How to find x if 11^(2x+1)=13.

The equation 11^(2x+1)=13 has to be solved for
x.

11^(2x+1)=13

Take the
logarithm of both the sides

`log(11^(2x+1))= log
13`

Use the property of logarithm `log a^b = b*log
a`

`(2x +1)*log 11 = log
13`

Isolate x to one of the
sides

`2x + 1 = (log 13)/(log
11)`

`2x = (log 13)/(log 11) -
1`

`x = ((log 13)/(log 11) -
1)/2`

The solution of the given equation is x = `((log
13)/(log 11) - 1)/2`

What conclusions can be drawn from the image in the link...

There are a number of conclusions that can be drawn from
this map.

First of all, you can conclude that trade caused
the spread of the Black Death.  This can be seen from the fact that the plague started
in China and then spread to parts of Europe that had trading connections with
China.

Second, you can conclude that trade by sea was
faster than trade by land.  We can see this in the fact that the Black Death reached
areas like England (that were accessed in part by water) more quickly than it reached
Muscovy (which was accessed only by land).

Finally, we can
conclude that Spain and Portugal were not yet important trading nations at this point in
their histories.  We can see that no major trade routes reached those
countries.

Give an example of any plane that passes through point (-2,3,5) and is parallel to the line (3+5t, 2t, -2+3t). Express your answer in...

We'll have to determinte the normal vector to both planes.
Since the vector n is perpendicular to the plane that contains the line (3+5t, 2t,
-2+3t), then "n" is perpendicular to the line, too.

The
coordinates of the given line are:

x = 3 +
5t

y = 2t

z = -2 +
3t

The vector of this line is: v = 5i + 2j +
3k

The n vector is: n = ai + bj +
ck

The "n" vector is orthogonal to any vector that is
located in the plane, therefore "n" is perpendicular to "v". Therefore, the dot product
of n and v must be zero:

n*v = 0 <=> (ai + bj
+ ck)(5i + 2j + 3k) = 5a + 2b + 3c = 0 (1)

Since n is
perpendicular to the plane that passes through the point (-2,3,5), then it is
perpendicular to any vector that passe through this point, located in this
plane.

Let's consider the vector p = -2i + 3j +
5k

Therefore, the dot product of n and p must be
zero:

n*p = 0

(ai + bj +
ck)(-2i + 3j + 5k) = -2a + 3b + 5c = 0 (2)

We'll find out
the variable "c" from (1) and (2):

5a + 2b + 3c = 0
=>  c = (-5a+2b)/3 (3)

-2a + 3b + 5c = 0 => c
= (2a-3b)/5 (4)

We'll equate (3) =
(4):

(-5a+2b)/3 =
(2a-3b)/5

We'll cross
multiply:

6a - 9b = -25a +
10b

31a = 19b

a =
19b/31

c = (38b/31 - 3b)/5

c =
(38b - 93b)/31*5

c =
-55b/31*5

c = -11b/31

The
coordinates of the vector n are: (19b/31 , b , -11b/31)

Let
b = 31

n:(19 , 31 , -11)

The
vector n is: n = 19i + 31j - 11k

We can write
the equation of the plane that passe through the point (-2,3,5) and it's parallel to the
line(3+5t, 2t, -2+3t):

19(x +
2) + 31(y - 3) - 11(z - 5) = 0

In Harper Lee's To Kill a Mockingbird, what does Dill say that causes Scout to accuse him of lying?

In Harper Lee's To Kill a
Mockingbird, Scout catches Dill lying about his father having a
beard.

Dill is talking about how Boo must have a very long
beard having been inside the house for so long. Scout mentions Dill's father's beard,
and Dill replies that he doesn't have a beard. Scout reminds him of
his story of his father with a beard, and though Dill makes excuses, Scout knows he
telling "tall tales" (lies). She expects that the mounted police uniform he has spoken
of will never show up either.

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Dill Harris could tell the biggest ones I ever
heard.

Scout then lists some
of Dill's other lies. Dill says he's flown in a mail plane seventeen times, had traveled
to Nova Scotia, had seen an elephant, and that his father was Brigadier General Joe
Wheeler, who allegedly left Dill a sword. Dill doesn't have the home life that Scout and
Jem do, and this may simply be his way of feeling more important rather than an outsider
at home. Scout realizes that Dill tells stories, but doesn't seem to resent him for
it.

Can a bullet be fired at a fast moving car to puncture its tyre?

Yes, a bullet can be fired towards a fast moving car to
puncture its tire. If you are asking this question with reference to the fact that the
car is moving at a fast speed and it would not be possible to aim at its tire and for
the bullet to hit it, it has to be kept in mind that a bullet fired from a gun travels
at over 1000 m/s. The fastest land speed record is that of a jet-propelled car at 345
m/s. The general speed of car is around 30-40 m/s. If the car being fired at were truly
moving at a very high speed, the gun can be aimed at a location where the car would
reach by the time the bullet travels the distance.

In
addition, the motion of the tire does not make a difference in the resistance of the
tire to be pierced by a bullet. A general bullet can easily pass through a thin sheet of
metal. The rubber that tires are made of would not present an obstacle to the motion of
the bullet.

What is the equilibrium expression for this equation 2HFH2+F2

The equilibrium expression for any chemical reaction can
be determined if the phase of each substance that constitutes the chemical equation is
known and the equation is balanced with the same number of atoms of each element on both
the sides.

The equilibrium expression can be in terms of
the concentration of each substance that makes up the equation or if there are gases
involved it can be terms of the partial pressure.

For the
equation given: 2HF<------->H2 + F2, the reactants as well as products are
gases.

2HF(g)<------->H2(g) +
F2(g)

The equation is balanced with two molecules of
hydrogen fluoride at equilibrium with one molecule of hydrogen and one molecule of
fluorine. The equilibrium expression is written in terms of the partial pressures of all
the constituent compounds.

Kp =
P(H2)*P(F2)/P(HF)^2, where P(X) is the partial pressure of X and it is
raised to the power equal to the number of molecules in the balanced chemical
equation.

In "Romeo and Juliet," Act 3, Scene 1, why does Tybalt refuse fighting Mercutio?

In Act 3, scene one, Tybalt's argument is with Romeo. He
is not interested in fighting Mercutio. Tybalt wants to fight Romeo for his
embarrassment of Romeo's appearance at the Capulet's masquerade
party.

Tybalt wants revenge because Romeo crashed the
party. Tybalt has no idea about Romeo's marriage to Juliet at this
point.

Romeo does not want to fight Tybalt since he is now
his relative. Mercutio begins to fight Tybalt, embarrassed by Romeo's submissive nature.
Romeo gets in between them and Tybalt kills Mercutio, stabbing underneath Romeo's
arm.

Romeo must kill Tybalt to avenge Mercutio's death. Now
Romeo must flee the scene to keep from being sentenced to death by the
Prince.