Homework Help v1.3

[DeathGuiseX]

int. 1/((9x^2 - 4)^1/2)) dx

Please help me with this simple integration problem and provide all the steps on how to do it. The teach told us something about using trig identies but I'm lost as this is the first problem that we had like this.

[ahme]

Originally Posted by DeathGuiseX

int. 1/((9x^2 - 4)^1/2)) dx

Please help me with this simple integration problem and provide all the steps on how to do it. The teach told us something about using trig identies but I'm lost as this is the first problem that we had like this.

When we look at the integral for the first time, we realize that it is a coefficient. As I said before, when doing integrals of coefficients, check if the numerator is the denominator’s derivative (up to a constant). Unfortunately, it is not the case in this situation but taking a look at the integral again we realize that it is one of the forms in which you will need to use the trigonometric substitution. So, let’s deal with the denominator first.

(9x^2 – 4)^1/2
When we do trigonometric substitution we use one of the identities: sin^2 x + cos^2 x = 1 or sec^2 x = tan^2 x +1. If we use the first identity, we will not gain anything but take a close look at the second identity. If we make a substitution y = a sec x with the proper value of a, we will be able to make what is under the square root equal to a tan^2 x.

(9x^2 – 4)^1/2 = (4(9/4 x^2 – 1))^1/2 = 2 (9/4 x^2 – 1)^1/2

Now we are ready to make the substitution x = 2/3 sec y for y in quadrants I and III (because y = inverse of sec x and inverse is defined in quadrants I and III, this is not standard but that’s what I’m used to). Thus, dx = 2/3 sec y tan y dy

So, (9x^2 – 4)^1/2 = 2 (sec^2 y -1)^1/2 = 2 (tan^2 y)^1/2 = 2 |tan y| = 2 tan y since tan y is positive in the quadrants I and III.
So, the integral looks like thins now,
int. 1/((9x^2 - 4)^1/2)) dx = int. 1/(2 tan y) * 2/3 sec y tan y dy = 1/(3 sec y) dy.

int. 1/3 sec y dy = 1/3 ln |sec y + tan y| + C and the integral is solved but we need to get back to our original variable x. The simplest way is to use our original assumption that x = 2/3 sec y and construct a right-angle triangle with y as one of its other two angles. If you do that you’ll see that tan y = (9x^2 – 4)^1/2/2.
int. 1/((9x^2 - 4)^1/2)) dx = 1/3 ln |3/2 x + ((9x^2 – 4)^1/2)/2| + C

You can stop at this point, but you will not generally see the answer in this form because the answer can be simplified a little bit more.
1/3 ln |3/2 x + ((9x^2 – 4)^1/2)/2| + C = 1/3 ln |3/2(x + ((9x^2 – 4)^1/2)/3| + C (taking 3/2 as common factor)
1/3 ln |3/2(x + ((9x^2 – 4)^1/2)/3| + C = 1/3 ln |3/2(x + ((x^2 – 4/9)^1/2)| + C (move the 3 under the square root)
1/3 ln |3/2(x + ((x^2 – 4/9)^1/2)| + C = 1/3 ln |(x + ((x^2 – 4/9)^1/2)| + ln (3/2) + C (properties of natural logarithm)
But ln(3/2) + C is still a constant which we can call C2
So the final answer is int. 1/((9x^2 - 4)^1/2)) dx = 1/3 ln |(x + ((x^2 – 4/9)^1/2)| + C2

I tried to be as clear as possible, but if you have further question then just ask

[Ice(v)an]

First Assignment of the Semester.
in C++


Write a program that sorts and evaluates bridge hands. The input is a stream of character pairs that represent playing cards. For example,

2C, QD, TC, AD, 6C, 3D, TD, 3H, 5H, 7H, AS JH, KH

Represents the 2 of club, queen of diamonds, ten of clubs, ace of diamonds, and so on. Each pair consists of a rank followed by a suit, where rank is A, 2,….,9, T, J, Q, or K, and suit is C, D, H or S. You can assume each input line represents exactly 13 cards and is error-free. Input is terminated by an end of file.

For each line of input, form a hand of 13 cards. Display each hand in a readable form arranged both by suits and by rank within suit (aces are high). Then evaluate the hand by using the following standard bridge values:

Aces count 4
Kings count 3
Queens count 2
Jacks count 1

Voids (no cards in a suit) count 3
Singletons (one card in a suit) count 2
Doubletons (two cards in a suit) count 1

Long suits with more than 5 cards in the suit count 1 for each card over 5 in number.

For example, for the previous sample input line, the program should produce the output

Clubs 10 6 2
Diamonds A Q 10 3
Hearts K J 7 5 3
Spades A
Points = 16

Because there are two aces, one king, one queen, one jack, one singleton, no doubletons, and no long suits. (the singleton ace of spades counts as both an ace and a singleton.)

Optional: see how much more flexible and fail-safe you can make your program. That is try to remove as many of the previous assumptions in input as you can.

[DeathGuiseX]

Some Chemistry gas problems. Please show all work or explanations.

1. A 44.8 liter vessel at 273K contains 2.00 mol of a gas X. The pressure is measured to be .900 atm. These data imply that... A) A small fraction of X has dissociated B) effects due to attractive forces are more important than those due to excluded volume C) effects due to attractive forces are excluded volume are equally important D) the gas is ideal E) effects due to attractive forces are less important than those due to excluded volume.

2. Nickel forms a gaseous compound of the formula Ni(CO)x. It is found that O2 effuses 2.31 times faster than this compound, under the same conditions of temperature and pressure. What is the value of x?

3. For a certain gas at atmospheric pressure and -50degreesC, (PV/nT) = 0.5 R. This deviation from ideal behavior results from the breakdown of which of the following statements? A) Molecules are in constant, random motion. B) All collisions are elastic. C) The average kinetic energy of a molecule is proportional to the absoltue temp. D) The volume occupied by the molecules is negligible compared with the volume of the container. E) Molecules do not attract each other.

[batman555]

Originally Posted by DeathGuiseX

1. A 44.8 liter vessel at 273K contains 2.00 mol of a gas X. The pressure is measured to be .900 atm. These data imply that... A) A small fraction of X has dissociated B) effects due to attractive forces are more important than those due to excluded volume C) effects due to attractive forces are excluded volume are equally important D) the gas is ideal E) effects due to attractive forces are less important than those due to excluded volume.

If you substitute the numbers into the ideal gas equation, you'll know that they don't equal, so it cannot be D). It cannot be A) because the number of moles is too high. If it is C), then it sounds like an ideal gas. I'm too lazy to think about the others... ><

2. Nickel forms a gaseous compound of the formula Ni(CO)x. It is found that O2 effuses 2.31 times faster than this compound, under the same conditions of temperature and pressure. What is the value of x?

This sounds like a Graham's law of effusion problem. You know the ratio of effusion, and you know the molecular weight of O2. So substitute the molecular weight of the unknown compound with (MW of nickel + (MW carbon + MW of oxygen)*x) and solve for x.

3. For a certain gas at atmospheric pressure and -50degreesC, (PV/nT) = 0.5 R. This deviation from ideal behavior results from the breakdown of which of the following statements? A) Molecules are in constant, random motion. B) All collisions are elastic. C) The average kinetic energy of a molecule is proportional to the absoltue temp. D) The volume occupied by the molecules is negligible compared with the volume of the container. E) Molecules do not attract each other.

It's not A) or B)...that's all I can come up with at a glance.

[DeathGuiseX]

Thanks for the second answer and your attempts at the other two.

Edit: I got all of them.

[zoeygirl]

Hey, I have two essays nearly done and unfortunately, most of my friends or anyone I know don't exactly possess a strong skill in analytical writing. I'm hoping someone who considers themselves pretty good in this style of writing could proofread my papers. (Red it, Tell me what's wrong, tear them apart if you have to, I just want these papers to be as tight as possible. I have a small problem with analytical writing, I tend to get off track, stray from my thesis, and use flowery styles with way too many extra words then I need. If someone could proofread I'd greatly appreciate it. Thanks

[batman555]

I can look over them for you. I also need the prompt and a deadline so I can pace myself.

[Ice(v)an]

Program due on Friday, can anyone do it? Or give me some hints, kinda like a psuedo code?

[o({})o]

Originally Posted by Ice(v)an

First Assignment of the Semester.
in C++


Write a program that sorts and evaluates bridge hands. The input is a stream of character pairs that represent playing cards. For example,

2C, QD, TC, AD, 6C, 3D, TD, 3H, 5H, 7H, AS JH, KH

Represents the 2 of club, queen of diamonds, ten of clubs, ace of diamonds, and so on. Each pair consists of a rank followed by a suit, where rank is A, 2,….,9, T, J, Q, or K, and suit is C, D, H or S. You can assume each input line represents exactly 13 cards and is error-free. Input is terminated by an end of file.

For each line of input, form a hand of 13 cards. Display each hand in a readable form arranged both by suits and by rank within suit (aces are high). Then evaluate the hand by using the following standard bridge values:

Aces count 4
Kings count 3
Queens count 2
Jacks count 1

Voids (no cards in a suit) count 3
Singletons (one card in a suit) count 2
Doubletons (two cards in a suit) count 1

Long suits with more than 5 cards in the suit count 1 for each card over 5 in number.

For example, for the previous sample input line, the program should produce the output

Clubs 10 6 2
Diamonds A Q 10 3
Hearts K J 7 5 3
Spades A
Points = 16

Because there are two aces, one king, one queen, one jack, one singleton, no doubletons, and no long suits. (the singleton ace of spades counts as both an ace and a singleton.)

Optional: see how much more flexible and fail-safe you can make your program. That is try to remove as many of the previous assumptions in input as you can.

Program ideas/description/pseudocode:

Define a card object with 2 variables (suit and rank) and the appropriate get/set methods. Also include a value function that returns an integer which is the sum of a selected value for each suit and card rank. For this, I'd suggest using clubs = 400, diamonds = 300, hearts = 200, spades = 100, a = 13, k= 12, ... This way, calling the value function (or whatever function is required for your desired sorting function), will return a value that will put the cards in the requested order by adding the suit and rank and returning the result.

Open file, read in data and make cards accordingly (storing them in an array).

Sort the cards.

Count all point cards (Ace, King, Queen, Jack) by going through the array. Add points to a score variable as they are found.

Count the number of cards in each suit. Voids, singletons, doubletons and long points can be accumulated immediately with long being the # in the suit -5.

Get next input line and repeat.

Close file.

This program shouldn't be very hard if you make good use of the available libraries for sorting, but even without them, writing your own simple sorting function will only take a short time. The input is likely to take the longest, so you might want to write the rest first and hardcode the input until you have tested everything else.

[Ice(v)an]

I remember in one of my classes last semester, my professor used a end of file without having to open a file. Because I didn't see a open.( blah blah b lah ) or anything. So is that possible?

And what library is the sorting in? And is there a library for Swap? I wasn't really taught about libraries of C++

::edit::

Also, {}, base on the information for the psuedo-code you gave, I should make a class call cards, and their data members are suit and rank?

Also, about the end of file business, does that work for vectors too? Cause can't we do this in vectors O_O When we reach the end of a vector, does end of file apply to vectors as well?

[Azn]

Um guys, i was wondering, can someone tell me in a nutshell what psychoanalytic means. I gotta write an essay on it about 2 literary works but i just don't understand =/

[batman555]

In psychology, it deals with analyzing the inner workings of the mind. It's most commonly associated with Freud. I'm sure the search engine can give you detailed results.

[OD Funk]

Originally Posted by AznMonster

Um guys, i was wondering, can someone tell me in a nutshell what psychoanalytic means. I gotta write an essay on it about 2 literary works but i just don't understand =/

Psychoanalytical, is the type of psychology which studies the unconcious mind, basically it says, everything mentally wrong, can be helped by looking into the concious, and subonconcious mind of said individual.

[4thseal]

The object of psychoanalytic literary criticism, at its very simplest, can be the psychoanalysis of the author or of a particularly interesting character. In this directly therapeutic form, it is very similar to psychoanalysis itself, closely following the analytic interpretive process discussed in Freud's Interpretation of Dreams. But many more complex variations are possible. The concepts of psychoanalysis can be deployed with reference to the narrative or poetic structure itself, without requiring access to the authorial psyche (an interpretation motivated by Lacan's remark that "the unconscious is structured like a language"). Or the founding texts of psychoanalysis may themselves be treated as literature, and re-read for the light cast by their formal qualities on their theoretical content (Freud's texts frequently resemble detective stories, or the archaeological narratives of which he was so fond).

Psychoanalytic literary criticism - Wikipedia, the free encyclopedia

So, basically, it's examining a literary work by applying a freadian thought and such towards characters, the author, or as mentioned above even the story's structure. For example, looking at what are the underlining pyschological causes of a characters actions. Or, examining the images in a story, much like you would psychoanalyze a dream.

To be honest, this was the type of literary criticism I sucked at the most in collage, so here are some resources that may help:

Psychoanalytic Approaches

Psychoanalytic Criticism

It might help if you said what books your looking at and even what are the guidlines for the assignment.

[Azn]

Mm. Thanks for the input. I'm sorta starting to understand what it means and would probably be still wondering without you guys. Already made the introduction paragraph and I feel a bit more confident about this now. Thank you for the help and hope you have a good night .

[Ice(v)an]

{} is there another way of doing this instead of opening a file and storing them in an array?