# Search results

1. ### Function Continuity Proof in Real Analysis

Homework Statement We've been given a set of hints to solve the problem below and I'm stuck on one of them Let f:[a,b]->R , prove, using the hints below, that if f is continuous and if f(a) < 0 < f(b), then there exists a c ∈ (a,b) such that f(c) = 0 Hint let set S = {x∈[a,b]:f(x)≤0} let c =...
2. ### Proof about limit superior

Homework Statement 2. Relevant equation Below is the definition of the limit superior The Attempt at a Solution I tried to start by considering two cases, case 1 in which the sequence does not converge and case 2 in which the sequence converges and got stuck with the second case. I know...
3. ### Python Python 3.0 , encoding="utf-8" for encryption

I had recently upgraded my version of python from 2 to 3. I had a program that encrypted a text file by converting a character to its Unicode value, altering it and then changing it back to a character using the ord() and chr() methods. This does not seem to work with python 3 and I was...
4. ### Angle relationships of a blazed diffraction grating

I am trying to understand how a blazed diffraction grating works and came across a deduction I don't understand. I believe that you don't need to know much about optics to answer this question as it is more geometry related. I have the diagram below of a diffraction grating with all the relevant...
5. ### Error propagation when dividing by exact number

Homework Statement Some Background - We are calculating the amount of acetylsalicylic acid in a sample using spectrophotometry. We were told to make sure to include the error in our answer. So first to calculate the moles of acetylsalicylic acid in a measured mass. 0.1620 ± 0.0005g measured...
6. ### Damped oscillation and time between displacement maximums

Homework Statement [/B] Question 3.9 Homework Equations equation for dampened ocillation[/B] The Attempt at a Solution In case this might appear confusing, I derived(with respect to t) the equation for dampened oscillation given above and tried to solve for when it equaled zero...
7. ### Underground living: Which project idea is better?

Hello, Physics forum community.I have a project for an intro to engineering class in which I must design a system to solve an environmental problem. This class is only an introduction so I'm not sure how detailed and specific our work has to be. I must have been feeling very sci-fi at the time...
8. ### Effect of mass on skid distance of car experiment

Homework Statement I know this is long, but that is only because this question requires me to be thorough, conceptually I think it isn't difficult. To make it easier to read I bolded the important parts. In Physics lab, we were told to conduct an experiment to investigate the effect off mass...
9. ### Using Kirchoff's laws to find current in complex circuit

Homework Statement Homework Equations V=IR and kirchoff's laws The Attempt at a Solution Number three is my attempt at finding a solution but I got stuck when I had to find an expression for loop one on the diagram. Thanks in advance for your help...
10. ### Two point charges and electric potential difference

Homework Statement In an experiment modeling point charges I had to find equipotential lines. I did so using a voltmeter. The results looked like this: Not a good quality picture, but the equipotential line on the right says 1.3 mV and the one on the left says 2.3mV. From this I had to...
11. ### Integrating this function

1. Homework Statement I'm trying to integrate this, the only variable is y the others(x,w) are all constants. Homework Equations The ways of integrating that I am familiar with are substitution, trigonometric substitution, by parts & partial fraction decomposition. The Attempt at a Solution...
12. ### Finding the interval of convergence

Homework Statement The question was to find the interval of convergence for a series. Homework Equations an+1/an The Attempt at a Solution
13. ### Electric force and electrons transfered

Homework Statement In a group assignment we had to find out how many electrons were transferred to pieces of tape after we pealed them of a table. The second part of the project asked us to imagine that one piece of tape was a distributed charge and that the other was still a point charge...
14. ### Finding wire with the right resistance

Homework Statement So we are doing an experiment where we are trying to place a 60W light bulb in a room. It is connected to the mains power supply, but we are imagining that it is DC instead of AC. Now we have to make sure that we only loose 0.1% of power in the wires. Homework Equations P=VI...
15. ### I What is the improper integral?

I find it easy to picture bounder integrals because they are the area under the graph but when it is unbounded what is it exactly. If we evaluate it we find the equation of a many possible graphs where the derivative is the function that was originally in the integral. How did we get from that...
16. ### Find common term for this sequence

Homework Statement 6 /(12 + 1), 1/(22 + 1),6/(32 + 1),1/(42 + 1) Homework Equations none The Attempt at a Solution I suspect this is not that hard, I get the denominators but the numerator alternates so I though I would need 6 to be the base of a power that alternates between 0 and 1 but I...
17. ### Force between electric dipoles along the dipole axis

Homework Statement Compute the force between two identical dipoles. See Problem P63 on page 544 to set up the problem. Explain why this result makes sense by comparing it to the force between two point charges and the force between a point charge and a dipole, in terms of the relationship to...
18. ### Electric force, theory and algebra.

Homework Statement This question has two parts. There is a quarter or radius R that is charged with a net force of Q. A point like charge of net charge q,is at a distance z from the center of the quarter. Q1: Under what condition could we use Coulomb's law to find the magnitude the force...
19. ### When is resistance large enough to be measurable?

Homework Statement We conducted experiments using copper wires to observe the effect length has on resistance. We measured lengths from 5 - 30 cm and used a multimeter to measure the voltage while supplying a constant current from a power supply package. The multimeter measures in mV. Plotting...
20. ### Find current induced in the photoelectric effect

Homework Statement A metal surface had dimensions of 1.5mm x 2mm. The intensity of light incident on surface is 4.5×10^-6 W/m^2. On average one electron is emitted for every 300 photons incident on the surface. Determine the initial current leaving the metal. ●wavelength of light incident is...
21. ### Pressure-volume graph and internal energy

Homework Statement There is a pressure volume graph with the gas changes shown, forming a rectangle. The corners are labled A to D starting from the upper left corner heading on to the right until it returns to point A again. The question is at what point, or line is the internal energy of the...
22. ### Calculating pH from pKw

Homework Statement pKw for water at 10 deg Celsius is 14.54. What is the pH of pure water at this temperature? Homework Equations kHw = [H+][OH-] The Attempt at a Solution I don't even know where to start on this one
23. ### Maclaurin series and general calculus question

Homework Statement This question has four parts which may follow up from each other so I incuded all the parts. The real problem I'm having is with d Consider the function f ang g given by f (x)=( e^x+[e^-x])/2 & g (x) =( [e]^x]-[e^-x])/2 a) show f'(x) = g (x) and g'(x) = f (x) b) find the...
24. ### Number of ways that seven toys can be distributed

Homework Statement Find the number of ways in which seven different toys can be given to three children, if the youngest vis to receive three and the others two. Homework Equations The Attempt at a Solution 7 combination 3 × 4 combination 2 × 2 combination 2 = 210 Is this the correct way of...
25. ### Normal distribution problem

Homework Statement A student sits a test and is told that the marks follow a normal distribution with mean 100. The student receives a mark of 124 and is told that he is at the 68th percentile. Calculate the variance of the distribution. Homework Equations...
26. ### Simple differential equation problem

Homework Statement Find constants a and b such that y=ax + b is a solution to the differential equation dy/dx = 4x - 2y Homework Equations The Attempt at a Solution I already have the solution that is: a=4x-2 (ax+b) (I'm fine with this part) a = (4-2a) x - 2b (what happened here?) 4-2a=0...
27. ### Use geometric series to write power series representation

Homework Statement Complete the proof that ln (1+x) equals its Maclaurin series for -1< x ≤ 1 in the following steps. Use the geometric series to write down the powe series representation for 1/ (1+x) , |x| < 1 This is the part (b) of the question where in part (a)I proved that ln (1+x)...
28. ### Find the induced EMF and Lenz' law

Homework Statement There is a magnetic feild directed inside/ towards the screen. There is also a single rectangular coil parallel to the screen where one of the sides are movable. The magnetc feild increases, what happens to this movable side of the coil. This is my description of the...
29. ### Stargazing Brightness of objects through a telescope

Hi my question is about how the brightness of stellar objects is effected when we look at them through a telescope. Firstly when I looked through a telescope I noticed there were more stars I could see. Is the reason because a telescope can gather more light than our eye or does it have...
30. ### Circular motion , the loop the loop

Homework Statement The loop-the-loop machine has radius R of 18m (a) What is the minimum speed at which a cart must travel so that it will safety loop the loop (b) what will the speed at the top be in this case Homework Equations Centipetal force = m*v^2/r Kinetic and potential energies =...