Find a power series representation for the function. determine the radius of convergence, r. (give your power series representation centered at x = 0.) f(x) = ln(10 - x)

You will get 25 points an image of a rectangular prism is shown below: part a: a cross section of the prism is cut with a plane parallel to the base. what is the name of the shape created by the cross section? explain your answer. (5 points) part b: if a cross section of the prism is cut perpendicular to the base, what would be the shape of the resulting cross section? explain your answer. (5 points)

The ratio of the perimeters of two similar triangles is 4: 3. what are the areas of these triangles if the sum of their areas is 130cm2?

1. an economy consists of three workers: larry, moe, and curly. each works 10 hours a day and can produce two services: mowing lawns and washing cars. in an hour, larry can either mow one lawn or wash one car; moe can either mow one lawn or wash two cars; and curly can either mow two lawns or wash one car. a. calculate how much of each service is produced under the following circumstances: a. all three spend all their time mowing lawns. b. all three spend all their time washing cars. c. all three spend half their time on each activity d. larry spends half of his time on each activity, while moe only washes cars and curly only mows lawns b. using your answers to part a, draw a production possibilities frontier and label points a, b, c, and d on your graph. explain why the production possibilities frontier has the shape it does. c. are any of the allocations calculated in part a inefficient? explain.