Question 1

a) Prove that if u and v are distinct vertices of a graph G, there exists a walk from u to v if and only if there exists a path (a walk with distinct vertices) from u to v.

b) Prove that a graph is bipartite if and only if it contains no cycles of odd length.

Please write legibly with step by step details. Many thanks!

Answer for a and be should be answered independently.

Let (X,d) be a metric space, and

a) let A ⊆ X. Let U be the set of isolated points of A. Prove that U is relatively open in A.

b) let U and V be subsets of X. Prove that if U is both open and closed, and V is both open and closed, then U ∩ V is also both open and closed.

Using only the rules of SD, derive the following rules of SD+:

a) Disjunctive Syllogism (one case) :

P v Q
~P

b) Commutation: (wedge only) :

P v Q <--> Q v P

c) Implication :

P ⊃ Q <--> Q ⊃ ~P

d) Double Negation

P <--> ~~P

e) DeMorgan

(~(P & Q) <--> ~P v ~Q only)

Use SL sentences rather than metavariables in your derivations. Each direction of replacement rules must be shown (that is, you are proving "equivalence in SD" in these cases)

Problem 3.030 SI Using the tables for water, determine the specified property data at the indicated states. (a) At p = 3 bar, v = 0.35 m3/kg, find T in °C and u in kJ/kg. (b) At T = 320°C, v = 0.23 m3/kg, find p in MPa and u in kJ/kg. (c) At p = 28 MPa, T = 700°C, find v in m3/kg and h in kJ/kg. (d) At T = 10°C, v = 10 m3/kg, find p in kPa and h in kJ/kg.

An Uncontrolled Full-Wave full-bridge rectifier with RL-Source load and Discontinuous load
current is to be designed based on the following assumptions and constraints. Design the circuit
and calculate the parameters of the rectifier based on the following assumptions and constraints.
Simulate the designed rectifier in PsPice and compare the simulated and the calculated results.

a) The AC source is 220 V rms at 50 Hz. Vdc= 65 V, power absorbed by the resistor is 360
W.
b) The AC source is 220 V rms at 50 Hz. Vdc= 70 V, power absorbed by the resistor is 400W.

You are give a system about which two things are known: the relation between pressure,

volume and temperature, and the heat capacity at constant volume (α is a constant) PV^3=αT; CV =A(V)T

Please
(a) Find the derivative of entropy with respect to volume at fixed T

(b) Show that the coefficient A(V ) in the specific heat is independent of V

(c) Find S(T,V) in terms of the (assumed known) value S0 of the entropy at a given temperature and volume T0, V0, S0 = S(T0, V0).

(d) Find the heat capacity at constant pressure

Describe a client from your clinical setting or previous experience who experienced depression or mania. Include a brief history and 3-5 most pertinent medications.

v Identify one problem that was not resolved with the treatment regimen. What are the reasons it may not have been successful? Include nursing as well as other team members.

v Identify one effective nursing intervention and why you feel it worked.

v Overall, do you feel this client was kept safe? Why or why not?

v Please provide supporting evidence for your answers.

A photovoltaic solar collector with an area of 2 m2 is tracking the sun for 8 hours on a sunny day. Assume that, the solar flux on the collector is constant through the day as 1000W/m2. PV Solar collector properties are:

FF: %75, Efficiency: %18.2

V (MPP, nominal) = 28 V

V (Open Circuit) = 32 V

a) What is the total amount of energy converted to electricity?

b) Assume a reasonable price for the cost of electricity and then calculate the value of electricity ($) produced for whole day.

c) Calculate the generated current and Short Circuit Current.

Question:1

Calculate the density, in g/cm³, of a metal that has a volume of 41.3 L and a mass of 70.05 kg.

Question:2

You have 20.0 L of a 8.18% by volume (% v/v), water-based dye solution. Calculate the volume of pure dye and water that were used to prepare the solution. You may assume that volumes are additive.

Question:3

How many mL of pure (100.0%) food dye are needed to prepare 437.4 mL of 34.8% by volume (%v/v) food dye solution? You may assume that volumes are additive.

1. A CSTR and a PFR of equal volume (VCSTR = VPFR = V) are used to degrade a compound in a first-order manner under steady-state conditions.

(a) If the CSTR gives a 80% degradation what is the efficiency of the PFR?

(b) If instead of one CSTR of volume V, you use 5 CSTRs in series, each having a volume of 0.2V, what would be the overall degradation efficiency?

(c) Show that the overall efficiency will be equal to that of the PFR (volume V) if you use an infinite number (n→∞) of CSTRs in series each having a volume of V/n.