Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length a (see figure below) if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.

Which number is main idea? i need answer quick. (1) people may think that love and romantic feelings are enough of a basis for choosing a spouse. (2) the chances of a marriage surviving, however, would improve if prospective marriage partners considered a few unromantic questions before deciding on matrimony. (3) for example, do the two individuals involved share a common socioeconomic background? (4) the more similar they are in their social, economic, religious, and cultural backgrounds, the more similar their expectations about married life will be. (5) in addition, what are their goals? (6) it’s a big advantage to the marriage if they know and share one another’s goals concerning career, lifestyle, and family. (7) finally, and maybe most important, how does the prospective spouse treat others in his or her life? (8) during the courtship, the boyfriend or girlfriend may get special consideration, but in the long run, spouses will probably treat each other about the same way they treat their own family members.

Afarmer began a new method of reducing grain spills. this reduced the number of mice on the farm. the number of snakes in the surrounding area decreased at the same time. the snakes depended on the mice that lived in the field. what’s the likely reason the snake population decreased? a. the number of snake predators increased. b. the number of mice increased. c. the number of mice decreased. d. the pesticides affected the snakes. e. a new breed of mice moved into the field.

The graph shows a trend in an ecosystem over time caused by increased pollution in the region. what can you conclude from the graph? a. there’s lower biodiversity among birds. b. there’s a higher reproductive rate among birds. c. there’s a significant decline in the number of producers. d. other types of animals were unaffected by pollution.