Find dy/dx if x^5 + 4xy^3 – y^5 =2

To find dy/dx if x^5 + 4xy^3 – y^5 =
2.

The relation between x and y in this equation is
implicit. In such cases we straight away differentiate term by terrm and  try to get
dy/dx by solving for dy/dx  from the
equation.

Differentiating both sides of the given equation
with respect to x, we get:

(x^5 + 4xy^3 – y^5)'
=(2)'

(x^5)' + {4xy^3}' – {y^5}' =
0

{x

5x^4 +{4(x)'y^3
+4x(y^3)'}-{5y^4*dy/dx} = 0.

5x^4+4y^3
+4x*3y^2dy/dx-5y^4dy/dx = 0. We try to solve for dy/dx from this
equation:

5x^x+4y^3 +{12x^3y^2 - 5y^4) dy/dx =
0

(12x^3y^2-5y^4)dy/dx.

Divide
both sides by the coefficient of dy/dx, that is,
12x^2-5y^4.

dy/dx = -(5x^4+4y^3)/(12x^3y^2-5y^4).
Or

dy/dx =
(4y^3+5x^4)/(5y^4-12x^3y^4)

What are two examples of Perpeteia in Oedipus the King? Line numbers would be appreciated.

Peripeteia or a "reversal" or turning
point" occurs throughout the story innumerable times. Even in the very beginning by
sending Creon to the Oracle at Delphi, Creon returns with bad news that Oedipus doesn't
want to listen to. Also, Tiresias knows everything already but has tried to make himself
forget. By Oedipus accusing Tiresias of being in a conspiracy with Creon, turns the play
deeper and deeper into Oedipus'sdarkness. Oedipus even subconsciously realizes that he
is probably part of his own downfall when others mention bandits killed Laius and
he repeats "bandit" as singular, twice. Also, Jocasta is quick to learn of the situation
and tries to stop Oedipus from revealing any more part of the story of how he was found
on the hilltop and rescued.

How an anti-Indian typical British outlook is projected in the character Mr Turton ?

Mr. Turton is not an awful sort.  He is shown to be a
typical British person in India.  He is not really concerned with getting to understand
the different culture that India is.  Rather, he is more animated by the idea of being a
"little god" of India.  He is not like Fielding in that he seeks to establish bonds with
those in India.  He is a representative of England, of "the Queen," and carries himself
as such.  He does represent an anti- Indian perspective in that he only wishes to know
Indians who accommodate themselves to the British manner and demeanor.  The "bridge
party" is a great example of that, as it does not feature the diverse and eclectic
nature of the people who live on the subcontinent.  Rather, it is a collection of "pre
approved" Indians.  Turton would represent the Anti- Indian attitude projected
throughout the British Raj because he demonstrates little in way of seeking to broaden
the connection and understanding between both groups.

Solve: x+y+ 4z = 6, 3x +2y +z =4 2x+ 2y + z =9 If the roots of the equation ax^2 + bx + c are 6 and 5 what are values of a and b?

Since the given equations of the system are all linear
equations, we'll solve the system using another
method.

We'll calculate the determinent of the system. The
determinant of the system is formed from the coefficients of the variables, x, y and
z.

We'll note the determinant as det
A.

             1   1   4

det
A =  3   2   1

              2   2  
1

We'll calculate det A:

det A
= 1*2*1 + 3*2*4  + 1*1*2 - 4*2*2 - 2*1*1 - 3*1*1

det A = 2
+ 24 + 2 - 16 - 2 - 3

We'll eliminate and combine like
terms:

det A = 7

Now, we'll
calculate the variable x using Cramer formula:

x = detX /
detA

Det X is the determinant whose column of coefficients
of the variable that has to be found (in this case x) is substituted by the column of
the terms from the right side of the equal (6 , 4 ,
9).

            6   1   4

det
X = 4   2   1

            9    2  
1

det X = 6*2*1 + 4*2*4 + 1*1*9 - 4*2*9 - 6*2*1 -
4*1*1

We'll eliminate like
terms:

detX = 32 + 9 - 72 - 12 -
4

det X = -47

x =
detX/detA

x =
-47/7

            1   6  
4

det Y = 3   4  
1

             2   9   1

det Y
= 4 + 108 + 12 - 32 - 9 - 18

y =
detY/detA

y =
65/7

We'll calculate z substituting the
values of x and y into the first equation:

x+y+ 4z =
6

4z = 6 - x - y

z = (6  -x -
y)/4

z = (6 + 47/7 - 65/7)/4

z
= -12/7*4

z =
-3/7

find f(x) if f'(x) = 3x^2 - 5x + 3

We know that F'(x) = f(x), where Int f'(x) dx =
f(x).

We'll apply the indefinite integral to the expression
of f(x):

Int f'(x) dx = Int (3x^2 - 5x +
3)dx

We'll apply the additive property of indefinite
integrals:

Int (3x^2 - 5x + 3)dx = Int 3x^2dx - Int 5xdx +
Int 3dx

Int 3x^2dx = 3x^3/3 +
C

We'll simplify and we'll
get:

Int 3x^2dx = x^3 + C
(1)

Int 5xdx = 5x^2/2 + C
(2)

Int 3dx = 3x + C (3)

We'll
add  (1),(2),(3):

f(x)
=  (1)+(2)+(3)

f(x) = x^3 + 5x^2/2 + 3x +
C

Note: C+C+C = C (family of
constants)

In "Two Kinds", why were "Pleading Child" and "Perfectly Contented" referred to as two halves of the same song?

This is a great question! In this short story we have
observed the conflict between Jing-Mei and her mother from its highs to its lows. This
of course finds its climax in the piano recital and the bitter argument that happens
afterwards. At the end of the story we advance forward a few years to Jing-Mei as an
adult, after her, as she puts it, "failing her mother so many times", but each time
"asserting my own will, my right to fall short of expectations." It is when her mother
gives her the piano that Jing-Mei begins to change in her attitude. She describes the
piano using an interesting metaphor, "a shiny trophy", because she had won it on her own
terms and not her mother's.

At the end, Jing-Mei receives
the piano and she beings to play "Pleading Child" again. The last paragraph is worthy of
some serious analysis:

readability="11">

And for the first time, or so it seemed, I
noticed the piece on the right-hand side. It was called "Perfectly Contented." I tried
to play this one as well. It had a lighter melody but the same flowing rhythm and turned
out to be quite easy. "Pleading Child" was shorter but slower; "Perfectly Contented" was
longer but faster. And after I played them both a few times, I realised they were two
halves of the same
song.

Jing-Mei realises that
just as these two pieces of music go together inseparably, being "two halves of the same
song", so in her life, the stage of "Pleading Child", which interestingly is described
as short but slow, is inextricably linked to "Perfectly Contented", which was longer and
faster. Jing-Mei, through her childhood was the "Pleading Child", wanting her mother's
attention and praise, and now, as an adult, she has reached the stage of being
"Perfectly Contented", knowing who she is as an adult and being happy in her identity.
However, what she realises is that she can't have one without the other - both are
irreplaceable parts of life's journey.

How does our own personal context give meaning to/alter the landscape?For example, how do the beliefs and values of aboriginals alter their view of...

This is such an interesting question!  Let's talk about
the aborigines and a few other examples of how personal context makes a
difference.

Aboriginals, traditionally, are hunters and
gatherers, and they have religious beliefs that are strongly rooted in the land and its
natural features.  This means that the landscape has meaning to them that is not
necessarily the same meaning that a person raised in a city, for example, would
find.

If the land is what supports a group, through hunting
animals and gathering plants, the people in that group perceive the entire landscape as
a food source, which means that while others might see a beautiful meadow, the aborigine
is likely to be seeing or looking for animals to slay or plants to eat.  People who buy
their meat and vegetables at the supermarket do not usually look at a landscape  like
this!

The aboriginal religious beliefs include a belief in
beings who created the landscape, beings whose manifestation is in the landscape itself.
This means that the entire landscape is "worshiped" as a representation of deities. 
This makes "place" central in the beliefs of the
aboriginal.

This might seem like a very different way of
viewing things, but our preferences make all of us view things differently.  To give you
a personal example, my father was an electrical contractor for over 50 years.  I am
someone who loves to admire trees and flowers.  When my father looks at a street, what
he sees is the wires between the trees, cables leading into houses, and the design of
the street lights.  What I see is trees and flowers.  Each of us is viewing the
landscape through a personal context.  Can you think of any examples of the way you and
others view your landscape differently?