(a) two hypothetical planets are moving about the sun in elliptical orbits having equal major axes. the minor axis of one, however, is half that of the other. how do the periods of the two planets compare? (b) the moon revolves about the earth in 27.3 days in an elliptical orbit whose semimajor axis is 60 times the earth’s radius. what would be the period of a satellite revolving close to the earth’s surface? (since the satellite is close to the earth’s surface, let its semimajor axis be the earth’s radius, r.)

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

Damon makes 20 cups of lemonade by mixing lemon juice and water. the ratio of lemon juice to water is shown in the tape diagram. lemon juice\text{lemon juice} lemon juice water\text{water} water how much lemon juice did damon use in the lemonade? cups

Design an er diagram for keeping track of information about votes taken in the u.s. house of representatives during the current two-year congressional session. the database needs to keep track of each u.s. state's name (e.g., texas', new york', california') and include the region of the state (whose domain is {northeast', midwest', southeast', southwest', west'}). each congress person in the house of representatives is described by his or her name, plus the district represented, the start date when the congressperson was first elected, and the political party to which he or she belongs (whose domain is {republican', democrat', 'independent', other'}). the database keeps track of each bill (i.e., proposed law), including the bill name, the date of vote on the bill, whether the bill passed or failed (whose domain is {yes', no'}), and the sponsor (the congressperson(s) who sponsored - that is, proposed - the bill). the database also keeps track of how each congressperson voted on each bill (domain of vote attribute is {yes', no', abstain', absent'}). additional information: