If log a = 35 and log b= 20 calculate : log (ab) , log (a/b) , log (1/a) and log (1/b)

Given that:

log a =
35

log b = 20

We need to
calculate the values of the following:

1.log
(ab)

We will use the logarithm properties to
solve.

We know that log a + log b  = log
ab

==> log ab = 35 + 20 =
55

==> log ab =
55

2. log
a/b

We know that: log a - log b = log
a/b

==> log a/b = 35 -20 =
15

==> log a/b =
15

log
(1/a)

Let us rewrite as a negative
exponent.

==> log 1/a = log
a^-1

Now we know that log a^b = b*log
a

==> log a^-1 = - log a = -
35

==> log (1/a) =
-35

4. log (1/b) = log b^-1 = -1*log b =
-1*20 = -20

==> log (1/b) =
-20

In Antigone, how does Creon act unwise? How does Antigone act wise?

In Antigone, Creon acts unwisely by
refusing to heed the advice of others who try to counsel him.  For example, the blind
prophet Teiresias tries to tell Creon that the people of Thebes stand behind Antigone's
decision to bury Polyneices and that they feel sympathy for her situation.  Teiresias is
known throughout Thebes as a voice of truth, yet Creon does not listen to him.  Instead,
Creon insults Teiresias by assuming that he has been bribed to take Antigone's side in
the matter. 

On the other hand, Antigone acts wisely by not
allowing the baseless threats of others influence her decision to do what she believes
is morally the right thing to do.  Ismene disagrees with her sister about the burial of
Polyneices and tells Antigone that she will suffer terrible consequences as a result of
her decision.  However, Ismene speaks out of fear and a false sense of loyalty to Creon,
so Antigone is wise to disregard Ismene's words.

What are the similarities between the poems "Out, Out -" by Robert Frost and "Empty-Cradle Sad" by Bette Wolf Duncan?

1. Both the
poems are based on true life
incidents:

Frost's poem is based on a true
incident which is believed to have happened in April 1915; Raymond Fitzgerald, the son
of Frost’s friend and neighbour, lost his hand to a buzz saw and bled so profusely that
he went into shock, and died of cardiac arrest in spite of the best efforts of the
doctor.  Frost’s title invites us to compare the poem’s shocking story with Macbeth’s
speech on learning of his wife’s death:

The key to
understanding the theme of Frost's "Out, out-" lies in the intertextual reference to
Shakespeare's "Macbeth" Act V Sc.5, where Macbeth
soliloquizes bitterly on the futility of life after he learns of the death of his
wife:

readability="14">

Out, out, brief
candle!
Life's but a walking shadow, a poor
player,
That struts and frets his hour upon the stage,
And then is
heard no more. It is a tale
Told by an idiot, full of sound and
fury,
Signifying
nothing.

Frost's poem
ironically comments on the death of a small boy who dies tragically at such a young age
because of an accident when he was sawing wood.  His life is compared to a "brief
candle."

Bette Wolf Duncan's poem deals with an incident
which took place in the life of her late husband's grandmother. The mother in the poem
is her husband's grandmother and the infant is her
father-in-law.

2. Out door
work: Frost's poem describes a group of people sawing wood. Bette Wolf
Duncan's poem describes the mother engaged in agricultural
operations:

readability="7">

Down below, with seeds and hoe,
Emma
sowed the garden
ground.

3.
Children are at the center of both the poems. In Frost's poem it was a
small boy and  in Bette Wolf Duncan's poem it was a new born
baby.

What is the meaning of this line from As You Like It: "but as all is mortal in nature, so is all nature in love mortal in folly?"Said by Touchstone...

This is the ending line from Touchstone's speech in which
he makes fun of lovers and the things they say.  Here, Touchstone is saying that all
people who are in love act in stupid ways.  He is also implying, though, that the
foolishness does not last.

First, Touchstone says that all
in nature is mortal, meaning that everything that is natural will die sometime.  He then
says that the nature of love is to be foolish.  This is what he has been trying to get
across by all his silliness about kissing cows' udders and such.  Finally, he is saying
that the folly of love is mortal just like everything in the natural
world.

Overall, then, he is saying something along the
lines of "Everything in nature dies sometimes and so does the foolishness of people in
love."

Solve the system of equations algebraically x^2+y^2=100 x-y=2

Given:-

(x^2) + (y^2) = 100
..........(1)

x - y =
2...........(2)

Squaring (2) on both sides we
get

(x-y)^2 = (2)^2

or, (x^2)
+ (y^2) - 2xy = 4

Putting the value of (x^2) + (y^2) from
(1) in the above equation we get

100 - 2xy =
4

or, 2xy =
96...........(3)

Now, (1) + (3)
 gives

(x^2) + (y^2) + 2xy = 100 +
96

or, (x+y)^2 = 196

or,
(x+y)^2 = (14)^2

or, (x+y) =
14.........(4)

or, (x+y) =
-14..........(5)

Now, (2) + (4)
gives

2x = 16

or, x =
8 

Thus, y =
6...........(6)

Also, (2) + (5)
gives

2x = -12

or, x =
-6

Thus, y =
-8..........(7)

Hence the two values of (x,y) are (8,6)
& (-6,-8)

The right angled triangle ABC has AB=6, BC=8 and AC is the hypotenuse. Find sinA, cosA and tanA.

Given the the right angle triangle ABC such that AC is the
hypotenuse.

Then, the right angle is
B.

==> Given the legs
are:

AB = 6

BC =
8

Then, we will calculate the hypotenuse AC using the
formula.

==> AC^2 = BC^2 +
AB^2

==> AC^2 = 6^2 + 8^2 = 36+64 =
100

==> AC = 10

Now we
need to find the following:

sinA = opposite/
hypotenuse.

We know that the side that is opposite to the
angle A is BC

==> sinA = BC/AC = 8/10 =
4/5

==> cosA = adjacent/
hypotenuse

                 = AB/AC = 6/10 =
3/5

==> tanA = sinA/cosA =
4/3

==> sinA = 0.8

==>cosA =
0.6

==> tanA =
4/3

In Dylan's poem "Blowing in the Wind," what is meant by the lines "How many times must a man look up/Before he can see the sky"?

Bob Dylan's song combines the romantic and the political
quite beautifully. The two strands complement each other in the song. In these lines,
Dylan comes back to the central question of what does it take to be human, which he
keeps repeating in different forms throughout the song. He examines the values of human
experience, the limits to human tolerance, indifference and habituality, before it all
breaks free in the revolutionary upsurge--" How many years will it take till we
know/That too many people have died".

These questions are
rather unanswerable and the answer will always be blowing in the wind. In the lines
quoted in the question, Dylan questions the onset of intuition, sensibility and
awareness in temporal terms. How many occasions does a man need to arouse his sense of
insight into his own social responsibility. However, at a more individual level, the
lines may also refer to the timing of epiphanic knowledge. The following lines make the
sense clear--"How many years must one man have/Before he can feel, he can cry". This is
a clarion-call to man's waning sensibility at the wake of social
disasters.