Let ω be a convex region in r2 and let l be a line segment of length i that connects points on the boundary of ω. as we move one end of l around the boundary, the other end will also move about this boundary, and the midpoint of l will trace out a curve within ω that bounds a (smaller) region γ. using the corollary to green’s theorem for finding area, find an expression that relates the area of γ to the area of ω in terms of the length i of the line segment.

Giving 100 points asap bev has to cut her grandma's grass this weekend and wants to know exactly how much area she will be cutting. calculate the area of the polygon. be sure to show all your work and explain your answer.

The boiling point of water at an elevation of 0 feet is 212 degrees fahrenheit (°f). for every 1,000 feet of increase in elevation, the boiling point of water decreases by about 2°f. which of the following represents this relationship if b is the boiling point of water at an elevation of e thousand feet? a) e = 2b - 212 b) b = 2e - 212 c) e = -2b + 212 d) b = -2e + 212

Astudent is determining the influence of different types of food on the growth rate of spiders. she feeds one group of spiders two caterpillars twice a week. the other group received similarly-sized beetles twice a week. she records the amount of time required for individuals to reach sexual maturity. her hypothesis is that the spiders feeding on caterpillars will have a faster growth rate because caterpillars have a higher protein content compared to beetles. in this experiment, what is the dependent variable? spiders assigned to different feeding groups. time required to reach sexual maturity number of prey items fed twice a week. growth rates of each group.