The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume is th of the volume of the cone, at 1 27 what height above the base is the section made?

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) = .

These tables represent a quadratic function with a vertex at (0, -1). what is the average rate of change for the interval from x = 9 to x = 10?

Find the condition that the zeros of the polynomial f(x) = x^3+3px^2+3px+r may be in a.p.