Minimum Definition and 1000 Threads

Does anyone know if or when Dr Susskind is coming out with a “ Theoretical Minimum Quantum Field Theory “ ?

Homework Statement You should shoot a basketball at the angle ##\theta## requiring minimum speed. Avoid line drives and rainbows. Shooting from (0, 0) with the basket at (a, b), minimize ##f(\theta)= 1/(a \sin (\theta) \cos (\theta) -b \cos^2 (\theta))##. (a) If b =0 you are level with the...

Homework Statement Show that A is a scalar matrix kI if and only if the minimum polynomial of A is m(t) = t-k Homework EquationsThe Attempt at a Solution f(A) is monic f(A) = 0 since A = kI Next we must show that deg(g) < deg(f) I guess I'm not sure where g comes from. Is it merely an...

Hi, I am trying to solve a control problem where I have to minimize the fuel consumption of a vehicle: $$J=\int_{0}^{T} L(x(t), u(t),t) + g(x(T),T)dt$$ ##L(u(t),v(t))=\sum\limits_{i,j=0}^{2} K_{i,j} u(t)^i v(t)^j ## is convex (quadratic) and the term ##g(x(T),T)## is to have a constraint in the...

Homework Statement A homeowner wishes to enclose a rectangular garden with fencing. The garden will be adjacent to his neighbour’s lot. There will be fencing on all four sides. His neighbour will be paying for half the shared fence. a) What should the dimensions of the garden be if the area is...

Homework Statement Prove that snell's law ## {n_1}*{sin(\theta_1)} ={n_2}*{sin(\theta_2)} ## is derived from using euler-lagrange equations for the time functionals that describe the light's propagation, As described in the picture below. Given data: the light travels in two mediums , one is...

Homework Statement Part (d) is the bit I am having trouble doing (the question is in the attachment). Homework Equations Apart from what is shown, I also have to use F = dV(r) / dr The Attempt at a Solution For Part (b), I showed this by differentiating the potential energy and equating this...

Homework Statement Two loudspeakers are placed 3.00 m apart horizontally.They emit 425 Hz sounds, in phase. A microphone is placed d= 3.20 mid distant from a point midway between the two speakers, where an intensity maximum is recorded. (a) How far must the microphone be moved to the right to...

Not withstanding the fact that most neutronium is produced in neutron stars, what is the lowest mass required to keep neutronium stable? I've heard it could be as low as 0.1 solar masses. Could it be even smaller than that? Can you make an Earth mass neutronium ball and have it stay stable due...

Homework Statement 14.100 Calculate the maximum and minimum distances in kilometres between the centers of the Earth and moon, taking the eccentricity of the moon's orbit into account. Use the data given in Prob. 14.99 Homework EquationsThe Attempt at a Solution Can you check my solution...

Why do we have minimum deviation of prism? physical explanation is needed!

Homework Statement In order to solve a question, I need to find the minimum and maximum resultant of three vectors, their magnitudes are given to me. Homework Equations Magnitude of vector A = 1 Magnitude of vector B = 3 Magnitude of vector A = 5 The Attempt at a Solution The maximum part was...

Hello, can anybody help me with solving the problem. Homework Statement :[/B] Calculate minimum uncertainty? A horizontal beam of laser light of wavelength 604 nm passes through a narrow slit that has width 0.0600 mm . The intensity of the light is measured on a vertical screen that is 2.40...

Homework Statement Realization of given three functions $$ \begin{array}{c} f_{1}=x_{1}\bar{x}_{2}\bar{x}_{3}+x_{2}x_{3}\bar{x}_{4}\\ f_{2}=\bar{x}_{3}x_{4}+x_{1}\bar{x}_{2}\bar{x}_{3}\\ f_{3}=x_{2}x_{3}\bar{x}_{4}+\bar{x}_{3}x_{4} \end{array} $$ using the PLA. Homework Equations I don't know...

Is it possible to do DNA test from fallen hair, or skin cells? Or no, since the cells die and lose their core before they fall from the body? Do dead cells still have somekind of unique "fingerprint"?

Homework Statement Homework Equations V = IR And R becomes 2(r of one conductor) because of return path. The Attempt at a Solution V minimum is at third junction. At VD Using KVL we get: [/B] Drop at AB = (10 + 20 + 50) * 2 * 0.1 = 16 V Drop at BC = (20 + 50) * 2 * 0.08 = 11.2 Drop at CD =...

Homework Statement I have a sphere, it's imperfectly spherical, I put it on an incline and apparently it needs a minimum friction to start rolling or moving. Homework Equations I = 2/5 MR^2 torque = I*alpha = R x F The Attempt at a Solution [/B] before anything, I don't get why there's a...

We just discovered the maximum mass of a neutron star, discovered after the recent neutron star merger event back in Aug. They say that the maximum mass of a neutron star is approximately 2.16 solar masses. So I always assumed that the lowest mass for one is 1.4 solar masses, the Chandresekhar...

In scientific experiment, we often have a physical property that can change but have no detectable impact on the measurement. For example, suppose I have a mass of (say) 30 grams attached to a string passing over a pulley. I can add up to another 2 grams and the system doesn't budge. In our...

Hey! :o Let $A = QR$, where $Q$ is an orthogonal ($m\times m$)−matrix and $R$ is an upper ($m\times n$)-triangular matrix of rang $n$ ($m>n$). I want to show that $$\min_{x\in \mathbb{R}^n}\|Ax-y\|_2=\|(Q^Ty)_{n+1}^m\|_2, \ \forall y\in \mathbb{R}^m$$ It is $(a)_k^l=(a_k, \ldots , a_l)^T$...

Homework Statement I Type I Cost per pupil I I Full session I $50 I I Half session I $30 I The above table shows the cost of lessons per month to students attending a private class. The class operates under the following limitations...

Hi, I think this is a topology question, but I'm honestly not 100% sure. Feel free to move. On a number line, I am trying to find the minimum number of moves to get from one point to another, given certain allowed step sizes. For example, My allowed steps might be +/-2, +/-3, and I want to move...

Hi, I'm quite stuck on this past paper question and would really appreciate some help on it. Below I have attached the questions and solutions; it asks me to determine where the maximum tensile and compressive strain in the beam using the bending moment diagram (attached as separate figure...

Homework Statement Finding the minimum time for crossing a river[/B] how is the minimum time crossed by distance between the banks/velocity of swimmer with respect to ground as mentioned in the video? Homework EquationsThe Attempt at a Solution The minimum time is only possible when...

Homework Statement Homework EquationsThe Attempt at a Solution Effiency of a heat pump is given as ## \eta = \frac { T_h }{T_h – T_c} = 30 ## W * 30/s = 6000*4.2 cal /s Minimum consumption rate = W/s = 840 watt Is this correct?

Currently design of turbomachinery (impellers/turbines) is more a form of art than an engineering process. One has to guess a bunch of parameters and check if they are right in much later stages of design. I was thinking about designing the other way: we know the initial and the final velocity...

Homework Statement Homework EquationsThe Attempt at a Solution for this class, we were not taught with contact ratio equations, nor the pressure angle is given, so for this type of problems, do we just assume that minimum number of teeth on a pinion will be 12? 3 integer factors of 180 can...

Homework Statement I was asked to design a beam from the beginning to detailing . I encountered that the shear force for minimum links is greater than the maximum shear force , is it possible ? Homework EquationsThe Attempt at a Solution I have checked thru the working , it seems that...

Homework Statement The temperature of a 12-oz (0.354-L) can of soft drink is reduced from 20 to 5 ºC by a refrigeration cycle. The cycle receives energy by heat transfer from the soft drink and discharges energy by heat transfer at 20 ºC to the surroundings. There are no other heat transfers...

Homework Statement A crate is being transported on a flatbed truck. The coefficient of static friction between the crate and the bed is 0.470. What is the minimum stopping distance if the truck, traveling at 70 km/h, is to decelerate uniformly and the crate is not to slide forward on the bed...

Homework Statement Homework Equations At local minimum or maximum the first derivative equals zero The Attempt at a Solution a) $$f'=2x-\frac{a}{x^2},~~2\cdot 2-\frac{a}{4}=0~\rightarrow a=16$$ Near 0 from the left a/x gets large negative values, smaller than for a=16. that's my proof for...

Homework Statement This is an attempt to solve a problem I asked about here https://www.physicsforums.com/threads/can-a-car-ever-sit-like-this.929453/ Homework Equations F = kx spring force The Attempt at a Solution using the largest angle down it can get with the front spring compressed all...

Homework Statement A woman holds a book by placing it between her hands such that she presses at right angles to the front and back covers. The book has a mass of m = 0.75kg and the coefficient of static friction between her hand and the book is μs = 0.59. What is the minimum force she must...

Homework Statement A great deal of effort has been expended to find “high temperature superconductors”: materials that are superconductors at temperatures higher than the boiling point of liquid nitrogen (77 K). Most of the older superconductors had to be operated with liquid helium (boiling...

...from suffering inbreeding and decline into a non-viable number of animals? Assume a creature somewhat larger than the average human. And with bigger feet. Mods, if this needs moved go for it.

Homework Statement Formulate a proof that the energy minimum principle implies the entropy maximum principle. That is, show that if the entropy were not maximum at constant energy then the enrgy could not be minimum at constant entropy. HINT: First show that the permissible increase in entropy...

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 A baby falls from the top of a ##45 m## building. What is the minimum speed that Spiderman must push off from the same building one second later in order to catch the baby before she strikes the ground? Homework Equations Please see below. The Attempt at a Solution I tried...

Homework Statement Homework EquationsThe Attempt at a Solution I assume that the wheels are 8ft apart in both x and y direction. Let's denote the length and width of the car by 2l = 8 ft. The torque about an axis connected the contact points of rear wheels : ##\vec \tau = [\{l( \hat x +...

how many minimum number of H+ ions are required during ATP production in citric acid cycle (CAC)?

Find the minimum of the expression: $$a^4+b^4+c^4-3abc$$ - if $a,b$ and $c$ are real numbers satisfying the conditions: $a \ge 1$ and $a+b+c = 0$. Hint:

Homework Statement FInd min mass so that block loses contact with ground. Spring is initially in its natural length, the mass attached to spring is on ground(M) Homework Equations Equations of conservation of energy The Attempt at a Solution Min compression = 2mg/k to lift up object, Normal...

Homework Statement A car of mass m is initially stationary on a smooth track at distance h above the ground. What would be the minimum value of h required in order for the car to remain on the track throughout its journey around the loop of radius r? Homework Equations KE(bottom)>PE (top)...

I have some data collected from experiment and I want to calculate the max and min values for this data. Please note that these data not a result of function. What is the best mathematical way to get the max and min without just picking them by directly observation.

Homework Statement Ans: c) Homework EquationsThe Attempt at a Solution I can solve this problem if only I understand the setup . I am sure the diagram is missing something . Can someone help me understand the problem statement in context of the setup ?

Homework Statement Two identical speakers, 10.0 m apart from each other, are stimulated by the same oscillator, with a frequency f, of 21.5 Hz, at a place where the speed of sound is 344 m/s. a) Show that a receiver at A will receive the minimum intensity of sound (Amin) due to the...

It has been my understanding that a brown dwarf was defined by when an object has achieved sufficient mass to begin deuterium fusion. Much like a star is defined by when it has achieved sufficient mass to begin hydrogen fusion. The minimum mass to begin fusing deuterium is estimated to be...

so df/dy' is yy'/ √(1+y'^2) then we are supposed to do y' . [ yy'/ √(1+y'^2) ] - y√(1+y'^2) how does this bring equation 2 in the image ?

Homework Statement A block of mass 7 kg is pushed against a wall by force P. The coefficient of static friction between the block and the wall is 0.42. Determine an expression for the force P as a function of θ such that the block will not slide up the wall or fall down the wall. a.) Draw a...

Homework Statement The minimum resistance obtained by connecting 50 resistances of 0.25 ohm each is A)50/4ohm B)4/50 ohm C)200 ohm D)1/200 ohm 2.Relevant equations 1.When resistances are connected in series, ▪R(equivalent)=summation of all individual resistances 2.When resistances are...