Water of varying density flows in an estuary, 5 meters deep. The density varies linearly from 1025 kg/m3 at the bottom to 1000 kg/m3 at the water surface. The velocity distribution is given by the equation, V = 8 - ((1/2)(z-4)^2) m/s, where z is elevation above the bottom.

a)Sketch (or plot using software such as Excel or Matlab) the density (ρ) profile, the velocity (V) profile, and the momentum (ρ V) profile

b)Find the two values of z for which velocity equals 7.5 m/s. Does the water have the same momentum at these points? Why or why not

C)Calculate the total momentum, ∫ ρ V d ∀ , for a volume of water 5 m deep, 1 m wide, and 1 m long.

4) Okun's law states that one extra percentage point in unemployment causes A) a 2 percent fall in GDP B) a 0.5 percent fall in GDP C) a 2 percent fall in the rate of inflation D) a 0.5 percent fall in the rate of inflation

5) If output is at its full-employment level, then A) the actual unemployment rate is zero B) the natural rate of unemployment is zero C) there are no frictions in the labor market since wages have reached their market-clearing level D) there is still some positive level of unemployment due to frictions in the labor market

6) The income velocity of money can be calculated using the following formula A) V = M/(PY) B) V = (MY)/P C) V = (PY)/M D) V = MY

You are studying myosin V, a class of myosin which can be used in cells to transport vesicles by “walking” along actin filaments, towards the plus ends of these filaments. You have identified a mutation in the gene for myosin V that affects its ATP binding site. This mutant myosin V (M) can still perform the entire cross-bridge cycle, but it takes much longer to hydrolyze ATP compared to a wild type myosin V (W).

a) Would the duration of the cross-bridge cycle be longer in M or W?Explain?

b) Would the duty cycle (the proportion of the cross-bridge cycle in which myosin is bound to actin) be longer in M or W?Explain?

c) How would this difference in duty cycle affect the ability of M to transport a vesicle along an actin filament? Explain.

1. a. Consider the following sequences, which are pieces of a larger, independently folding polypeptide. Which sequence is more likely to form an alpha helix, and which is more likely to form a beta-hairpin—a two-stranded antiparallel beta-sheet in which the strands are separated by a turn?

Sequence A: I F I C T T G P N A T V I C V F V

Sequence B: M D R L M E A M A K L D H L L A E

b. How do the structures of the residues I, V, and T versus L and M contribute to the conformational preferences of these two sequences?

c. Which residues likely form the turn between the stands in the beta-hairpin? Why are these residues suited for this structure?

1. The total market value of fish caught by a fleet of fishing boats (per month) is given by:

V = $40,000B - $1000B²

Where B is the number of boats engaged in fishing.   The cost of running one fishing boat for one month is $18,000, giving the total cost of running B fishing boats as $16,000B

1. Write down an expression for total net profit for the entire fishing fleet
2. Find the number of boats that would maximize this total net profit
3. Suppose that when B boats operate, each boat gets V/B (catch is split equally). Each boat captain can decide to operate in a given month or not. How many boats will choose to operate?
4. What is V and V/B with the number of boats you found in 3)c)?

The electric potential immediately outside a charged conducting sphere is 220 V, and 10.0 cm farther from the center of the sphere the potential is 140 V.

(a) Determine the radius of the sphere.

. cm

(b) Determine the charge on the sphere.

nC

The electric potential immediately outside another charged conducting sphere is 250 V, and 10.0 cm farther from the center the magnitude of the electric field is 360 V/m. (c) Determine all possible values for the radius of the sphere. (Enter your answers from smallest to largest. If only one value exists, enter "NONE" in the second answer blank.)

(d) Determine the charge on the sphere for each value of r. (If only one value exists, enter "NONE" in the second answer blank.)

1. For each of the following propositions construct a truth table and indicate whether it is a tautology (i.e., it’s always true), a contradiction (it’s never true), or a contingency (its truth depends on the truth of the variables). Also specify whether it is a logical equivalence or not. Note: There should be a column for every operator. There should be three columns to show work for a biconditional.

a) (P Λ ¬Q) ⇔ ¬(P ⇒ Q)

b) (¬? V¬?) ⇔ ¬(P Λ Q)

c) (P V Q) Λ ( ¬(? Λ Q) Λ (¬?))

d) (P ⇒ (Q Λ R)) ⇔ ((P ⇒ Q) Λ (Q ⇒ R))

e) (P ⇒ (Q ⇒ R)) ⇔ ((P ⇒ Q) ⇒ R) f) ((P V R) ⇒ (Q V S)) ⇒ ((P⇒ Q) Λ (R ⨁ S))

with biconditional and There should be a column for every operator

A DAG is a directed graph that contains no directed cycles.

Define G = (V, E) in which V is the set of all nodes as {v₁, v₂, ..., v_i , ...v_n} and E is the set of edges E = {e_i,j = (v_i , v_j ) | v_i , v_j ∈ V} .

A topological order of a directed graph G = (V, E) is an ordering of its nodes as {v₁, v₂, ..., v_i , ...v_n} so that for every edge (v_i , v_j ) we have i < j.

There are several lemmas can be inferred from the definition of DAG. One lemma is: if G is a DAG, then G has a node with no incoming edges. Given the above lemma, prove the following two lemmas:

If the graph G is a DAG, then G has a topological ordering.

If the graph G has a topological order, then G is a DAG.

(i) Consider a CMOS inverter supplied at V_DD= 5V with transistor parameters of K_N=K_P=50µA/V² and V_TN=-V_TP=1V. Then consider another CMOS inverter supplied at V_DD= 10V with the same transistor parameters. Draw the VTC of both inverters showing all regions of operation and the middle voltage VM. Verify your results using PSpice.

            (ii) Draw the square root of the CMOS inverter current versus the input voltage for the two CMOS inverters in given in part (i) biased at either V_DD=5 V or V_DD=10 V. Determine the peak current of the CMOS inverter at V_DD=5 V & V_DD=10 V. Verify your results using PSpice.

part(ii) required

PSpice for both parts

A photovoltaic module is used to supply constant 12 V that needed by a Tablet. Depending on insolation from the Sun, the photovoltaic module’s output voltage is changing between 18 V to 36 V (dc). Thus, a buck converter is used between the netbook and the photovoltaic module.

1) What is the duty ratio range of the dc/dc converter?

2) If the inductance of the buck converter inductor is 40 uH, what is the minimum switching frequency to limit the current ripple in the inductor to less than 1 A? 3) At constant 12 V, what is the minimum power consumption of the Tablet to keep the inductor current always continuous?

4) For the operation condition stated in 3), draw (not simulate and plot) the waveforms of i) switching status, ii)voltage cross the diode , and iii) inductor current; mark the values for each waveform