Calculate the mean in this data set number of sites- 15 total number of shield darters found - 75

1. writing an equation for an exponential function by 2. a piece of paper that is 0.6 millimeter thick is folded. write an equation for the thickness t of the paper in millimeters as a function of the number n of folds. the equation is t(n)= 3. enter an equation for the function that includes the points. (-2, 2/5) and (-1,2)

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) = .

In the diagram, points d and e are marked by drawing arcs of equal size centered at b such that the arcs intersect ba and bc. then, intersecting arcs of equal size are drawn centered at points d and e. point p is located at the intersection of these arcs. based on this construction, m , and m