NikolaTesla

Working on some differential equation homework over the weekend and I can't get help with it...

because it's the weekend. So I ask you, oh wise people of yahoo answers.

Given the second order differential equation:

x'' + 2tx' + x = 0

we can say x_1 = x and x_2 = x' and get the system of first order differential equations:

x_1' = x_2

x_2' = -2tx_2 - x_1

I'm certain the system is linear, but is it homogeneous? There is no separate term b(t) in either equation, but one of the coefficients in the second equation is a function of t. If someone could explain whether it's homogeneous or not I'd appreciate it.

Our sun peaks in the blue and green spectrum, and so we and other organisms are adapted to use that light. But what if the light peaked in red? Would plants be red too then?

In number theory, what does the notation (m, p) = 1 mean? I can t remember if it means GCF of m and p is 1, or if it means something else.

So the college I attend requires all students to have health insurance and provides their own little insurance plan that all students are forced to buy if they don't have private insurance. It's expensive and absolutely of no value to me; I don't want it but I'm forced to get it.

So I had myself a little idea. What if i started a legal insurance company that insures only one person, me? It exists as a legal entity only, allowing me to "have private insurance" and get out of having to pay for insurance that I don't want.

Does anyone have any knowledge about the level of difficulty and expense in creating an entity of this sort? If it's less than $1000 it's worth it as far as I'm concerned.

Been puzzling over this for awhile and couldn t find any help online, so hopefully someone here can point me in the right direction.

E⃗ (x,y,z,t)=17ẑ cos(3x5‾√+6y5‾√−79t)

We have 2.451 moles of an ideal gas at an initial temperature of 25.2 C. The gas is heated at a constant volume with 1758 J. What is the change in entropy?

My work so far: Change in Temperature = Q/(n Cv)

Change in entropy = Q/T = n Cv Ln[Temp final/Temp initial]

This has thus far yielded incorrect answers. Anybody know what I'm doing wrong and how to fix it?

I m brand-new to LaTeX but have an assignment to complete in it, I just need to figure out how to get my equations to center on the paper. I ve tried the normal

\[equation stuff\] syntax, but it just gives me error about too many endings or something like that. For reference, the code is below:

$\title{Homework}

\begin{flushright}

\textsc{Name} \\

Math 290\\

Date September 29th 2017

\end{flushright}

\begin{center}

\textsf{Assignment LaTeX Intro} \\

\textsf{Exercises: Full}

\end{center}

\begin{exercise}{1}

Write the two paragraphs in LaTeX

\end{exercise}

\begin{proof}[Solution]

The Cartesian product (or simply the product $A\times B$) of two sets $A$ and $B$ is the set consisting of all ordered pairs whose first coordinate belongs to A and whose second coordinate belongs to B. In other words,

$A \times B = \{(a, b) : a\in A \text{ and } b\in B\} $

For example, if $A = \{x, y\}$ and $B = \{1, 2, 3\}$, then

$A \times B = \{(x, 1), (x, 2), (x, 3), (y, 1), (y, 2), (y, 3)\};$

while

$B \times A = \{(1, x), (1, y), (2, x), (2, y), (3, x), (3, y)\};$

Since, for example, $(x, 1) \in A \times B$ and $(x, 1) \notin B \times A$, these two sets do not contain the same elements; so $A \times B \neq B \times A$. If $A = \emptyset$ or $B = \emptyset$, then $A \times B = \emptyset$

For the sets $A$ and $B$ just mentioned, $|A| = 2 \text{ and } |B| = 3$; while $|A \times B| = |B \times A| = 6$

Indeed, for all finite sets A and B,

$|A \times B| = |A| \cdot |B|$

\end{proof}

$

My landlord had written into my contract a tri-monthly $30 fee for carpet cleaning at my off campus student housing. I had 5 roommates, for a total of $180 each trimester and a total of $540 for the year.

Here's the rub: Cleaning the carpets for an apartment our size costs about $120 (I checked with a friend who actually does it for a living), and he only had them do it once and presumably pocketed the other $420.

Is this fraud, to charge a fee over and above rent and not use the money to provide the designated service, even if the fee is written into the contract?

I work as a TA for a college science class and the students need to access these "active figures" basically mini programs that change a image based on a slider for a variable or something similar. Problem is that the course materials are a few years old and all the active figures are saved in an old format, I think as SWF files which no one's computer seems to be able to open as anything other than a gibberish text edit document. Anyone know how to get around this or what plugin/software everyone should download to be able to read the files?

Internet browser is google chrome.

Say you have a sphere of radius r filled with water accelerating to the right with an acceleration a. There is a small air bubble in the sphere at a pressure of 1 atmosphere. What is the pressure at the center of the sphere?

I previously solved this problem using Pascal s law (P = P atmosphere + density * acceleration * height of fluid above point of interest). I vector summed acceleration due to gravity and the actual acceleration and made the height the radius and got the right answer, but my professor said that while this renders the correct answer it is not a conceptually valid way to solve the problem. He wanted it solved using forces and pressure differences. Could someone show me how to do this?

I understand a fair bit about what it is and how it acts, but how is it generated in the first place? I understand that the movement of charges creates magnetic fields, but why do they do that? I'm guessing it has to do with the electrostatic force, but I'm kinda fuzzy as to how.

My textbook explained it in terms of the standard model and frankly their explanation simply doesn't work if you actually look closely at it.

I'd like to understand the cause of diamagnetism in terms of the standard model of the atom, and why the opposite magnetic field is generated.

Please explain this in terms no more complex than single variable calculus.

Thanks in advance!

1 Ohm is 1 volt / Ampere, so does that mean that the base units for Volts are Joule seconds?

V/A => J/C//C/S = JS

Say you have a positive charge inside a hollow spherical conductor with thickness. To find the electric potential or voltage in the conductor:

dV = kdq/r -> V = kQ/r

I thought I would just use the inner radius of the conductor, but apparently I'm supposed to use the outer radius. Can someone explain why? And would that change at all if the positive charge was not centered?

A ball of mass 5g going 250m/s hits a block of mass 2.2kg at rest and bounces off elastically (KE is conserved). The velocity of the block is then given by 2 * mass of the ball * the initial velocity of the ball all divided by the combined masses of the block and the ball. (2 * .005 * 250) / (2.2 + .005).

The block is attached to a massless spring of spring constant k = 53. There is friction, the friction constant = .55.

How far does the spring compress?

So far, I know that the potential energy of the spring (.5 * k * d^2) = the kinetic energy of the block (.5 * 2.2 * v^2) - the work done by friction (umgd),

When I do the quadratic, I always get an answer for d of .08098, which is wrong. The correct answer is .098.

What am I doing wrong?

A crate of mass 0.812 kg is placed on a rough incline of angle 35.3∘. Near the base of the incline is a spring of spring constant 1140 N/m. The mass is pressed against the spring a distance x and released. The mass is not connected to the spring, so when the spring reaches its relaxed length, it does not pull back on the mass. Instead the mass slides freely up the slope before coming to a stop. The total distance (d) the mass moves (from the compressed point to the final point) is 0.235 m. If the coefficient of kinetic friction is 0.195, how far was the spring compressed?

I attempted to solve this by setting the initial energy - the energy lost to friction = final energy:

PE(spring) - Work(done by friction) = PE(gravitational)

1/2 * k * x^2 - u*m*g*cos (35.3) * d = m*g*d*sin (35.3)

and solve for x, but I got the wrong answer. The correct answer for these particular variables is 0.0492 m.

Please help me see what I'm doing wrong so I can solve this problem with other variables!

I did the this problem earlier and though I think I came out with the right answer (the units were right at least) it was such a convoluted process I'm sure there must be an easier way to do it.

a. A ball is launched vertically with a velocity v. At that same moment, another ball at height h directly above the first ball is dropped. Gravity is denoted by a positive g. How far above the ground in terms of v, h and g is the spot at which the balls impact?

b. What is the maximum value of h in terms of v, h, and g such that the balls impact before the launched ball begins to fall back down?