t days later. N(t) = Preview b. Use your calculator to graph your function on the interval 0 < t < 90. c. When should hospitals expect to be treating 106, 496 cases? Use algebraic methods to find your answer, and verify on your graph. days later Get Help: Video еBook Points possible: 1 License This is attempt1 of 7. Message instructor about this question
1. Explain a real-world situation that can be described using stepwise or piecewise function. Must be specific(how situation works).
5. Consider the piecewise-defined function that is graphed above. The point A=(-3/2,0). (a) Find the equation of the piecewise defined function graphed above. You may assume that the ends of the pieces shown end with an open circle (an empty point). (b) Calculate the inverse of each of the pieces by swapping 2 andy and solving for y.
Please help me solve this problem.
Extra Problem: A sprinter runs the 100-yard dash in 10 seconds in the following fashion. She starts at rest (0 velocity), and for the first 6 seconds she speeds up to her highest speed. Unable to maintain that speed, she is slowing down for the last 4 seconds. You are to sketch a graph of her position along the track (in yards) as a function of time (in seconds). Be aware that she does not turn around and run toward the starting line, and she runs through the finish line rather than coming to a stop at the finish line.
4 2 1 The graph shows how the value of a copier has depreciated over time. Use the graph to complete each statement. value of copier (in thousands of dollars) 1 3 time from date of purchase (years) 4 5 6 7 a. Complete the function, V(x) that gives the value, in thousands of dollars, x years from date of purchase: V(x)=x+- Hint: It will help to first complete these two statements: The value of the copier is decreasing at a rate of - thousand dollars per year. The value of the copier at the time of purchase was. b. Use the function you wrote in part (a) to determine the number of dollars that the copier is worth 2.5 years after purchase. Show your work. thousand dollars.

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