Find the measure of the angle indicated. Assume that lines which appear tangent are tangent. K
L
M
87°
?
149°
N

Find the perimeter of the figure shown above. a. 18 yds c. 20 yds b. 10 yds d. 24 yds select the best answer from the choices provided

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) = .

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