Find the derivative of f(x) and the indefinite integral of g(x). f(x) = 9x; g(x) =x5 f' ( x ) = 9( x ) dx = [Find the consumers' surplus (to the nearest dollar) at a price level of p = $2.089 for the price-demand equation p = D(x) = 9 - In (x+ 2). Use x computed to the nearest higher unit. CS = $ (Simplify your answer. Round to the nearest dollar as needed.)Use absolute value on a graphing calculator to find the area between the curve and the x-axis over the given interval. y= x ex; - 25x52 The area between the curve and the x-axis over the given interval is. (Type an integer or decimal rounded to two decimal places as needed.)K Illustrate the integral graphically and describe what the integral represents in terms of areas. Six - 2) ex dx O Illustrate the integral graphically. Choose the correct answer below. O A. O B. O c. OD. Ay 10- 5- Describe what the integral represents in terms of areas. Choose the correct answer below. O A. The integral represents the negative of the area between the graph of (x - 2)ex and the x-axis from x = 0 to x = 1. O B. The integral represents the area between the graph of (x - 2) and the x-axis from x = 0 to x = 1. O C. The integral represents the negative of the area between the graph of (x - 2)ex and the x-axis from x = - 1 to x = 0. O D. The integral represents the area between the graph of (x - 2)ex and the x-axis from x = - 1 to x = 0.K The concentration of particulate matter (in parts per million) t hours after a factory ceases operation for the day, is given by the following formula, C(t). Find the average concentration for the period from t = 0 to t = 5. C(t) = 10 In (t + 12) (t + 12 )- The average concentration of particulate matter, for the time period from t = 0 to t = 5, is approximately |parts per million. (Do not round until the final answer. Then round to four decimal places as needed.)K The Gini index of income concentration for the Lorenz curve with equation y = x ex -1 is 0.585. Interpret these results with both a graph and a description of the graph. Graph the Gini index of income concentration for the given Lorenz curve. Choose the correct graph below. O A. O B. Ay O c. Ay OD. 2- 2 7y Ay y = x y= x y= X'ex-1 y = x3ex -1 y = x y= x y= xex -1 y =xsex+1 X Describe the Gini index of income concentration in the graphical representation. Choose the correct answer below. O A. The area bounded by y = x and the Lorenz curve y = x ex -1, from x = 0 to x = co O B. The area bounded by y = x and the Lorenz curve y = x ex-1, multiplied by the area under the graph of y = x from x = 0 to x = 1 O C. The area bounded by y = x and the Lorenz curve y = x ex-, divided by the area under the graph of y = x from x = 0 to x = 1 O D. The area bounded by y = x and the Lorenz curve y = x ex -1, from x = 0 to x = 1 Interpret the Gini index of income concentration for the Lorenz curve with equation y = x ex - 1. The closer the index is to 0, the more the income is, and the closer the index is to 1, the more the income is . equally distributed concentratedIn a particular business college, it was found that an average student enrolled in an advanced typing class progressed at a rate of N'(t) = (t+ 6)e-0.25t words per minute per week t weeks after enrolling in a 18-week course. A particular student who can type 50 words per minute enrolls in the course. Use the given information to answer the following three questions. How many words per minute N(t) would the student be expected to type t weeks into the course? N(t) = (Type an exact answer.) Use a graphing calculator to determine, to the nearest week, the amount of time it should take the student to achieve the 65-word-per-minute level. It will take the student about weeks to achieve the 65-word-per-minute level. (Round to the nearest whole number as needed.) How many words per minute should the student be able to type by the end of the course? By the end of the course, the student should be able to type about |words per minute. (Round to the nearest whole number as needed.)Evaluate the integral. K xeax dx [ xeax ax =The integral can be found in more than one way. First use integration by parts, then expand the expression and integrate the result. K J (x - 3)(x + 4 ) 2 dx Identify u and dv when integrating this expression using integration by parts. u=], dv= ( dx Expand the terms within the integrand. (Simplify your answer.) Evaluate the integral. (x - 3)(x + 4)2 dx =The number of voters (in thousands) in a certain city is given by K N(t) = 19 + 2t - 5te-0.1t where t is time in years. Find the average number of voters during the period from t = 0 to t = 5. The average number of voters during the period from t = 0 to t= 5 is approximately (Round to the nearest whole number as needed.)