Answer the following problem below. Please make the handwritten clear and easy to read/easy to understand. Thank youu

1. Vascular Branching. A small blood vessel of radius r branches off at an angle 0 from a larger vessel of radius R to supply blood along a path from A to B. According to Poiseuille's Law, the total resistance to blood flow is proportional to T = asino-blose + b SINO Ry sinory Where a and b are as in figure below. Show that the total resistance is minimized when cose = (r/R)* 2. Bird Migration Ornithologists have found that the power (in joules per second) consumed by a certain pigeon flying at velocity v m/s is described well by the function P() = 13 + _ Assume that the pigeon can store 7 x 10' J of usable energy as body fat. (a) Show that at velocity v, a pigeon can fly a total distance of D(v) = (7 x 10' ) v/ P(v) if it uses all of its stored energy (b) Find the velocity vp that minimizes P(v). (c) Migrating birds are smart enough to fly at the velocity that minimizes distance traveled rather than minimizes power consumption. Show that the velocity V. which maximizes D(v) satisfies P' (va) = P(va)/va . Show that v. is obtained graphically as the velocity coordinate of the point where a line through the origin is tangent to the graph of P(v) as shown in the figure below. (d) Find ve and the maximum distance D(Va). Power (Jis) Minimum power consumption distance traveled 10 15 Velocity (m/s)3. A basketball player stands d feet from the basket. Let h and a be as in the figure below. Using physics, one can show that if the player releases the ball at an angle 0, then the initial velocity required to make the ball go through the basket satisfies N (E - phe ) p = N ( 1 - sin e )(tan e - tan a ] dd (a) Explain why this formula is meaningful only for a