Increasing Definition and 449 Threads

If i wanted to increase the gravitational potential energy of a ball do I always have to apply a force times a distance? In this case the force would be the weight of the ball and the distance would be the height. What if I kicked the ball upwards? I wouldn't be applying a force times a distance...

Hey everyone, so for fiber optic networks we can either (in analogy) increase how fast the cars or photons move or add more lanes to increase the amount of data. What if now we use the color of the light to interpret several times more data?

The thermal conductivity of most solids and liquids decreases with increasing temperature, but water is an anomaly because it actually increases with increasing temperature. I don't understand why though. I suppose it is something about the material itself and its hydrogen bonding, but not sure...

Hello! Yesyerday I saw a bycicle which had attached to its back a box on wheels. Supposing that the coeficient of friction is the same as the coeficient of friction at the surface between bike`s wheels and ground, what of the 2 following cases is worser for the cycler ( he has to make more...

Hey there folks, As a forward: I'm trying to build a "high fantasy" universe in which to write stories, but within its historical timeline of events there are some cosmological happenings that I'd prefer to not just wave a wand at, so to speak. I'd like there to be at least SOME solid...

I am not sure if this would be where i would post this but here goes a question i been wondering about earth 3.6 or 3.7 billion years ago life emerges on our planet.. so we go from a rock that is not getting any bigger on its own with life that grow and grows when it dies there is leftovers...

Here is a python function to check whether a given list or string contains duplicate values: def has_duplicates(x): t = [] for i in x: if i not in t: t.append(i) if t != list(x): return True else: return False But I am sure this approach will be slow for...

Hello, Looking for some advice on increasing bending stiffness of a mild steel 1" x 0.065" round tube. This is for a motorcycle frame and clearance is an issue. There is a fuel tank above and the engine below this top tube (two running parallel) that I wanted to reinforce against bending...

I am trying to understand how a gaussian packet varies in time. Suppose we have a Gaussian wave packet that is displaced form the origin by an amount x0 and given initial momentum p0. So the wave function in coordinate space is ψ(x,0) =\frac{√β}{√√\pi}exp(-β2(x-x0)2/2)*exp(ip0x/ħ) where...

If the amplitude of a light wave increases does that mean that the intensity of the wave increases, and thus the number of photons? I'm thinking here re the wave/particle duality of light.

three inductors in-series, of increasing inductance , say 1μH , 10μH and 100μH , wire-gauge constant and wire has some resistance which is constant per unit length. Is it possible to make the middle inductor, (10uH), the hottest of the three by adjusting the frequency of the AC passing...

A homogeneous and isotropic Universe is described by the FLRW metric: ds^2 = c^2dt^2 + a^2(t)\ d\Sigma^2, where ##a(t)## is the scale factor and ##d\Sigma## is an interval of uniformly curved co-ordinate 3-space which is independent of cosmic time ##t##. If we set ##dt=0## then we find that...

If ##\left\{ a_{n} \right\}## is monotone increasing and there exists ##M \in \Re## such that for every ##n \in N## ##a_{n} ≤ M## prove that ##\left\{ a_{n} \right\}## converges. (Hint: Use the Cauchy sequence property. Recall: 1) ##\left\{ a_{n} \right\}## is Cauchy if and only if...

Hey there! How do I determine whether this function is growing or decreasing without using any calculator or graphing tools? y=ln(\frac{1}{x}) I know that y=ln(\frac{1}{x}) \ \Leftrightarrow \ e^y=\frac{1}{x} \ \ \ (1) Then I tried to use the formula f(x)=a^x and then determine whether...

Maybe I'm over-analysing this but if we take a simple example of a tube within which steam is flowing. Why does the temperature (and pressure) of the steam increase as the mass flow rate is increased? Is it simply because as more mass is added in the flow, the pressure within the system...

Homework Statement In the image below we start with the integer 1 marked in yellow. We will fill the rest of the table in counterclockwise manner with integers to infinity. What will be the sum of the numbers right above and below the number 2008? Homework Equations - The Attempt...

My question is in the attached image. Before going right at it, I thought it would be best to clarify a few details. Ohm's Law only shows that current and potential are linearly related, correct? So R is constant in the case of a material that follows Ohm's Law (metal conductors for the most...

Homework Statement Understanding the bode plot for, G(s) = \frac{1}{2s-1} Homework Equations The Attempt at a Solution Usually when I am drawing bode plots for either real poles or zeros, I simply solve for the break frequency knowing that a zero/pole will give me a +/-20dB/decade asymptote...

Homework Statement I'm trying to do a lab and none of my data is making sense. It's making it very difficult for me to draw conclusions and make sense of the post-lab questions with the data I have. Here are the questions I am struggling with: 1. What happens to the force exerted as mechanical...

Hello, I have been performing an experiment in which I am observing the lifting capacity of DC electromagnets while changing variables including current, number of turns, and length of the core. It is a fairly basic experiment as all the theoretical values can be obtained using the formula...

In my textbook there is an equation for the precession frequency: Ω = τ/Iω The derivation in the book shows no difference in the spin angular momentum at time t = 0 and t = delta t but when I tried it I got that the denominator of the above equation must be the 'new' angular momentum (at t...

Hey all Is there a clever, and elegant way to change a sinc^2 function so that its side lobes will be larger?

If you are given a ratio, say apples to eggs and you were to increase the number of eggs but keep the number of apples the same, would you say that the ratio of apples to eggs is reduced, as when you divided apples by eggs, the number would be smaller if eggs are increased and apples remain...

I have to design a system to increase the relative humidity in a bunker. I would like to use a spray nozzle and service water. How could I determine how much the relative humidity would raiser per volume of water sprayed into the bunker. Known: - Volume of Bunker - Temperature - Initial...

Homework Statement I have to find the ratio of RB/RA where R is electrical resistance. Both objects A and B have circular cross section and length L, and are made of the same material. A has radius r0. B has radius r0/2 at the bottom and increases linearly to 2r0. Homework Equations...

I have the following function f=\frac{B}{y^{3}}+\frac{C}{y^{4}}\mid\frac{dy}{dx}\mid where B and C are constants and where y is a monotonically decreasing function of x (\mid\frac{dy}{dx}\mid stands for absolute value of derivative). According to my model, all signs indicate that f is a...

Consider a function f(x), such that for all points x0 in the domain, the nth derivative of f evaluated that x0 is less than the n+1th derivative of f evaluated at x0. A quick example is f(x) = e^(ax) where a > 1, what others are there (not including just changing e to something else)? Is...

The volume of a cube is increasing at a rate of $$\displaystyle\frac{10 cm^3}{\text {min}}$$ How fast is the surface area increasing when the length of an edge is $$\displaystyle 30 \text{ cm}$$ The answer to this is $$\displaystyle \frac{4}{3} \text{ cm}^2$$ $$V=x^3$$ and $$SA=6x^2$$ and...

Homework Statement Prove that if ##0<c<1## then llim##c^{\frac{1}{n}}=1## using the monotone convergence theorem. Homework Equations The Attempt at a Solution I let ##c_n=c^{\frac{1}{n}}## and it follows since ##0<c<1 \implies 0<c^{\frac{1}{n}}<1## Thus ##c_n## is bounded above...

Homework Statement A spaceship is in a vertical free fall towards an airless moon. It starts out at 1,247,000m above sea level and has an initial vertical speed of -132 m/s. The moon's radius is 200,000m and gravity at sea level is 1.63 M/s^2, but decreases with distance. Calculate the...

Homework Statement Question from my professor: "Consider the sequence {a(n)} (from n=1 to ∞) defined inductively by a(1) = 0, and a(n+1) = √(a(n) + 2) for n ≥ 1. Prove that {a(n)} (from n=1 to ∞) is increasing". Here's the first part of the answer from my professor: "Consider...

Hello everyone. My understanding of a dipole moment is it defines the strength of various dipole interactions, eg the common example of torque in an electric field. My confusion stems from the fact that the magnitude of the dipole moment is proportional to the charge separation. In many...

Hi! I have the following question. Let f be continuous on [0,\infty[, f(0)=0, f^\prime exists on ]0,\infty[, and f^\prime is increasing on ]0,\infty[. the question is to prove that the following function is increasing that is g(x)=f(x)/x on ]0,\infty[. I tried to show that the first...

According to my prof, increasing intensity of the light source in a photocell for the photoelectric effect does not increase the kinetic energy of photoelectrons emitted. Instead, the number of electrons emitted (and current) increases. Changing the colour of the light causes an increase in...

First please forgive my general lack of intelligence of this matter. I am a saxophone player looking to help new sax players and need some expertise for a training aid I'd like to create. On a saxophone, a player blows air through a mouthpiece creating a sound wave. The very tip of the...

Hello everyone, Can you please show me how to 'determine weather this funtion -3[(x-3)^2-9] is increasing or decreasing on the the domain [0,6] Thanks in advance .

L'Hopital's rule greatly simplifies the evaluation of limits of indeterminate forms, especially those with polynomial terms. This is because every time you take the derivative of a polynomial, the exponent decreases by 1, until it becomes a constant function, at which point the limit can be...

Is there a formula or something? When I solve quadratic equation I get two roots of x1 and x2. how can I find out the length? Thank you

Heat of vaporization of water slightly decreases with temperature. https://en.wikipedia.org/wiki/Enthalpy_of_vaporization Does anybody know of a simple explanation of this fact based on molecular theory? Or any explanation whatsoever. The Wikipedia article says " The heat of...

From the standpoint of temperature (not pressure), would components that could experience fission experience a higher fission rate toward the center of the Earth because of the higher temperature, or at ordinary room temperature conditions?

Do you know of any material/compound/alloy which have low coefficient of heat conduction at room temperature and higher one at greater temperatures?

Homework Statement I have the series an = (-1)^{n} cos(1/n) and I have to determine whether it converges or diverges. Homework Equations I used the Leibniz criterion The Attempt at a Solution However, I determined that bn = cos(1/n) is a decreasing function because: n+1 > n 1/(n+1) < 1/n...

I am currently in an engineering project which is attempting to hook up some solar panels to run an irrigation pump. Right now, the pump that we have is a marine Bilge pump that says that at 12 Volts and 7 Amperes it can pump at around 3.3 Gallons Per Minute. We were provided with a standard...

Hello! I understand that by increasing the number turns the magnetic field is strengthened. But would that "extra" turns demand more power input from the power source?

Octagonal Cross Section with Parabolically Increasing "Span" Hi all, could some one tell me what I am doing wrong in my analysis in the attached file? Its a parabolical flare column with an octagonal cross section. The effect of the parabolic flare simply stretches the octagon so that the...

Homework Statement Which of the following will most likely increase the electric field between the plates of a parallel plate capacitor? (a) Adding a resistor that is connected to the capacitor in series (b) Adding a resistor that is connected to the capacitor in parallel (c) Increasing the...

Hi! When calculating the attraction/repulsion force generated by a magnetic field should I consider the flux density of both and add them to the calculation? By increasing that vector would it increase the total force generated or it has no relevance at all?

Hi. Could help me with the following problem? Let f be a real function, increasing on [0,1]. Does there exists a sequence of functions, continuous on [0,1], convergent pointwise to f? If so, how to prove it? I would really appreciate any help. Thank you.

Homework Statement I have the function h(x) = \begin{cases} x^2\sin{\left(\frac{1}{x}\right)}+\frac{x}{2} & \text{if } x \neq 0 \\ 0 & \text{if } x =0 \end{cases} and need to show that h'(0)>0 but there is no neighborhood of 0 on which h is increasing Homework Equations...

I am currently looking at charlieplexing that can in theory cause me to be able to control eight 7 segment displays using 8 microcontroller pins, however in practice there is not enough current to drive all the displays. What I need is to increase the current drive from the microcontroller...