Sitting on a park bench, you see a swing that is 100 feet away and a slide that is 80 feet away. the angle between them 30°. what i the approximate distance between the swing and the slide? a: 24 feet b: 50 feetc: 148 feetd: 161 feet

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) = .

The two box p digram the two box plots show the data of the pitches thrown by two pitchers throughout the season. which statement is correct? check all that apply. pitcher 1 has a symmetric data set. pitcher 1 does not have a symmetric data set. pitcher 2 has a symmetric data set. pitcher 2 does not have a symmetric data set. pitcher 2 has the greater variation.ots represent the total number of touchdowns two quarterbacks threw in 10 seasons of play

Look at this system of equations. -3x + 3y = 12 y = x + 4 the solution set of this system is best explained by which of these statements? a) the graphs of the equations are the same line because the equations have the same slope and the same y-intercept. the system has infinitely many solutions. b) the graphs of the equations are parallel lines because they have the same slope but different y-intercepts. the system has no solution. c) the graphs of the equations are lines that intersect at one point because the equations have the same slope but different y-intercepts. the system has exactly one solution. d) the graphs of the equations are lines that intersect at one point because the equations have the same slope and the same y-intercept. the system has exactly one solution.