Please solve fully

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.8 − 11 +

121

8

  −

1331

64

  +  

Step 1

To see 8 − 11 +

121

8

  −

1331

64

  +    as a geometric series, we must express it as

∞	ar n − 1
n = 1

.

For any two successive terms in the geometric series

∞	ar n − 1
n = 1

, the ratio of the the two terms,

ar n

ar n − 1

, simplifies into an algebraic expression given by  

$$r

   .

Step 2

In our series 8 − 11 +

121

8

  −

1331

64

  +   , the ratio

−   1331 64

121 8

is r = -11/8  

-11/8

.

Step 3

In the series 8 − 11 +

121

8

  −

1331

64

  +   , the n = 3 term is

121

8

.

If this is to equal ar ² = a

−

11

8

	2

, then a = 8  

8

.

Step 4

Similarly, −

1331

64

  =  

−

11

8

	3

.

1a) Starting at the level of the external environment, identify the environmental condition and series of steps that would be required to hyperpolarize an ‘on’ bipolar cell. Assume that the photoreceptor is wired directly to the bipolar cell.

1b) How would the environmental condition and/or series of steps in part 1a) be different (if at all) if you had hyperpolarized an ‘off’ bipolar cell? Again, assume that the photoreceptor is wired directly to the bipolar cell.

1c) In question 1b), the stimulus would have been received in the center of an “off centre, on surround” receptive field. What would the response of the ‘off’ bipolar cell be if the same stimulus as question 1b) had been received in the ‘on surround’? Include all steps necessary to explain your answer starting at the glutamate release from the photoreceptor.

A 38 g ball with a radius of 25 mm rolls back and forth in a hemispherical bowl of radius 7 cm.

(a) What is the period of the oscillation if the ball is solid?


(b) What is the period of the oscillation if the ball is hollow?


(c) What is the percent difference between the two?

A grandfather clock has a pendulum that consists of a thin brass disk of radius 36 cm and mass 1.8 kg that is attached to a long, thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite the disk. The pendulum should be designed so that its period is 2 s for small oscillations when the gravitational acceleration is 9.8 m/s².

(a) What should the length of the rod be?


(b) If this were a simple pendulum, what would the rod's length have to be?


[Don't forget to account for the physical size of the disk.]

(c) What would the percent error be in using the equations for a simple pendulum?

A thin circular sheet of glass with a diameter 5 meters is rubbed with a cloth on one surface and becomes charged uniformly. A chloride ion (a chlorine atom which has gained one extra electron) passes near the glass sheet. When the chloride ion is near the center of the sheet, at a location 0.8 mm from the sheet, it experiences an electric force of 8e-15 N, toward the glass sheet. In this problem, use the value ε₀ = 8.85e-12 C²/(N·m²)

How much charge is on the surface of the glass disk? (give amount, including sign, and correct units)

A particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of 0.995c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 3.3 × 10^-8 s. (a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart?

Discuss various types of pumping that can be used in lasers.            [10]

At a factory, a noon whistle is sounding with a frequency of 480 Hz. As a car traveling at 61.0 km/h approaches the factory, the driver hears the whistle at frequency fi. After driving past the factory, the driver hears frequency ff. What is the change in frequency ff - fi heard by the driver? Assume the speed of sound in air is 343 m/s.

A)Please give brief answers to rolling process questions below;

1) Which parameters affect possible maximum draft in rolling operations? Please also explain that process and product effects if these parameters increased and decreased.

2) Please explain effect of material speed during rolling process.

3) Please explain what kind of effects could be seen on process and product if rolling force increased and decreased more than its optimum value?

B)Please give brief answers to extrusion process questions below;

1) What kind of products can be manufactured by using extrusion process? Give product examples which are composed of metal and plastic.( 6 metal, 3 plastic)

2) Please indicate extrusion die angle on a basic hand drawing sketch, and explain what happen if the die angle increased and decreased.

3) What is impact extrusion?

C) Please give brief answers to deep drawing process questions below;

1) What is LDR for deep drawing process? Explain its effect on process and product if it is increases and decreases.

2) What are the most common observed defect types during deep drawing process? Please also illustrate them with a simple hand sketch.

3) Which parameters affects drawing force? Please comment on them.

D)Please give brief answers to shearing process questions below;

1) What is punch and die mission during shearing process? Explain why punch and die clearance is important?

2) Please explain the shearing process types. At least give 3 types with 2 product examples.

E)Please explain the processes asked below;

1) What is Mannesmann process? Please explain Mannesmann effect. Give at least 3 product examples

2) What is rotary swaging process? Give at least 3 product examples.

I REALLY NEED YOUR HELP IN THIS HOMEWORK. PLEASE:) THNAK YOU SO MUCH!!

You have been hired to plan a mission to Mars. Your employer knows very little about space travel; they simply want to be the first individual to send a mission to Mars. They have vast but not unlimited resources. Your first step is to educate them about the realities of space flight and the pros and cons of various options.

A. Give at least one advantage for each option. For example, answer both “What is an advantage of one-way over round trip travel?” and “What is an advantage of round trip over one way?” Try to be as specific as you can.

(a) One way vs. round trip

(b) Crewed vs. Uncrewed

(c) Hohmann vs. fast transfer

(c) Landing vs. orbiting

B. Your employer says “If you were to send a mission to Mars, what kind would it be? Describe it for me.”

C. After listening to your presentation, your employer says “What I really want to do is to land a spacecraft on Mars and dig down into the surface to find water. Can you tell me how to do this with minimal cost? Also, once I have the water, how might I use that to benefit future Mars missions?”   What is your response?

A potential difference of V0 is maintained between the inner and outer conductor of a coaxial cable of length L, inner conductor radius a, and outer conductor radius b. (a) Calculate the current through the medium (∈,σ) using the analogy of ?⃗ and ?⃗⃗⃗. (b) Now, assume that V0 = 500 V, L = 50 m, a = 2 cm and b = 6 cm, and the relative permittivity and the conductivity of the medium are ∈?=3 and σ=5 μS/m, respectively. Determine the current and the power dissipated in the medium.

6. Describe the different types of dispersion in an optical fiber. (1718)

7.Discuss how a Bragg Grating can be used to compensate for dispersion. (1718)

You can entangle position and momenta of two atoms by using entangled light. Atoms A and B are located at sites A and B. You get entangled light by parametric-down-conversion and send one photon to atom A and the corresponding entangled photon to atom B. You keep on sending entangled pairs until atom A and B come to a steady-state and they will be entangled with each other. Essentially what is happening is that "entanglement is transferred from a pair of quantum-correlated light fields to a pair of trapped atoms in a process of quantum state exchange."

enter image description here The atom is trapped in the x direction. The atom is stuck in a harmonic potential. The entanglement is only in x direction.

position are anti-correlated between two atoms: (q1 = -q2) and momentum are correlated (p1 = p2)

You can measure the position and momenta of each particle using homodyne measurement techniques. So, if I were to measure the position of atom A very very precisely, then its momentum would be very uncertain. Its distribution would be so smeared out that it'd be approaching a uniform distribution of momentum, if position is a sharp delta function. At this point, there would exist a probability that the momentum is very large, and thus its kinetic energy would be very large too! KE = p^2/2m. (Need a checking here) Would there be a non-negligible probability that the energy of the atom would be so large it would escape the harmonic oscillator trap?!

Since the two atoms are entangled, p1 = p2, thus atom B would also have correlated momentum which translates to correlated kinetic energy. Atom B would also have enough energy to escape the harmonic trap as well.

If everything I have stated is correct, haven't I found a method to communicate via translational entanglement, because I can control the outcome of the measurement? (Unlike spin...) Let's say we have an ensemble of these entangled atoms. A scientist at Lab A can send a binary message by choosing to measure the position of an atom at Lab A to high precision thereby causing the atom at Lab B to escape the harmonic trap. Not measuring would keep the atoms trapped. The presence or absence would correspond to a 1 or a 0. Since there would exist chances that the momentum would not be large enough to cause an escape, then we could have batches of entangled atoms that would represent one bit. Very costly, but you can interact instantaneously over large distances...

1. A helium nucleus (called an alpha particle) contains 2 neutrons and 2 protons with no electrons. If any electrons are added, there is a negligible amount of mass added but obviously one negative charge per electron is added. Three particles are injected into a constant B-field of 2T at a velocity of 3×106ms. The first particle is only the alpha particle (He++), the second particle is a nucleus with 1 electron (He+), and the third particle is a nucleus with 2 electrons (He). They are injected into the B-field at the same point, and they need to complete one half circle to land on the detector. What is each of their radii? How far apart on the detector are they? The masses of a neutron and proton are each 1.67×10-27kg, and the magnitude of the charge of an electron and proton is 1.6×10-19C. (Note: you need the total charge of each particle.)

Suppose a company needs a analytical balance and a top loader of 2 kg capacity and 0.01 g readability.

2. What five tests do they need to conduct on each of these new balances?

Since they are new they don't usually need a hysteresis test.