Screen sizes of rectangular television sets are measured on the diagonal. If Joe owns a television with a 62-inch screen, and Daniel owns a geometrically similar television with
a 31-inch screen, what is the ratio of the area of Daniel’s screen to the area of Joe’s
screen? Express your answer as a common fraction.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

How many zeroes do we write when we write all the integers 1 to 243 in base 3?

Gray looks up the definition of point. a point is a location in a region. what is true about the statement describing the word point? 1. the statement uses the terms location and region that are defined based on an understanding of a point. 2.the statement precisely defines the concept of a point. 3. the statement does not include information needed to fully define a point. 4. the statement is an incorrect description of a point because it does not use mathematical words.