510 120 + 128 64 Q6/ 96 6528 186 456 18 128 16 A. The region in the first quadrant bounded above by the line y = 2, below by the curve y=2 sinx, 0≤x≤ and on the left by the y-axis. Find the volume of the solid generated by revolving the region about the line y = 2 456 Mark

Solve the ff. use indicated technique

Consider a species of elk that can be split into 4 age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years, and those aged 3-4 years. The population is observed once a year. Given that the Leslie matrix is equal to 0 1.1 1.7 1.3 0.8 0 0 0 L = 0 0.6 0 0 0 0 0.2 0 and the initial population distribution is 40 of the first age group, 17 of the second age group, 10 of the third group, and 5 of the oldest age group, answer the following questions. The initial population vector is xo = How many elk aged 1-2 years are there expected to be after 10 years? How many elk aged 0-1 years are there expected to be after 20 years? How many elk are there expected to be after 30 years? Calculate the dominant eigenvalue of the Leslie matrix good to 3 decimal places. 11 = What is the long-term growth rate of this population of elk as a percent? growth rate = over/under 100%.) Are the elk thriving, static, or going extinct? ? (The growth rate is the percentage of growth

Find the volume of the solid obtained by rotating the region bounded by the given curvesabout the specified line. Sketch the region, the solid, and a typical disk or washer.