Suppose that a parallel-plate capacitor has circular plates with radius R = 60.0 mm and a plate separation of 4.6 mm. Suppose also that a sinusoidal potential difference with a maximum value of 360 V and a frequency of 120 Hz is applied across the plates; that is

V=(360.0 V)sin((2.*π)*(120 Hz * t)).

Find Bmax(R), the maximum value of the induced magnetic field that occurs at r = R.

Find B(r = 30.0 mm).

Find B(r = 120.0 mm).

Find B(r = 180.0 mm).

PLEASE WRITE ANSWER IN YOUR OWN WORDS BECASUE I HAVE TO SUBMIT THE ANSWER ON TURTIN

1. Provide an appropriate answer to the following questions:

a. What are the main differences between preference shares and ordinary shares? Explain.

b. Explain the concept of “Diversification” in finance.

c. Explain the terms systematic risk and unsystematic risk.

d. Explain each of the components of the Weighted Average Cost of Capital formula below:

WACC = [ D/V × (1 − Tc)r_debt] + (E/V × r_equity)

D =

V =

Tc =

r_debt =

E=

r_equity =

For each reaction listed, determine its standard cell potential (in V) at 25°C and whether the reaction is spontaneous at standard conditions.

(a)

Co²⁺(aq) + Mg(s) → Co(s) + Mg²⁺(aq)

ΔE° = V

(b)

2 Al(s) + 3 Cu²⁺(aq) → 2 Al³⁺(aq) + 3 Cu(s)

ΔE° = V

(c)

Ag(s) + Cu(NO₃)₂(aq) → AgNO₃(aq) + CuNO₃(aq)

ΔE° =

(d)

Ni(s) + Zn(NO₃)₂(aq) → Ni(NO₃)₂(aq) + Zn(s)

ΔE° =

An object with mass 40.5 kg is given an initial downward velocity -3ms in a medium that exerts a resistive force with magnitude proportional to the square of the speed. The resistance is 80 N when the velocity is -4m/s. Use g=10m/s^2

a. Write out a differential equation in terms of the velocity v, and acceleration a



b. Find the velocity v(t) for the object

v(t)=

c. Upload a document with the work for parts a and b and a computer generated solution curve with a window appropriate for this situation.




d. State and interpret the end behavior for the solution found in part b.

Q1- V Company had the following select transactions.

Apr. 1, 2017 Accepted G Company’s 12-month, 12% note in settlement of a $30,000 account receivable.

July 1, 2017 Loaned $25,000 cash to T on a 9-month, 10% note.

Apr. 1, 2018 Received principal plus interest on the G note.

Apr. 1, 2018 T dishonored its note; V expects it will eventually collect.

Instructions Prepare journal entries to record the transactions. V prepares adjusting entries once a year on December 31.

Five kilograms of ammonia (NH3) undergo a refrigeration cycle
detailed as:
• Process 1-2: isothermic expansion from saturated vapor at 10ºC, to P = 3 bar with
Q = 400 kJ.
• Process 2-3: isochoric cooling to 0 ◦C.
• Process 3-4: isobaric compression.
• Process 4-1: isochoric heating.

Calculate:

a) the P −v and T −v diagrams.

b) the states table detailing P, v, T and u.
c) the process table for Q, W and ∆U.
d) the performance coefficient, β, of the cycle.

A) Find the directional derivative of the function at the given point in the direction of vector v. f(x, y) = 5 + 6x√y, (5, 4), v = <8, -6>

Duf(5, 4) =

B) Find the directional derivative, D_uf, of the function at the given point in the direction of vector v.

f(x, y) =ln(x²+y²), (4, 5), v = <-5, 4>

D_uf(4, 5) =

C) Find the maximum rate of change of f at the given point and the direction in which it occurs.

f(x, y) =3 y²/x, (2, 4)

direction of maximum rate of change (in unit vector) = <    ,   >
maximum rate of change =

D) Find the directional derivative of f at the given point in the direction indicated by the angle θ.

f(x, y) = 2x sin(xy), (5, 0), θ = π/4

D_uf =

A parallel-plate capacitor has plates of area 0.15 m² and a separation of 1.00 cm. A battery charges the plates to a potential difference of 100 V and is then disconnected. A dielectric slab of thickness 4 mm and dielectric constant 4.8 is then placed symmetrically between the plates.

(a) What is the capacitance before the slab is inserted?
pF

(b) What is the capacitance with the slab in place?
pF

(c) What is the free charge q before the slab is inserted?
C

(d) What is the free charge q after the slab is inserted?
C

(e) What is the magnitude of the electric field in the space between the plates and dielectric?
V/m

(f) What is the magnitude of the electric field in the dielectric itself?
V/m

(g) With the slab in place, what is the potential difference across the plates?
V

(h) How much external work is involved in the process of inserting the slab?
J

Consider N massless non-interacting spin-s fermions in a three-dimensional box of volume V .
(a) Find the Fermi energy E_F as a function of N, V , and s.
(b) For zero temperature, find the pressure in terms of N, V , and E_F .
(c) Plot the occupation of states as a function of the energy at a temperature of T =E_F /(10k). Your graph can be a sketch by hand. However, the effect of the finite temperature should be indicated clearly.
(d) Suppose that you start with a gas of these particles in a box of volume V near T = 0.
Now suppose that a valve is opened such that the gas can undergo a free expansion, allowing it to come to equilibrium at a new volume that is twice as large as the initial volume. Assuming no work or heat transfer occurs during the expansion, does the temperature of the gas go up, down, or stay the same? Explain your reasoning.

1. A square-based pyramid has the volume V. If the vertical height is H (the normal distance from the square base to the point), write a MATLAB function that:

has V and H as input arguments

calculates the length of the side of the square (S)

has S as an output argument

Write MATLAB code that tests the function for the values:

V = 10 m³ and H = 2 m.

V = 2.586×10⁶ m³ and H = 146.6 m (the original dimensions of the Great Pyramid of Giza).

2. Repeat SPIDER 2 Q1, but write a function that accepts a year as an input argument and determines whether that year is a leap year. The output should be the variable extra_day, which should be 1 if the year is a leap year and 0 otherwise.

You must write a script file that thoroughly tests whether your function works correctly.