Design and simulate a DC power supply using Zener diodes to produce 15 V if you have two Zener diodes of Zener voltage 7.5 V when the dc link voltage 24 V. The assignment report should include the following information: Assignment objectives, introduction, design procedure, simulation with simulation results, and conclusion.

An ac generator with a frequency of 30.0 Hz and an rms voltage of 14.0 V is connected to a 65.0 μF capacitor.

1. What is the maximum current in this circuit?

2. What is the current in the circuit when the voltage across the capacitor is 4.30 V and increasing?

3. What is the current in the circuit when the voltage across the capacitor is 4.30 V and decreasing?

True/False Question: If sppan{u,v}=W where u not equal to v. Then dim(W)=2.

Answer: False

Reasoning let u=1, v=2 then span(1,2}=R but dim(R)=1 not 2.

I know the answer is false. please tell me whether my reasoning is correct.

Write a MATLAB function that will generate chi-square random variables with v degrees of freedom by generating v standard normal, squaring them and then adding them up. This uses the fact that is chi-square with v degrees of freedom. Generate some random variables and plot in a histogram. The degrees of freedom should be an input argument set by the user.

A voltaic cell consists of a Mn/Mn²⁺ electrode (E° = –1.18 V) and a Zr/Zr⁴⁺ electrode (E° = –1.53 V). Calculate [Mn²⁺] if [Zr⁴⁺ ] = 1.0x10⁻⁴ M and E_cell = 0.40 V at 25°C.

(1) 0.49 M           (2) 0.24 M           (3) 0.040 M         (4) 1.8 M            (5) 2.0 M

3.5.4 ([Ber14, Ex. 3.6.14]). Let T : V → W and S : W → U be linear maps, with V finite dimensional.

(a) If S is injective, then Ker ST = Ker T and rank(ST) = rank(T).

(b) If T is surjective, then Im ST = Im S and null(ST) − null(S) = dim V − dim W

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)