Average Definition and 1000 Threads

Dear Everybody, A 2.80 kg steel gas can holds 20 L of gasoline when full. What's the average density (in kg/m^3) of full gas can, taking into the volume occupied by steel as well as by gasoline? Work: Given the mass of the steel gas can= 2.80 kg The Total Volume of Gas can= 20.0 L The...

Homework Statement A car starting from rest accelerates to the left. It takes 14 seconds to travel a distance of 20 meters. What is the car's average velocity? I'm really confused by this question I'm not sure whether to use change in displament divided by change in time or (Velocity Initial...

I would like to find the average chord length of a circle. And I have 2 methods, which gave different answers... [The chord is defined as the line joining 2 points on the circumference of the circle.] The general formula for a chord length is ##d=2R\sin(\delta/2)=2\sqrt{R^2-u^2}## Method 1...

Homework Statement What is the Average Force between m1 and m2. Show all work. Note that the masses are both at rest, and begin to push off of each other in opposite directions. Their velocity is measured when they reach 20cms distance. (I calculated the velocity when they reached this point...

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I was given the averages (AVG) and the corresponding standard deviation (SD) of sets of data. I have no copy of the raw data for each data point that were used to calculate the AVG and SD. I performed further data treatment on the data. I want to ask what is the relationship between the...

I was reading the statistical physics textbook and was really confused with the notation: I don't understand the last part of the section. Why is that \sum_{\sigma = \pm1} \sigma P(\sigma) equals to \left< \sigma \right>? And what does \left< \sigma \right> actually mean? Is it the average...

Question: A car is moving north at 100km/h. An hour later it is moving east at 100km/h. Its average acceleration during this hour is: a) A vector pointing northeast b) A vector pointing southeast c) A vector pointing southwest d) A vector pointing east e) Zero Attempt: I confidently chose a) A...

Homework Statement One type of tuning circuit used in radio receivers is a series LCR circuit. You like listening to a station1 that transmits 99.3 MHz in . The government wants to make 100.1 MHz available to station2. Assume that the transmitters of the two stations are equally powerful and...

Homework Statement [/B] 1. Using the Schematic of a 555 in astable mode from the Wikipedia entry on '555 Timer IC," resistor R1 = 8 kOhms and capacitor C = 3 micro-Farads. Determine the value of R2 so that the output duty cycle is D = 0.7. Note that D is not expressed as a percentage here for...

Homework Statement At one instant a bicyclist is 20.5 m due south of a park's flagpole, going due east with a speed of 14.1 m/s. Then, 3.95 s later, the cyclist is 36.3 m due west of the flagpole, going due north with a speed of 18.3 m/s. For the cyclist in this 3.95 second interval, find each...

Homework Statement Find the average y coordinate of the points on the semicircle parametrized by C:[0,##\pi##]-->##R^3##, ##\theta##-->(0, a*sin##\theta##, a*cos##\theta##); a>0 Homework EquationsThe Attempt at a Solution I think the answer should be an integral of the circle in the y...

Homework Statement A half wave rectifier circuit has a transformer inserted between the source and the remainder of the circuit. The source is 240Vrms and 60 Hz, and the load resistance is 20ohms. 1) Determine the required Turns Ratio of the transformer such that the average load current is...

Homework Statement Homework EquationsThe Attempt at a Solution The average of \##\cos \theta ## for ##\theta## going from 0 to ##\pi## is - ##\pi/2##. Is this correcct?

Hey! :o Can the minimum of the average variable cost function be negative? (Wondering) Suppose we have the cost function $K(x)=x^3-9x^2+11x+100$. The variable cost function is then $K_v(x)=x^3-9x^2+11x$. The average variable cost is $k_v(x)=\frac{K_v(x)}{x}=\frac{x^3-9x^2+11x}{x}=x^2-9x+11$...

Homework Statement I've been given a list of lengths of the side of a small metal sheet in the shape of a square. The length of the side of this square sheet varies with temperature. I have to calculate areas for each length and then calculate the average area. What should be the uncertainity...

Homework Statement If a ball is thrown into the air with a velocity of 40 ft/sec, its height (in feet) after t seconds is given by s(t) = 40t -16t^2. Find the average velocity, vAV (t), of the ball over the time interval (t, 2), for 0 < t < 2. Homework Equations change of x/change of...

Homework Statement A car travels along a straight line at a constant speed of 44.5 mi/h for a distance d and then another distance d in the same direction at another constant speed. The average velocity for the entire trip is 28.5 mi/h. NOTE: this is a practice problem. Homework Equations...

I am stuck on this concept in my physics book where the author claims that in a low density ionic gas the average of the time between collision and average of the time taken from last collision in ions is same. He further states that the average time to the next collision is same as the average...

Homework Statement Prove that A(X(ωk)2)≥A(X(ωk))2 if and only if X(ωk) has the same value for every k such that pk>0 for every category which actually occurs in the population Homework Equations A(X)=1/N∑nkX(ωk)=∑pkX(ωk) The Attempt at a Solution A[(X-A(X)2)]=A(X2)-A(X)2 and i believe the...

Homework Statement Suppose that a heated gas comprised of electrons glows bright orange when it is in use. Estimate the average speed of the electrons in the gas. Model this gas as an ideal gas. Homework Equations None. I have no clue. This is a "review" question on a chapter titled "Current...

How much negative mass would it take to warp, say, an average guy across town?

Homework Statement If you walk to school at 4 mph and jog home at 6mph, what was your average speed? Homework Equations S = D/T The Attempt at a Solution Is the average speed not just (4 + 6)/2 = 5mph ? If not, why not?

Hello Maths Help Board Users, I was hoping for some guidance on the following problem. Thanks in advance for your contributions and time. "A fish population grew according to the following quadratic model - the number of fish on day t is given by P (t) = 800t - t2" Q) Find the average growth...

Homework Statement Homework Equations Q(t) = Aei(wt+Φ); dQ/dt = i*w*Q(t); E = (L/2)(dQ/dt)2 + Q2/2C i = √-1 E above is average energy The Attempt at a Solution When I plug in Q(t) & dQ/dt into equation above (E) I get: A2L/2(w02-w2)cos[2(wt+Φ)] w02 = 1/LC After I plugged both of them in...

Hi, I've been asked to solve below as part of an assignment. Below is pretty much what I've submitted but it has been concluded to be incorrect. I am unsure as to why hence the question. Is it due to the fact that I have not taken the mass or forces into consideration? I have only taken these...

Hello All I am designing some very basic components for a motorcycle project at home, and because I am interested, thought I'd use it as an opportunity to refresh my memory in order to reduce the risk of the parts failing. To begin, I want to do some basic hand calcs if possible so have...

Homework Statement A person jumps from the roof of a house 4.2-mhigh. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.66 m . If the mass of his torso (excluding legs) is 43 kg , find the magnitude of the average force exerted...

Homework Statement [/B] Homework EquationsThe Attempt at a Solution Solution for Q1: Solution for Q2: Solution for Q3: Are they correct?

<< Mentor Note -- Thread moved from the technical forums so no Homework Help Template is shown >>[/color] I'm particle physics at the moment and I don't get why the average value of cosˆ2 is 1/3. The section : My solution is : < cos^{2}(\alpha)> = \frac{1}{\pi - 0} \int_{0}^{\pi }...

Homework Statement Starting from rest an airplane lifts off the ground after 40s and 1.8km. What is its speed at takeoff and its average acceleration during the takeoff run? Homework Equations V= distance/time Acceleration= (Vf-Vi)/time The Attempt at a Solution The airplane travels 1.8km in...

Hi all, I got accepted to 2 Astrophysics phd programs ( University of Connecticut and the University of Cincinnati). To be honest, I am not thrilled by the prospect of attending either school but my only other option is to retake the GREs again and wait another year to attend graduate...

Homework Statement A saucer of mass 1.75x10^9 enters 1.the gravitational field of PlanetX and enters its atmosphere; the gravitational field of the planet is 10.6 m/s2 and is considered uniform throughout the 80-km thick atmosphere. If the saucer enters the atmosphere at 460 m/s and slows...

Homework Statement Calculate the mean number of photons in a cavity at temperature T and the mean energy per photon. Homework Equations In the large volume limit, the log of grand canonical partition function is: ##log(Z_g) = \frac{gV}{h^3}\int log(1-e^{(E-\mu)/kT})dp^3 ##, with g - spin...

Homework Statement a car starts from hither , goes 50km in a straight line to yon , immediately turns around, and turns to hither . the time for this round trip is 2 hours . the average speed of the car for this round trip is ? Homework Equations average velocity = disrance covered /time The...

I have been refreshing my fundamentals. Average specific heats are confusing for me. Why they are average? Are there different values for them so the averages are taken? Would you please explain this? Source: Fluid Mechanics Fundamentals and Applications by Çengel/Boles. Thank you.

Hi all, I am thinking a problem of drawing a ball in a sealed box. Assuming there is a box, contains plenty red and white balls, the number of red and white balls are unknown but let's assume there will be ##p## chance to draw a red ball and ##q=1-p## chance to get a white one. Those...

Hello. I was having a hard time determining how the formula for the average value of the waveform can be achieved. I've read that the ave since the waveform is symmetric is (Imin+Imax)/2. I want to know how to derive it using calculus. Thanks.

Homework Statement Given a wave function that is the super position of the two lowest energies of a particle in an infinite square well ##\Psi = \frac{\sqrt{2}}{\sqrt{3}}\psi _1 + \frac{1}{\sqrt{3}}\psi _2##, find ##\langle E \rangle##. Homework EquationsThe Attempt at a Solution I'm not sure...

Hi. I'm trying to prove that [\Omega] = \int dq \int dp \, \rho_{w}(q,p)\,\Omega_{w}(q,p) where \rho_{w}(q,p) = \frac{1}{2\pi\hbar} \int dy \, \langle q-\frac{y}{2}|\rho|q+\frac{y}{2}\rangle\,\exp(i\frac{py}{\hbar}) is the Wigner function, being \rho a density matrix. On the other hand...

Homework Statement Homework Equations Δ[A]/aΔt = Δ[ B]/bΔt The Attempt at a Solution Δ[ I]/3Δt = Δ[H]/2Δt = 7.8E-4. What exactly am I supposed to do for this?

Homework Statement I have a range of numbers numbers n_i, each with a different weight w_i that sum up to 1. To keep things simple, let's take the case where we have three numbers with the following weights: n_i w_i ------------------------------...

Is there a general average number of neurotransmitters a given cell would "work with"?

Homework Statement http://imgur.com/a/lv6Uo Homework Equations Look below The Attempt at a Solution I was unsure where to start. I thought that parseval's theorem may be helpful. I know the Potential energy is equivalent to .5kx^2 and T will be the integral of the force. So i have $$<E> =...

Homework Statement The problem is as follows; A boy begins to walk eastward along a street infront of his house and the graph of his displacement from the house is shown in the figure. His average speed for the whole time interval is equal to...

Homework Statement There are 100 employees in an organization across five departments. The following table gives the department-wise distribution of average age, average basic pay and allowances. The gross pay of an employee is the sum of his/her basic pay and allowances. There are limited...

Homework Statement How to calculate the average given the uncertainties in each measurement 8.70 +/- 0.28, 9.680 +/- 0.046, 9.700 +/- 0.055, 9.720 +/- 0.067? Homework EquationsThe Attempt at a Solution I know I add the values and divide by 4. I also know I add the absolute uncertainties but...

The average angle made by a curve ##f(x)## between ##x=a## and ##x=b## is: $$\alpha=\frac{\int_a^b\tan^{-1}{(f'(x))}}{b-a}$$ I don't think there should be any questions on that. Since ##f'(x)## is the value of ##\tan{\theta}## at every point, so ##tan^{-1}{(f'(x))}##, should be the angle made by...

Homework Statement Determines the average energy of rotation (per molecule) of a rarefied gas of HF at T = 50 K, knowing that the wave number of rotational absorption for the transition L = 2 → 3 worth 121.5 cm-1. [Hint: it performs the calculation by limiting the number of levels taken into...

Lets suppose a radiating body moving relative to a frame. At a certain time because of relativistic beaming one observer in that frame would observe a different luminousity of the body. But observes placed at a different angle in that frame relative to the body would also observe different...