Nectar foraging by bumblebees suppose that, instead of the specific nectar function in example 2, we have an arbitrary function n with ns0d − 0, nstd > 0, n9std . 0, n0std , 0, and arbitrary travel time t.

(a) interpret the conditions on the function n.
(b) show that the optimal foraging time t satisfies the equation n9std − nstd t 1 t
(c) show that, for any foraging time t satisfying the equation in part (b), the second derivative condition for a maximum value

Nina has prepared the following two-column proof below. she is given that ∠oln ≅ ∠lno and she is trying to prove that ol ≅ on. triangle oln, where angle oln is congruent to angle lno step statement reason 1 ∠oln ≅ ∠lno given 2 draw oe as a perpendicular bisector to ln by construction 3 ∠leo ≅ ∠neo transitive property of equality 4 m∠leo = 90° definition of a perpendicular bisector 5 m∠neo = 90° definition of a perpendicular bisector 6 le ≅ en definition of a perpendicular bisector 7 δole ≅ δone side-angle-side (sas) postulate 8 ol ≅ on cpctc nina made two errors in the proof. identify and correct the errors.