m = 10 and d=29 please replace each m with 10 and d with 29 and follow the instructions attached below and use geogebra
3. Suppose that the velocity of a moving object is given by the function v(t) = d.te- +1 where t is measured in seconds and v(t) is measured in feet per second. (Hint: This function is in terms of t. In Geogebra, you can use either x or t, but you can't use both in the same equation. Be consistent. Be sure to type a multiplication between t and e-". Otherwise a slider might appear.) The goal is to estimate the distance traveled by the object on the interval [0,4] as accurately as possible. a. Draw a variety of Riemann sums using Geogebra. Use left, right, and midpoints for the height of the rectangles. Hint: You might want to start with 1000 rectangles. Include a sentence stating your function, what it represents, and the time interval provided. Report your best estimate of the distance traveled, using appropriate notation to illustrate what method and the number of rectangles used, and include units of measurement on the answer. Explain why you think this is the best estimate. You do not need to provide a graph of your work. b. Find the LEAST number of rectangles that will achieve your answer in part a using midpoints to determine the height of the rectangles. Include a copy of your Geogebra graph. Adjust the numbers on the axes so that you provide the best view of the graph and rectangles as possible. Explain the graph by using similar wording provided in quotation marks in problem #1a State the area using appropriate notation. u 5 MATH 235 c. Find the LEAST number of rectangles that will achieve your answer in part a using rectangles whose left sides determine the heights. Include a copy of your Geogebra graph. Adjust the numbers on the axes so that you provide the best view of the graph and rectangles as possible. Explain the graph by using similar wording provided in quotation marks in problem #1a State the area using appropriate notation. Geogebra Overview To create graphs like the ones above, we do the following in Geogebra: 1.) Type the function into the input line and press enter. 2.) Type the Geogebra command RectangleSum into another input line, using the syntax provided below, and press enter. RectangleSum(
, , , ) The "Position for rectangle start" tells the program whether you want the left or right side of each rectangle to intersect the graph as follows: U 2 MATH 235 for a left rectangle sum, use "O" for a right rectangle sum, use "1" The numerical value of the sum of the areas of the rectangles automatically appears on the graph. Be sure that you set the rounding option to 5 decimal places for this report. Example: To graph the function f(x) = -x + 1 and approximate the area under the curve on the interval [0.4, 3.2) using 5 rectangles with the right side of the rectangle determining the heights, we use the following two commands in separate input lines: f(x) = -x2 + 12 rectanglesum(f(x), 0.4, 3.2, 5, 1) Both commands must be used every time you are asked to determine an area. Setup for the Problems The functions used in each problem contain a constant m and/or d so that each student works with a slightly different function. These constants are based on your birthday. The m represents the number of the month you were born, while d stands for the day of the month you were born. For example, if your birthday is March 19th, then m = 3 and d = 19. It is important for the professor to know what numbers you are using for m and d. Do not use the letters m and d in your report. Type the numbers they represent instead. 3. Suppose that the velocity of a moving object is given by the function v(t) = d.te- +1 where t is measured in seconds and v(t) is measured in feet per second. (Hint: This function is in terms of t. In Geogebra, you can use either x or t, but you can't use both in the same equation. Be consistent. Be sure to type a multiplication between t and e-". Otherwise a slider might appear.) The goal is to estimate the distance traveled by the object on the interval [0,4] as accurately as possible. a. Draw a variety of Riemann sums using Geogebra. Use left, right, and midpoints for the height of the rectangles. Hint: You might want to start with 1000 rectangles. Include a sentence stating your function, what it represents, and the time interval provided. Report your best estimate of the distance traveled, using appropriate notation to illustrate what method and the number of rectangles used, and include units of measurement on the answer. Explain why you think this is the best estimate. You do not need to provide a graph of your work. b. Find the LEAST number of rectangles that will achieve your answer in part a using midpoints to determine the height of the rectangles. Include a copy of your Geogebra graph. Adjust the numbers on the axes so that you provide the best view of the graph and rectangles as possible. Explain the graph by using similar wording provided in quotation marks in problem #1a State the area using appropriate notation. u 5 MATH 235 c. Find the LEAST number of rectangles that will achieve your answer in part a using rectangles whose left sides determine the heights. Include a copy of your Geogebra graph. Adjust the numbers on the axes so that you provide the best view of the graph and rectangles as possible. Explain the graph by using similar wording provided in quotation marks in problem #1a State the area using appropriate notation. Geogebra Overview To create graphs like the ones above, we do the following in Geogebra: 1.) Type the function into the input line and press enter. 2.) Type the Geogebra command RectangleSum into another input line, using the syntax provided below, and press enter. RectangleSum( , , , ) The "Position for rectangle start" tells the program whether you want the left or right side of each rectangle to intersect the graph as follows: U 2 MATH 235 for a left rectangle sum, use "O" for a right rectangle sum, use "1" The numerical value of the sum of the areas of the rectangles automatically appears on the graph. Be sure that you set the rounding option to 5 decimal places for this report. Example: To graph the function f(x) = -x + 1 and approximate the area under the curve on the interval [0.4, 3.2) using 5 rectangles with the right side of the rectangle determining the heights, we use the following two commands in separate input lines: f(x) = -x2 + 12 rectanglesum(f(x), 0.4, 3.2, 5, 1) Both commands must be used every time you are asked to determine an area. Setup for the Problems The functions used in each problem contain a constant m and/or d so that each student works with a slightly different function. These constants are based on your birthday. The m represents the number of the month you were born, while d stands for the day of the month you were born. For example, if your birthday is March 19th, then m = 3 and d = 19. It is important for the professor to know what numbers you are using for m and d. Do not use the letters m and d in your report. Type the numbers they represent instead
