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.

The van der Waals equation for 1 mole of gas is given by (p +av^-2)(v - b) = RT. In general, curves of p versus v forvarious values of T exhibit a maximum and a minimum at the twopoints where (δp/δv)_T = 0. The maximum and minumum coalesceinto a single point on that curve where(δ²p/δv²)_T = 0 inaddition to (δp/δv)_T = 0. This point is calledthe "critical point" of the substance and its temperature,pressure, and molar volume are denoted by T_c,p_c, and v_c, respectively.
    (a) Express a and b in terms of T_cand v_c.
    (b) Express p_c in terms ofT_c and v_c.
    (c) Write the van der Waals equation in terms ofthe reduced dimensionless variables T' ≡ T/T_c , v'≡ v/v_c , p' ≡ p/p_c
This form should involve neither a nor b.

1) Which of the following components of IT contingency planning is most important?

a. Verification of systems routines

b. Security over the contingency site

c. Documentation of the plan

2) Which of the following is the best answer regarding differences between the COSO and ERM frameworks;

i) Monitoring

ii)Information

iii)Risk Response

iv) Strategical Objectives

v) Control Activities

Group of answer choices

a. i, iii, & v only

b. ii & v only

c. iii & iv only

d. i, ii & v only

d. Integration of the IT disaster recovery plans with the business plans.

3) Recommendations should be included in final audit communication to:

a. Provide management with options for addressing audit observations

b. Ensure that problems are resolved in the manner suggest by the auditor

c. Minimize the amount of time required to correct audit observations.

d. Guarantee that audit observations are addressed.

Hipsterville economy has 4sectors: Kale(K), mason jars (M),vintage goods(V), and bicycle repair (B). The economyis in equilibrium. Suppose the following:Sector Kalesells 10% of its output to M , 25% to V, and retains the rest Sector Mason jars sells 30% of its output to K, 35% to V, 25% to B, and retains the rest Sector Vintage sells 30% of its output to K, 15% to M, 40% to B, and retains the rest Sector Bike repair sells 20% of its output to K, 10% to M, 30% to V, and retains the rest

a) Construct the exchange table(table ofinputs/outputs) for this economy. You can give your answer in table form or in matrix form, but be sure that the meaning of rows and columns is clear.

b)Find a set of equilibrium prices for the economy.

Demonstrate an understanding of an aspect of either Atkinson & Shifrin's model or Baddeley's model of memory. For instance, one stage of memory (Sensory, Short-Term/Working, or a type of Long-Term) can be defined and exemplified. Is there a factor that would impact the accuracy of encoding or retrieval for the memory chosen?   

After establishing how memory works for most of us, examine one of the links for people with either incredible or impaired memories. Discuss one way in which the memory of one of these differs from most people's memory. Include differences in automatic or effortful processing if applicable.   

- Clyde: The Man with a 30 Second Memory

- https://www.youtube.com/watch?v=WmzU47i2xgw

- H.M.

- https://www.youtube.com/watch?v=SQASyR0w8Qo

- The Mind of the Savant

- http://topdocumentaryfilms.com/beautiful-minds-the-psychology-of-the-savant/

- Five Incredible Memories

- https://www.youtube.com/watch?v=aAbQvmf0YOQ

- https://www.youtube.com/watch?v=1th1fVIc8Vo

create "bitty.c" that uses bitwise operators and return statements to implement the functions in "bitty.h".

"bitty.c" that can only implement "bitty.h"

_____________________________________________________________

bitty.h:

// Returns 1 if v is an even number, otherwise returns 0

unsigned char isEven(unsigned char v);

// Returns 1 if v is zero, otherwise returns 0

unsigned char isZero(unsigned char v);

// Returns 1 if a and b have the same value, otherwise 0

unsigned char equals(unsigned int a, unsigned int b);

// Returns a if a is greater than or equal to b, otherwise returns b

// You may use if but may not use comparison operators or else

// e.g. if(a) is allowed but if(a<b) and if(b==0) are not allowed

unsigned char geq(unsigned char a, unsigned char b);

// Returns the number of bits that are 1

unsigned char tally(unsigned int n);