1. BRANCHING BLOOD VESSELSFigure 1: A Picture of Blood CapillariesThe blood vascular system consists of blood vessels (arteries, arterioles, capillaries, and veins) thatconvey blood from the heart to the organs and back to the heart. This system should work so as tominimize the energy expended by the heart in pumping the blood. In particular, this energy is reducedwhen the resistance of the blood is lowered. One of Poiseuille's Laws gives the resistance R of theblood by the following equation:R = Cwhere L is the length of the blood vessel, r is the radius, and C is a positive constant determined bythe viscosity of the blood.Figure 2: Vascular Branching Sketch1Answer the following questions:(a) Looking at Figure 2, express the total resistance R given by Equation 1 of the blood along thepath ABC as a function of the branching angle 0. Meaning that, you need to find the followingequation:+ CBC|R(0) = Cwhere length |AB| and the length |BC| of the blood vessel are written in terms of the branchingangle 0. Solve this question as follows:i. express sin 0 in terms of length b and length |BC|and then make |BC|the subject of theformula.ii. express cos 0 in terms of length |BD|and length |BC\|and then make |BC|the subject of theformula.' 2!iii. express length |BD| in terms of length a and length |AB| and substitute this answer into theequation you found in question ii above., ?!iv. equate the expressions for |BC|, thus producing an equation for the length |AB|||v. substitute the answers you found in question i) and question iii) into Equation 2.

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