My car gets 24 miles per gallon, and gasoline costs $2.80 per gallon. If we consider only the cost of gasoline, how much does it cost (in dollar) to drive each mile? Round your answer to the nearest cent.

Choose the TWO fractions that are multiplied together to calculate the solution using dimensional analysis. Make sure that the units of the fractions you choose cross-cancel to produce the unit of your desired answer. You must have the correct two fractions selected at the same time to get credit when you check your answer. You get two attempts to check your answer. 

If we consider only the cost of gasoline, how much does it cost (in dollar) to drive each mile? Round your answer to the nearest cent.

$ ______ per mile

 

3. If an electrical circuit consists of two resistors R, and R2 connected in parallel, then the total resistance R of the circuit is given by All resistances are measured in ohms (S2). Assume R2 has a constant resistance equal to 512, but Ri is a variable resistor. (a) Find dk. What are the units of this quantity? (4 marks) (b) Suppose the current resistance of R1 is 1l and it is is increasing at a rate of 0.2 2/sec. How fast is the total resistance of the circuit increasing? State your answer with appropriate units. (6 marks)

If two resistors with resistances are connected in parallel, as in the figure, then the total resistance R, measured in ohms (), given by

If and are increasing at rates of , respectively, how fast is R changing when and ?

The blood vascular system consists of blood vessels (arteries, arterioles, capillaries, and veins) that convey blood from the heart to the organs and back to the heart. This system should work so as to minimize the energy expended by the heart in pumping the blood. In particular, this energy is reduced when the resistance of the blood is lowered. One of Poiseuille’s Laws gives the resistance R of the blood as

where L is the length of the blood vessel, r is the radius, and C is a positive constant determined by the viscosity of the

(a) Use Poiseuille’s Law to show that the total resistance of the blood along the path ABC is

where a and b are the distances shown in the figure.

(b) Prove that this resistance is minimized when

(c) Find the optimal branching angle (correct to the nearest degree) when the radius of the smaller blood vessel is two-thirds the radius of the larger vessel.