Solve for the value of b

Adriana sold 50 shares of a company’s stock through a broker. the price per share on that day was $22.98. the broker charged her a 0.75% commission. what was adriana’s real return after deducting the broker’s commission? a. $8.62 b. $229.80 c. $1,140.38 d. $1,149.00

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) = .

Rhombus adef is inscribed into a triangle abc so that they share angle a and the vertex e lies on the side bc . what is the length of the side of the rhombus if ab=c, and ac=b.