Max Definition and 1000 Threads

This is a UK A-Level question that I'm really struggling with, and can't seem to find any resources online that explain it well. I've been given the following details: mass of gokart + driver = 520kg radius of track = 42m Maximum frictional force between tyres and road on flat track F = 20%...

For this problem, For part(a) the solution is, However, how did they know that the max speed is reached in the vertical position? For part (d) the solution is, However, I thought the solution would be because there is net gravitational torque in clockwise direction (torque due to small mass...

For this problem, The solution is, I don't understand how they got from ##\frac {sin^2\theta_i}{sin2\theta} ## to ##\frac{tan\theta_i}{2}##. Would somebody please show me the immediate steps? I also don't understand is why they say the ignore the trivial case where ##\theta_i = 0~rad##...

Hello, i am programming my fpga with certain logic. With the sof file the logic is working fine and correct. but when i am programming pof file i am getting error. (programming is successful, but doesn't work as per the logic).

For this problem, The solution is, However, I don't understand why they say just before the proton escapes? Are they assuming that the B-field is only at a portion of region which means that only half or so of the circular path is within the B-field so only half of the path have a magnetic...

Hi PF! I'm trying to find the max length of a sub-string palindrome. My logic is to have a left-most index called start that starts from string loc 0 and traverses to the end of the string via a for loop. Next I was thinking a while loop as long as L < R: I'd have a left index L=start and a...

What should I do when the f(x, y) function's second derivatives or Δ=AC-B² is zero? When the function is f(x) then we can differentiate it until it won't be a zero, but if z = some x and y then can I just continue this process to find what max and min (extremes) it has? What I've done is...

Vvertical=15sin30 = 7.5m/s d=Vvertical*t+0.5atsquared 0=(7.5m/s)t+0.5(-9.81m/s)t squared 0=t(7.5m/s-4.9t) t= 1.53s t=1.53/2 t= 0.76s to reach the maximum height Is this correct?

https://www.washingtonpost.com/obituaries/2022/08/08/olivia-Newton-john-grease-singer-dies/

How am I supposed to solve this problem? I did it in a way that's analytically not correct at all lol.. As a first I was thinking about how to relate it to the motion equations to no avail.. (of course with having the condition that normal force board on pebble = force of gravity on pebble)...

Please tell me if I need to post my solution for this.., but I just have a question more or less 'conceptual' question about (c). so I know that from Newton's 2nd law for centripetal acceleration --> ##F_{rope} - mgcos(\theta) = ma_n## where ##a_n = \frac {v^2}{R}## such that where the normal...

Hi. I was reading Lighthill, Introduction to Fourier Analysis and Generalised Functions and in page 17 there is an example/proof where I can't make sense of the following step: $$ \left| \int_{-\infty}^{+\infty} f_n(x)(g(x)-g(0)) \, \mathrm{d}x \right| \le \max{ \left| g'(x) \right| }...

Hi PF! I am wondering the differences between the discrete and continuous case for expected value of minimum of 3 integers uniformly distributed from 1 to 13 vs 3 reals from 1 to 13. The real case is direct: ##F = ((x-1)/12)^3 \implies f = 3(x-1)/12)^2## for CDF ##F## and PDF ##f##. Thus the...

Homework Statement:: project not homework Relevant Equations:: vectors Hi,I am trying to determine the maximum linear velocity of a propeller tip when subject to flowing water with velocity ##\vec V##. For simplicity, I will assume that rotational inertial is negligible. The drawing below...

This is more of a check that I solved this assignment correctly. I got to an answer but I’m not sure it’s correct. First, I decided that I needed to solve for the maximum stretch of the bungee. To do that I think I needed the length of the bungee (which is also the initial compression). So...

Hi I am trying to do an artisanal EV car and I would like to know how do I choose the right motor. I already have one in mind but I don't know how to calculate the max mass that it can move. (see attached pdf) Gear Ratio : 2.39 Diff Ratio : 4.88 Wheel Diameter: 26in I would like to know the...

I know that friction on a surface has a maximum value. When an object is pushed with a force greater than the maximum friction value, the object will move. But when a free-falling object falls from a height, does air resistance have a maximum value as well?

Can I get a hint on how to start with this problem ? Thanks in advance I can't really think of anything...

Hello, I've worked through the free-body diagram to compute the answer: tan(𝜃) = 0.67 𝜃 = arctan(0.67) = 33.822... The answer is supposed to be approximately 42. Yet, tan(42) is not 0.67, is the suggested answer wrong?

Assuming it’s one body whose initial speed is u. First it attains height h then H. t1 and t2 are two times at which they attain h and H. ##h=ut1-\frac12gt1^2## ##H=ut2-\frac12gt2^2## ##\frac {t1}{t2}=1/3## Replacing t2 with 3t1, I am stuck.

My guess is that while the voltage between the two plates is lower when a dielectric is present, the maximum voltage that the capacitor can hold will actually increase because the maximum strength electric field generated by the charges on the two plates will be higher due to the opposing...

Hi guys, thanks for helping me! I am working on a home project that includes a privacy shade for my backyard. I have a 6'x15' vertical shade attached to two portable posts that are held up right by four legs ("X" shaped footprint). the surface footprint of the legs covers an area of 46"x70". I...

Did Max Tegmark talk about his Mathematical Universe hypothesis at this event (https://www.zimbio.com/photos/Brian+Cox/Michio+Kaku/rAcvFyE88Ul/World+Science+Festival)? And if that's the case, what was the opinion of Michio Kaku?

I've double-checked my equations and can't find what's wrong. First I calculate the partials: $$f_x = (2x - 2x^3 -4xy^2)e^{-x^2, -y^2}$$ $$f_y = (-2yx^2 + 4y - 4y^3)e^{-x^2, -y^2}$$ By setting f_x = 0 I get: $$x^2 = 1 - 2y^2$$ Then I calculate f_y = 0 $$-2yx^2 + 4y - 4y^3 = 0$$ I plug in the...

I calculate f_x to be $$f_x = (2x - x^2)e^{-x-y}$$ $$f_y = (1 - y)e^{-x-y}$$ f_x = 0 when x_1 = 0, x_2 = 2 f_y = 0 when y = 1 This gives two critical points: (0, 1) and (2, 1) which yields e^-1 and 5e^-3 respectively. I then check the x line and y lines by doing $$f(x, 0) = x^2e^{-x-y}$$ $$f_x...

Can a solid vibrate with only one frequency-Debye maximal frequency?

Below shows the generic V-N diagram for most of the civil aircrafts. Now, I have the CFD results available for multiple combinations of angles of attack of the aircraft, with the deflection angle of the flap. I have to choose a couple, to input into my structural analysis of the flaps. How to...

Although a function cannot have extreme values anywhere other than at endpoints, critical points, and singular points, it need not have extreme values at such points. It is more difficult to draw the graph of a function whose domain has an endpoint at which the function fails to have an extreme...

Hi, PF Although a function cannot have extreme values anywhere other than at endpoints, critical points, and singular points, it need not have extreme values at such points. There is an example of how a function need not have extreme values at a critical point or a singular point in 9th edition...

Hi, I'm currently looking into the forces exerted on a cable if the cable was to go from slack to taut due to a falling object that is pivoted about a lower hinge - such as a drawbridge but instead of slowly lowering, there is slack in the cable causing the bridge to freely rotate about the...

I couldn't fit in the title, but this is with a hollow circular cross section So currently I am trying to figure what occurs when two, perpendicular bending moments are applied to a hollow circular cross section (one about the z axis, and the other about y). I know that if I was dealing with a...

Summary:: Question: a car of mass 800kg, 3600N driving force experiences resistive forces of 120v Accelerates from rest. Form equation and show max speed is 30 ms^-1, assuming driving force does not change. my attempt at a solution -I can not see how to rectify it as I don’t think I did...

How can i find the angle that a projectile is fired where the maximun height is the same as the traveling distance? I need to find this first in a theoretical way, then i need to confirm this with a simulation. And i need to use only this y=yo+Voyt+1/2gt^2 x=Voxt

Problem: Let ## f: \Bbb R \to \Bbb R ## be continuous. It is known that ## \lim_{x \to \infty } f(x) = \lim_{x \to -\infty } f(x) = l \in R \cup \{ \pm \infty \} ##. Prove that ## f ## gets maximum or minimum on ## \Bbb R ##. Proof: First we'll regard the case ## l = \infty ## ( the case...

[Mentor Note: Two threads with similar titles merged] First calculate the equivalent force on the car from the max torque. An average tire is 15 inch diameter = about .2 meter radius Since T = F X R , F = T/R = 660/.2 = 3300 Newtons. since F = M X A, A = F/M = 3300/2083 = 1.6 m/sec^2...

I had heard that computer processors are reaching the speed of light. Is this true, and if it is how do we combat this cap?

A company called SpinLaunch claims it can get something to 2200 m/s by spinning it up on a carbon fiber composite arm. I'm trying to figure out the limit of that approach. How fast can you go with existing materials? I tried to work it out for a constant with cable with no payload (result...

I have a Intel(R) Xeon(R) E-2274G CPU @ 4.00GHz 4.01 GHz machine which has a published max speed of 5.0 GHz. However, when I run it under load on all 4 cores, it only gets up to about 4.5 GHz: Could someone explain to me why it's not ramping up to the full 5.0 GHz or what I could do to...

The derivative of a point of maximum must be zero, and since $$y'=3ax^2+2bx+2 \rightarrow y'(-1)=3a-2b+2 \rightarrow 3a-2b+2=0$$ we get the first condition for ##a## and ##b##. Now, since we want ##x=-1## to be a local maximum, the derivative of the function must be positive when tending to...

My attempt: p and T allows us to calculate ##Z=402 \frac{kg}{sm^2}## using ## Z=p*\sqrt(\frac{\gamma*M}{R*T})## . The sound intensity level at 10 meters allows us to calculate the intensity at 10 meters to be I=10``````^{-7} W/m^2 using ##50 = 10*log(I/I_0)##. Then, using the formula...

Hi, IIRC, Maximum Likelihood Estimators ( MLEs) satisfy an " Inheritance" property , so that if ##m_1,m_2,..,m_n## are MLEs for ##M_1,M_2,...,M_n## respectfully and f is a Random Variable of the ##M_i##, then the MLE for f is given by ##f(m_1,m_2,...,m_n)##. Is this correct? If so, is there a "...

If the Summary is not clear, the following is an example translated from: https://telecombloger.ru/7335 '... air conditioning systems. For example, the efficiency of a compressor is about 85%. The remaining 15% is spent on friction, oil movement, overflows, heating, etc. The efficiency of the...

Hi! Instead of just describing my procedure and all my derivations, I really just want to ask if my approach makes sense (actually I have 2 options) to calculate the maximum energy. I am considering c=1 and the problem suggests to consider the neutrino massless: For the first decay, ##Z...

I have situation where i have drawn a concept with 1 sheet covering width of box for model. But now i need to draw up the manufacturing drawings and it needs to lifted and assembled by 2 people. So i need to know if person weighs 70 kg how much weight they can lift without using mechanical aid...

Im unsure if I am on the correct track or have gone off on a tangent. Any help or guidance would be appreciated. CMRR=20log10(Adiff/Acm) 120=20log10(10^5/Acm) 120/20=log10(100,000/Acm) 6=log10(100,000/Acm) taking antilogs 1,000,000=100,000/Acm Acm=100,000/1,000,000 Acm=0.1Max amplified...

Let $a$ and $b$ be real numbers and $r,\,s$ and $t$ be the roots of $f(x)=x^3+ax^2+bx-1$ and $g(x)=x^3+mx^2+nx+p$ has roots $r^2,\,s^2$ and $t^2$. If $g(-1)=-5$, find the maximum possible value of $b$.

From the probability density plot why it is max at the centre of the box...e.g probability to find the particle per unit le gth is max. at the centre of the box??why not at any other position??

it's late so I'll just start this \[ \dfrac{dy}{dx}=\dfrac{2\cos 2x}{3+2y} \] so \[(3+2y) \, dy= (2\cos 2x) \, dx\] $y^2 + 3 y= sin(2 x) + c$