P02 - of the blood as it travels through a vessel is R = K...

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Project 2 MAC 2311 1. What are all values of X for which sin( X ) = 0 ? In interval notation, what is the range of values for sin( θ ) ? Using the above information, solve the equation sin( π sin( θ )) = 0 . 2. For this problem we will work with the function f ( x ) = x . Give a quick sketch of the function f ( x ) on the axes below. Write a function d ( ω ) that represents the distance from the point ( 0 , 0 ) to the point on the graph of f ( x ) having x -coordinate ω . Illustrate this in your picture above by labelling the two points and drawing the line between them in the three cases when ω is chosen to be 1 , 4 , or 9 . What is the domain of the function d ( ω ) in this current context? If you were simply given your function d ( ω ) as a formula without any context, what would its natural domain be?
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3. Your vascular system designs itself to minimize resistance in order to reduce the energy that is required to convey the blood through your body. Poiseuille’s law states that the resistence
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Unformatted text preview: of the blood as it travels through a vessel is R = K L r 4 where r and L are the radius and length of the vessel respectively, and K is a constant that reects the viscosity of the blood. Suppose K = 1 . Show that the total resistance of the blood traveling from A to B to C is R ( ) = 16 9 [ 2-cot( ) ] + 9 csc( ) in the case of the vessels shown below. Use a calculator to nd the value of the resistence when has the values 1 , 1 . 2 , 1 . 3 , 1 . 4 , 1 . 5 radians. = 1 = 1 . 2 = 1 . 3 = 1 . 4 = 1 . 5 Resistance R ( ) Which of those angles produce the lowest resistence? What is its degree measure? Where would point B lie in that case? Later in the semester, we will be able to calculate the exact angle that minimizes the resistence in this case and a law for two vessels in general....
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P02 - of the blood as it travels through a vessel is R = K...

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