Minimum Definition and 1000 Threads

How close does does a particle and anti-particle pair have to be with each other in order to achieve annihilation?

Hi MHB, I've one problem that I think I've already solved half of it, but fact is I really don't know if I am on the right track... that problem is hurting my head so much... Problem: For all positive real $x$ and $y$, find the minimum of $x+y+xy$ and $x+y-xy$ if $(x+y+xy)(x+y-xy)=xy$...

I have a function: f(x) = Asin2(x) + Bcos2(x) + Csin(2x) and I want to find the minimum turning point(s). To start with, I calculated: f'(x) = (A - B)sin(2x) + 2Ccos(2x) Therefore, turning points occur when f'(x)=0, or: tan(2x) = 2C / (B - A) To find the minima, I then want to...

Homework Statement Let n be a positive integer. Determine the smallest possible value of $$|p(1)|^2+|p(2)|^2 + ...+ |p(n+3)|^2 $$ over all a monic polynomials p with degree n. The Attempt at a Solution Let the polynomial be x^n+c_{n-1} x^{n-1} +...+ c_1x+c_0 p(1) =...

EDIT: This is in the wrong section isn't it? How do I move it to the General Physics section? (My bad.) This isn't a homework problem (I'm not in a physics class) so hopefully this isn't the wrong section. My question is about finding the minimum velocity needed for an object (directly...

Let $m,\,n,\,p,\,q$ be the positive real numbers such that $\dfrac{1}{1+m^4}+\dfrac{1}{1+n^4}+\dfrac{1}{1+p^4}+\dfrac{1}{1+q^4}=1$, find the minimum of the product of $mnpq$.

Homework Statement Find the minimum time taken for the object to cover the distance x I'm given the following: x = the distance i need to cover V0 = the initial velocity which is zero a = the maximum permissible acceleration Vmax = the maximum permissible velocity Homework...

Hello, This might seem like a very basic problem for the most of you but I am a little bit confused as to the problem of maximum and minimum values. For, example I do understand why y = x^2 has no absolute maximum as y-->\infty as x-->\infty... However, in the closed interval, say, [0, 2]...

Find the minimum value of $(x-y)^2+\left( \sqrt{2-x^2}-\dfrac{9}{y} \right)^2$ for $0<x<\sqrt{2}$ and $y>0$.

Homework Statement A bag contains n identical red balls, 2n identical black balls and 3n identical while balls. If probability of drawing n balls of same color is greater than or equal to 1/6, then minimum number of red balls in the bag is equal to?The Attempt at a Solution P =...

Homework Statement Here is the question: I am confused about the solution. In the solution they found that the minimum capacity rate ratio R = C_min/C_max was zero. This is because of the term I circled in the red which I do not understand why it goes towards infinity. Here is the solution...

I'm just learning this theory and the maths is really trivial but the theory is slightly confusing me. I understand that if we have some function z=f(x,y) and we graph this on a three dimensional set of axis we will have some surface, we can then extend this by creating level curves in the...

Good evening PF! I'm having trouble figuring out how to attack this problem. I have tried two different ways but I don't know if either of them is correct. Homework Statement Using the provided virial coefficients, determine analytically the pressure at which the graph of PV versus P for N2 at...

Homework Statement There are two cubes of mass m. They are initially tied by a string tightly. They are kept from joining into each other because of a spring (which in this tied up state has a compression of ε) of coefficient of stiffness k. Find the minimum value of the quantity εk/mg so...

Find the values of b such that the function has the given minimum value. $$ f(x) = x^2 + bx - 25$$; Minimum value: - 34

Homework Statement Determine minimum value of integral ##B(y)=\int_{0}^{2}({y}')^2dx## for function ##y\in C^1(\mathbb{R})## and ##y(0)=y(2)=0## and ##\int_{0}^{2}y^2dx=4## Homework Equations The Attempt at a Solution IF I am not mistaken, the idea is to first find the function...

283) you want to build a volume "V" shaped geometric body torque limited cylindrical half-spheres. If the material lower semisphere costs twice as much as the material of the sides, and the material of the upper hemisphere costs three times, calculate the dimensions of the body more economic...

I recently wrote a program that implements a slightly modified version of Prim's Algorithm to find a minimal spanning tree and it seems to work correctly. However, I am doubtful because my prof claims that this certain tree has more than 1 solution but my program gives only one solution. Note...

Homework Statement A bullet of mass m and charge q is fired towards a solid uniformly charged sphere of radius R and total charge + q. If it strikes the surface of sphere with speed u, find the minimum speed u so that it can penetrate through the sphere. (Neglect all resistance forces or...

Confuses me. In which case is it the helmholtz free energy, the gibbs free energy, the energy that gets minimized and why? Also is it consistent with energy conservation and how is that possible if you use it on two systems exchanging energy. Can we know the total energy of the total system for...

Homework Statement Determine the minimum initial velocity V0 and the corresponding angle theta at which the ball must be kicked in order for it to just cross over the 3 m fence. Given: Horizontal distance=6m vertical distance=3m Homework Equations equation 1: Vy2=(V0)2+2a(y-y0)...

(2) Find the height of the cone's lateral surface minimum confined to a sphere of RADIUS R. the answer is (2 + sqrt(2)) R

Between all the cones whose generatrix length given is L, determine the one with the highest volume? :confused: the answer is h= L/sqrt(3) and R = Sqrt(6)L/2

First-Order Extrema in "Classical Mechanics", Theoretical Minimum In the 3rd lecture of Classical Mechanics, 2011, by Dr. Susskind in his Theoretical Minimum series, he talks about calculating extrema, saddle points, etc. to "first order". "if you move a little bit, the potential is zero, to...

[FONT=open-sans]Find a point $P$ on the line $3x+2y+10=0$ such that $PA+PB$ is minimum given that $A$ is $(4,2)$ and $B$ is $(2,4)$ My Try: Let Coordinate of point $P$ be $(x,y)$. Then $PA = \sqrt{(x-4)^2+(y-2)^2}$ and $PB = \sqrt{(x-2)^2+(y-4)^2}$ Now Let $f(x,y) =...

Homework Statement A heavy string is tied at one end to a movable support and to a light thread at the other end as shown in figure. The thread goes over a fixed pulley and supports a weight to produce a tension. The lowest frequency with which the heavy string resonates is 120 Hz. If the...

If anyone out there has worked through Susskind's book, I have two questions on the Lagrangian to Hamiltonian section, any help would be greatly appreciated: 1) In Lecture 8 exercise 2, he wants you to calculate take the Lagrangian of L=1/2ω d/dt q - ω/2 q^2 as a Hamiltonian and says it...

Hi all, How can I calculate the minimum distance between the perimeter of a disk in 3d space and a point above the disk? (the point can be inside or outside the area above the disk) I've been trying to work this out for a while, but I'm getting no where. For example, a point at (1,1,1)...

Hi, Homework Statement I would like to determine the position, magnitude and direction of the minimum force F required to turn over the box shown in the attachment (width - B, height - H). The (uniform) box is placed on a horizontal plane. The coefficient of friction between the box and the...

Hello friends, I would like to know the temperature dependence of LASER for its action. At What temperature the laser action is possible and realisable? Any references, links and help is appreciated.

Homework Statement ind the absolute minimum value of the function f(x,y) = 6 + 3xy -2x- 4y on the set D. D is bounded by the parabola y=x^2 and y=4 Homework Equations Partial derivatives and a theorem where if F is continuous on a closed bounded set in R(2) then F has an abs. max and...

Hi, If I were given a whole-body X-ray dose daily for many days (a year for example) What would be the highest dosage per day which would result in an increased cancer risk but no noticeable signs of radiation poisoning by the end of the year, or during? And also, I've read that a 2KRad dose...

First off, I want to apologize for posting more than one question. I just discovered this site, so I wanted to check my work while I am able to. Thank you again. Homework Statement A massless rope of length L = 1 m is swung in the vertical plane, with a bob of mass m = 1 kg attached to its...

The coefficient of static friction between the crate m1=3.00kg and the incline with θ=35° shown in the figure below is .300. What minimum force F must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline? mgsinθ μsmgcosθ f=ma I don't quite get...

I'm having an issue in comprehending the minimum deviation offered by a prism. The fact that we could use the symmetry argument about the angle of incidence and angle of emergence being equal for minimum deviation make sense to me but I couldn't understand why we can be so sure of exactly 1 such...

Hi Everyone, I am confused about how to calculate the minimum reserve factor against yielding and fatigue in an I-beam clamped at both ends. I have calculated the maximum bending stress from it's deflection due to a load in the middle of the beam, and I know the cross-sectional area of the...

If $\log_4 (a+2b)+\log_4 (a-2b)=1$, find the minimum of $|a|-|b|$.

Determine the minimum value of $\left( \sqrt{x^2-8x+27-6\sqrt{2}}+ \sqrt{x^2-4x+7-2\sqrt{2}} \right)^4$ where $x$ is a real number.

Homework Statement px+qy=40 is a chord of minimum length of the circle (x-10)^2 + (y-20)^2 = 729 . If the chord passes through (5,15), then p^{2013}+q^{2013} is equal to Homework Equations The Attempt at a Solution Let chord length be L \frac{L}{2} = 729-...

Hi guys, I've got a doubt concerning to the minimum mechanical work and the work-energy theorem. Consider the following Tippens' problem (8.4): A 5-kg hammer is lifted to a height of 3 m. What is the minimum required work? The answer looks very simple and inocent, W = weight times...

Homework Statement A rocket which has an exhaust speed of 8.0 km/s is to have a vertical acceleration of 8.0 m/s2. If the initial mass of the rocket is 6.0x106 kg, at what minimum rate must the rocket consume fuel? Homework Equations F = ma F = RVREL The Attempt at a Solution F...

Homework Statement I know the diameter is 30 m and the radius is 15 The period for one revolution I suppose is some multiple of 7.03 Homework Equations The Attempt at a Solution I couldn't think of an equation where friction was involved where rotational motion was concerned. I...

Homework Statement A sphere of mass M and radius R is moving on a rough fixed surface, having co-efficient of friction μ, with a velocity v towards right and angular velocity ω clockwise. It will attain a minimum linear velocity at time (take v>ωR) The Attempt at a Solution Since v>ωR the...

On an inclined plane (φ = 12°), calculate the minimum force P required to pull the roller over the step. The radius of the roller, r = 0.685m My attempt The sum of the Moment force about the system = 0 0 = mg(sin(φ)*(r-h) + mg(cos(φ)*√[r2-(r-h)2] - P(cos(θ)*r-h) P(cos(θ)*r-h) =...

Homework Statement I have the equation: x^2 + 2*x*y + 5*y^2 - 4*x - 6*y +7 and I have to find the minimum value I'm getting something that looks half like the correct answer, but not quite right... Homework Equations The answer from the answer book is: [x + 2*(y - 1)]^2 + (y + 1)^2...

Homework Statement Find the minimum and maximum values of x and the values of f(x) at these points if: f(x) = 10.9sin(0.7x)+2.1cos(0.7x) The range is (-.27,8.7) Homework Equations I don't know/think there are any The Attempt at a Solution I found f'(x) =...

The position function of a particle is given by r(t)=⟨−5t2,−4t,t2+1t⟩. At what time is the speed minimum? I found the speed function by taking the magnitude of the velocity which is lv(t)l = sqrt(108t^2 +4t + 17) I then took the derivative of the speed to find the critical point...

Homework Statement 4. If x1, x2 are two real number roots of real number coefficient quadratic equation: $$x^2 -2mx + m + 2 =0$$ Solve the following questions: (1) What are the values of m so that x1=x2? (2) What are the...

Homework Statement An unstable particle of mass M = m1 + m2 decays into two particles of masses m1 and m2, releasing an amount of energy Q. Determine the kinetic energies of the two particles in the CM frame. Given that m1/m2 = 4, Q = 1 MeV, and that the unstable particle is moving in...

Homework Statement Let a,b,c be in G.P. and a-b,c-a,b-c in H.P. If both roots of (a+c)x^2 + bx + 4b^2=0 are positive and minimum value of 'b' be k then value of |[k]| Homework Equations The Attempt at a Solution Let a,b,c be denoted by a,ar,ar^2. now \frac{2}{c-a}=\frac{1}{a-b}+\frac{1}{b-c}...