Why does Pip go to stay with his Uncle Pumblechook in Great Expectations?

Pip goes to stay with Uncle Pumblechook before his first visit to Miss Havisham’s house.

Pip has no idea what to expect from Miss Havisham, but he does not like his Uncle Pumblechook.  Pumblechook is an arrogant blowhard, and does not treat Pip very well.  He agrees with Pip’s sister that Pip is certainly not to be coddled.

Besides being possessed by my sister's idea that a mortifying and penitential character ought to be imparted to my diet,—besides giving me as much crumb as possible in combination with as little butter, and putting such a quantity of warm water into my milk that it would have been more candid to have left the milk out altogether,—his conversation consisted of nothing but arithmetic. (Ch. 8)

Pumblechook constantly asks Pip to calculate math problems because he thinks that it is good for him.  He also takes credit for Pip’s excursion to Miss Havisham’s house.  She is a rich lady, and he and Pip’s sister think that visiting her house will somehow enrich him.

For such reasons, I was very glad when ten o'clock came and we started for Miss Havisham's; though I was not at all at my ease regarding the manner in which I should acquit myself under that lady's roof.  (Ch. 8)

As if Pip is not already having a bad enough time, Miss Havisham’s house is decidedly creepy and the inhabitants strange.  Pumblechook is not allowed to enter, Pip later determines that he never actually knew her.  He just pretended that he did.

Pumblechook tries to use Miss Havisham’s wealth to add to his reputation.  Actually, the visits to Miss Havisham’s house do seem to enrich Pip.  She pays to apprentice him to Joe, and then later comes into a grand inheritance.  He thinks it is from her, but it turns out it actually isn’t.

Determine the center and the radius of the circle x^2+y^2+10y=0.

The general equation for the family of circles is

`(x-a)^2 + (y-b)^2 = r^2 `

with `(a,b) ` as center and `r` radius

Let us compare our equation with the general equation

there is only one x term, so a becomes 0, i.e., `(x-a)^2 = (x-0)^2 = x^2`

but there are two terms of y. To find b value we need to find the roots of the quadratic polynomial of `y^2 + 10 y` .

One of the ways to find roots of this polynomial is completing square method.

`(y)^2 + 2*y*5 + (5)^2 -(5)^2` (equating this to `a^2 + 2 ab + b^2` identity)

`= (y+5)^2 -25 `

Now combine `x` and `y` terms and write the equation for the circle

`(x-0)^2 + [y- (-5)]^2 -25 = 0 `

`(x-0)^2 +[y -(-5)]^2 = 5^2 `

`therefore` the center of the circle is (0,-5)

and the radius is 5 

In The Great Gatsby, how does Myrtle react when she is in New York?

Myrtle acts very differently when she in New York. She enjoys spending Tom's money, as we see when she asks for a puppy and when she stops to buy a magazine, some "cold cream" and perfume. Moreover, she boasts about the high cost of hiring a woman to come to the apartment to look at her feet.

Myrtle also likes to portray herself in a more glamorous light. One her arrival in New York, for instance, she changes into a "cream-colored chiffon" dress and is described by Nick as sweeping around the room when she moves.

Finally, Myrtle develops an inflates sense of self-importance: she moves as though she has a "dozen chefs" waiting her in the kitchen and claims that she has to keep on at "people" all the time, like the ice boy.

What does Jem do to win the bet?

In Chapter 1, the children begin to fantasize about the mysterious character known as "Boo" Radley, who never leaves his house. One day, Dill bet Jem "The Gray Ghost against two Tom Swifts" that Jem wouldn't knock on the Radley's door. (Lee 16) Jem is hesitant and fearful that Boo will come out of his house and attack them. Dill calls Jem scared, but Jem maintains that he isn't scared, "just respectful." On the third day, Jem stood at the Radley gate contemplating his next move. Dill made a concession to the bet and said that Jem had to touch the house instead of knocking on the door. Jem wins the bet by swinging open the fence and running into the Radley yard to touch the house. Jem slaps the side of the house and runs back onto his porch. Scout says that she thought they saw a shutter move when they looked at the window of the Radley house.

Explain why mud guards are used on the wheels of cycles, motor cars and other driving vehicles. Give reasons why in terms of physics.

Mud guards are used to stop mud, water and gravel that becomes unstuck to the surface of the tire, flies off and travels in a straight line. The mud guard stops the flying mud from making a mess and flying rocks from causing damage to the vehicle or other vehicles. If you ride a bicycle without mud guards or fenders through a puddle you'll end up with mud on your back as it flies off the top of the rotating back wheel.

Centripetal force is the force that makes a body follow a curved path. It's directed toward the center of the circle. When the centripetal force acting on a body is eliminated, as when the mud becomes detached from the tire, the body will cease to move in a circular path and will instead move in a straight line. Imagine that you are twirling a string with a weight attached in a circular path. If the string breaks, the weight will move in a straight line from the point where it was released, tangential to the circle its path was forming. In doing so it's following Newton's first law, an object in motion stays in motion unless acted on by a force. Mudguards provide a force to stop the debris from continuing in a straight line. 

A ball of mass m1= 0.08 kg starts from rest and falls vertically downward from a height 3 m. After colliding with the ground, it bounces up to a...

We can use equations of motion to solve this problem. Using 

`v^2 = u^2 + 2as`

for the part where the ball drops from the height of 3 m, we can calculate the ball's velocity as it hits the ground. Here, u = 0, a = g = 9.81 m/s^2 and s = 3 m.

Thus, v^2 = 0^2 + 2 x 9.81 x 3

solving the equation, we get, v = 7.67 m/s.

Thus, momentum of the ball immediately before collision = mv

= 0.08 kg x 7.67 m/s = 0.61 kg m/s.

After the impact, the ball rises up to a height of 2 m. Using the same equation of motion, we know that v = 0 m/s, s = 2 m and a = -g = -9.81 m/s^2

we can find u by: u^2 = v^2 - 2as = 0 - 2 x (-9.81) x 2 

solving this, we get, u = 6.26 m/s.

Thus the momentum of the ball immediately after collision with the ground is 

= m x u = 0.08 kg x 6.26 m/s = 0.50 kg m/s.

Force can be calculated as the rate of change of momentum. 

Thus, the average force exerted = (0.61 - 0.5)/0.005 = 22 N.

The impulse is nothing but the change in momentum and is equal to 0.11 kg m/s.

Hope this helps. 

What is the importance of diffusion in living organisms?

Diffusion is a transport mechanism (another example of a transport mechanism is advection) in which the material moves from a region of higher concentration to a region of lower concentration. Think of a cube of sugar in a glass of hot water. The sugar moves from the cube (a region of higher concentration) to hot water (a region of low concentration of sugar). 

Diffusion is very important for living organisms as it is essential for intake of useful materials and removal of waste materials. For example, oxygen is needed for our bodily functions, while carbon dioxide needs to be removed from our body. Fresh oxygen diffuses into our (oxygen-depleted) blood, while carbon dioxide is diffused out from (carbon dioxide rich) blood. This process also helps limit the loss of body heat to the environment. 

Hope this helps.