Approach Definition and 565 Threads

Hello, I came across the question attached. To approach this, I assigned S1 to car Y and S2 to car X. So the displacement of Car Y is S1=S2 + d(naught). Then using S1= ut+(1/2) at^2 for car Y and S2= uT , I got to uT + d(naught) = VT + (1/2)aT^2. However, I am stuck here as I can't relate...

##\dfrac{x+2}{y-4} +\dfrac{2(y-4)}{x+2} + 3=0## ##x-y=3## My approach, will call it brute force, i have ##y=x-3## then, ##\dfrac{(x+2)^2+2(y-4)^2}{(x+2)(y-4)}=-3## ##(x+2)^2+2(y-4)^2=-3(x+2)(y-4)## ##(x+2)^2+2(x-7)^2=-3(x+2)(x-7)## ##x^2+4x+4+2(x^2-14x+49)+3(x^2-5x-14)=0## ##6x^2-39x+60=0##...

Hello frens, How should one approach this sort of integral? Any tips would be appreciated. Let's say we have $$ \int_{(1)}^{(2)}\exp\left[ a+b\exp\left[ f(x) \right] \right]dx$$ ...where the limits of integration are not important. Any tips? Thanks!

My interest is on how they arrived at ##r^2 \sin θ## My approach using the third line, is as follows ##\cos θ[r^2 \cos θ \sin θ \cos^2 ∅ + r^2 \sin θ \cos θ cos^2∅ ] + r\sin θ [r\sin^2 θ \cos^2∅ + r \sin^2 θ \sin^2 ∅]=## ##\cos θ[r^2 \cos θ \sin θ[\cos^2 ∅+ \sin^2 ∅]] + r\sin θ [r\sin^2 θ...

I am interested in an algebraic approach. My lines are as follows; ##\dfrac{(x+1)(x+4)}{(x-1)(x-2)} -2<0## ##\dfrac{(x^2+5x+4) - 2(x-1)(x-2)}{(x-1)(x-2)} <0## The denominator will give us the vertical asymptotes ##x=1## and ##x=2## The numerator gives us, ##x^2+5x+4-2x^2+6x-4 <0##...

Ok in my approach i have the lines, starting with the inner integral, $$\int_0^1 xy \cos (x^2y) dx$$ I let ##u =x^2y , u(0)=0, u(1)=y## ... $$\dfrac{1}{2} \int_0^y \cos u du=\left[\dfrac{1}{2} \sin u \right]_0^y= \left[\dfrac{1}{2} \sin (x^2y) \right]_0^1=\left[\dfrac{1}{2} \sin y...

A. Correct answer is radius = 1770m, acceleration = 2.73*10^-3m/s. B. I don't know how to approach this problem. I don't know if I should start with forces, energy, or basic kinematics.

Wolfram gave the solution and a hint: i want to understand the hands on approach steps... In my approach (following Wolfram's equation) i have, ##(x-3)^2(2+12(x-3)+(x-3)^2=-25## ##(x-3)^2((x+3)^2-33)=-25## ##(x-3)\sqrt{((x+3)^2-33)}=-5i## ...

I saw this link; is the approach here correct...

In my approach i have, ##α + β = \tan^{-1} \left[ \dfrac{\dfrac{a}{a+1} + \dfrac{1}{2a+1}}{1-\dfrac{a}{a+1} ⋅\dfrac{1}{2a+1}}\right]## ... ##α + β = \tan^{-1} \left[ \dfrac{2a^2+3a+1}{(a+1)(2a+1)}\right] \div \left[\dfrac{2a^2+2a+1}{(a+1)(2a+1)}\right]## ##α + β = \tan^{-1}...

Ok in my approach i have, ##2 \tan^{-1} \left(\dfrac{1}{5}\right)= \sin^{-1} \left(\dfrac{3}{5}\right) - \cos^{-1} \left(\dfrac{63}{65}\right)##Consider the rhs, Let ##\sin^{-1} \left(\dfrac{3}{5}\right)= m## then ##\tan m =\dfrac{3}{4}## also let ##\cos^{-1} \left(\dfrac{63}{65}\right)=...

I want to use the Lagrangian approach to find the equation of motion for a mass sliding down a frictionless inclined plane. I call the length of the incline a and the angle that the incline makes with the horizontal b. Then the mass has kinetic energy 1/2m(da/dt)2 and the potential energy should...

I'd like to proceed in a linear fashion, taking each part on one by one. For the first part, we can write the Hamiltonian as ##H = \sum_{n}^{N} w(c_{An}^{\dagger}c_{Bn}+c_{Bn}^{\dagger}c_{An})+v(c_{Bn}^{\dagger}c_{A(n+1)}+c_{A(n+1)}^{\dagger}c_{Bn})##. We can convert the creation and...

TL;DR Summary: How do I approach the setup of this problem? It seems very different than a setup for a kinematics problem I'm self studying first year mechanics and am having a hard time with the following problem (screenshot attached). The example is from Intro to Mechanics by K&K. I'm...

Hello everyone, sorry if this is the wrong section. In this forum I'm a fish out of the bowl, my knowledge of physics is ages beyond most of the people on there, so please forgive my naivness. So, here's my problem, I'm a sort of "audio" engineer (won't enter much on detail) and on my free...

This is a text book example- i noted that we may have a different way of doing it hence my post. Alternative approach (using implicit differentiation); ##\dfrac{x}{y}=t## on substituting on ##y=t^2## we get, ##y^3-x^2=0## ##3y^2\dfrac{dy}{dx}-2x=0## ##\dfrac{dy}{dx}=\dfrac{2x}{3y^2}##...

Hi, I’m interested to understand some of the mechanics involved in meteorites that originate from the asteroid belt. I have researched several including the Barringer and the one in Northern Canada in 2008 that was caught on multiple CCTV cameras. They all have very similar velocities before...

I'm reading the book Deep Learning by Ian Goodfellow, Yoshua Bengio, and Aaron Courville, and currently reading this chapter on numerical methods--specifically, the section on constrained optimization. The book states the following. Suppose we wish to minimize a function...

In many standard texts the behavior of Foucault’s pendulum is solved by adding the Coriolis force term to equation of motion and deriving two coupled differential equations. Here’s an alternative approach: 4 assumptions are made: Mathematical pendulum (point mass attached to massless rigid...

Dear mathematicians, I am getting stuck solving this equation for "d". And what (free)software would you recommend to check this equation? Thanks a lot!

I am not sure why criss-cross approach would work here, but it seems to get the answer. What would be the reason why we could use this approach? $$\frac {z-1} {z+1} = ni$$ $$\implies \frac {z-1} {z+1} = \frac {ni} {1}$$ $$\implies {(z-1)} \times 1= {ni} \times {(z+1)}$$

I wonder if the following makes sense. Suppose we want to multiply ##\int_0^\infty e^x dx\cdot\int_0^\infty e^x dx##. The partial sums of these improper integrals are ##\int_0^x e^x dx=e^x-1##. Now we multiply the germs at infinity of these partial sums: ##(e^x-1)(e^x-1)=-2 e^x+e^{2 x}+1##...

https://www.feynmanlectures.caltech.edu/I_10.html https://www.feynmanlectures.caltech.edu/I_09.html Using Mathematical approach we can describe the motion of a falling body whose gravity is 32 m/s^2. Analysis shows that this is simply ##s-s_0=ut+1/2at^2##. Similarly we can describe the motion of...

I have read about several approcahes to bypass some classical restrictions to quantum facts such as the electron being in a torus-like shape to avoid ,the greater than speed of light, rotation paradox . Could you recommend websites , sources or books that give good classical analogy to quantum...

Summary: New black hole simulations that incorporate quantum gravity indicate that when a black hole dies, it produces a gravitational shock wave that radiates information, a finding that could solve the information paradox. Hello, Please excuse the rather "conversational" approach I'm using...

\( \int\frac{dx}{1+tanx} \)

Lim x->c f(x)=L means that for a given ϵ we can find a δ such that when |x-c|<δ-> |f(x)-L|<ϵ. To satisfy the criterion m<f(x)<M we choose ϵ=min (L-m, M-L) and for that ϵ we determine a δ. m<f(x)<M m-L<f(x)-L<M-L |m-L|<|f(x)-L|<|M-L| |L-m|<|f(x)-L|<|M-L| |L-m|<|L|+|m| |f(x)-L|<|f(x)|+|L|...

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Givens: Vyi=12.5 m/s Vyf=-12.5 m/s (at the same horizontal level) ay=-9.81 m/s^2 Δy= zero m (as the displacement on the y-axis, when the projectile reaches the same horizontal level, is zero m) Δt=? When I use Δy=[(vyi+vyf)/2]*Δt I get the time as undefined. Δt= 2Δy/(vyi+vyf) = 2*0 m/(12.5...

I am refreshing on the pde's, and i am trying to understand how the textbook was addressing change of variables, i find it a bit confusing. I will share the textbook approach, then later share my own understanding on change of variables approach. Here is the textbook approach; My approach on...

Homework Statement:: R1 = 2kOHms; R2 = 2kOHms; R3 = 3kOHms; R4 = 3kOHms; VS = 25V; IS = 10mA [5,5] a) Determine the power provided by the source dependent on current using method of the nodes [3.0] b) What is the value of electrical power dissipated in all resistors in the circuit? Relevant...

Hi all, Currently I am working on a home-project, making a trike. Now just for fun and because I like to calculate things, I calculated the deflection of a frame with a load. The frame is shown in the picture below, I added the force for clarity. With my analytical calculation I found a...

In the following review paper on scattering amplitudes, by Elvang and Huang: https://arxiv.org/abs/1308.1697 they calculate the amplitude for 6 particles with half of positive helicity and half of negative helicity in section 9.3.2. Their matrix C (a point in the relevant Grassmannian) is...

I read this article History of James Clerk Maxwell and it talks about Maxwell and Dirac also at some point. It is said that Maxwell thought geometrically, and also Dirac said he thought of de Sitter Space geometrically. They say their approach to mathematics is geometric. I see this mentioned...

Hi All, Huygens principle has been extended with two independent efforts in order to reform its original feature that gives rise to a back propagating wave. 1) Fresnel proposed the obliquity factor ##(1/2)(1 + \cos\theta)##. 2) Miller proposed two kinds of emissions (dephased). D. Miller...

Summary:: Control volume question that has a brine solution entering a tank and mass accumulates over time. Hello, I'm currently struggling with a control volume approach question that has a brine solution entering a tank. I get to a point where I have a first order differential equation. I...

I already have a degree in physics. Is there a book that describes the applications for a person who knows the underlying physics? Poking around, I can only found 1000 page tomes that are also teaching the underlying physics. In the back of my head I am thinking about 1) Systems of wheels...

I have a few questions on these graphs. For example if there is a way to tell directly from a complicated graph if it is "physical" in the sense that it describes an actual process. I have also questions on the building of graphs using BCFW bridges, on determining the value of the parameter "k"...

Hi, one of the most interesting experimental tests performed for rotating machinery (such as gas turbines) is blade containment test - if the blade detaches from the hub, it can't break through the cover of the turbine because it could result in catastrophic damage (especially in case of...

Majoring in electrical engineering imply studying Griffiths book on electrodynamics, so I have begun reading its first chapter, which is a review of vector calculus. A list of vector calculus identities is given, and I would like to derive each one, with one of them being ##\nabla \cdot (A...

I am curious about how top scholars or passionate physicists approach a new topic or a chapter. Do they just dive right in or they do something else before approaching the topic? What's their method of working? Also, I want to know the significance of online videos in understanding a topic...

I am beginning this new general physics course and I have encountered a question involved with what I assume to be cross products, a topic that I have very little experience with. I am not looking for a direct answer to the problem but advice on what steps should be taken in order to learn how...

(55x + 45y) = 520 (1) (45x + 55y) = 480 (2) So first I notice they are divisible by 5 so I go ahead and do that. (11x + 9y) = 104 (1) (9x + 11y) = 96 (2) 11 times 9 is 99 and 9 times 11 is 99 so I can cancel some terms. I proceed to do that by multiplying the top by 11 and getting: (121x +...

There is a beautiful demonstration, available in the text Robert S. Elliot, Antenna theory and Design, Wiley-IEEE Press, page 17 (Stratton-Chu solution), which shows how the electromagnetic field at each point ## \mathbf { r} ## of a volume ## V ##, with boundary ## S_1, ..., S_N ##: can be...

I'm not sure how to simplify this without spending a lot of time on it. Is there a pattern that I need to weed out?

Is my work and the answer correct? If not, how should I approach this problem? Thank you!

from problem I find \[ r = r_0 + At \] \[ x_0 = 3 + 2t\] \[ y_0 = -1 - 2t\] \[ z_0 = 1 + t\] and \[ A = (2,-2,1)\] but i don't understand What is the distance of closest approach? someone tell me to a formula please.

I'm trying to understand if the amount of effort/energy required to get to absolute zero approaches infinity, or if its a linear thing... is there a point in which dropping near 0 kelvin changes from a 1:1 to an exponential curve? Is the whole thing a curve or is there a static point, like 1...

I am close to graduating as an EE major but I have never been able to organize a step by step method on analyzing a circuit. It seems to me that every time I am trying to analize a circuit I end up with a bunch of equations and nothing more. I know that I should: 1. Know what I am solving for...