In the figure shown two lines intersect at a right angle and two semicircles are drawn so that each semicircle has its diameter on one line and is tangent to the other line. The larger semicircle has radius of 1. The smaller semicircle intersects the larger one, dividing the larger semicircle arc into the ratio 1:5. What is the radius of the smaller semicircle? Express your answer in simplest radical form.

In the given figure ar(adf) =ar(cda) and ar(cdf) = ar(cdf). show that abdc and cdfe are trapeziums.

Describe how making an ‘and’ compound sentence effects your solution set

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.