Minimum Definition and 1000 Threads

In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema), or on the entire domain (the global or absolute extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.
As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum.

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  1. orlan2r

    Calculate the minimum work to extract a body of the water

    A hemisphere of 8 kg mass and 20 cm radius is at the bottom of a tank containing water. Find out the minimum work that an agent must to do to extract the hemisphere of the water.(g = 10 m/s2) Please help me
  2. P

    Minimum of Normal Distribution Function

    Homework Statement Show that there is no minimum for the normal distribution function e^(-(x-μ)^2/(2 σ^2))/(sqrt(2 π) σ) Homework Equations The Attempt at a Solution I figured I'd take the derivative and set it equal to 0, but then what?
  3. deep838

    Minimum velocity at bottom of pendulum

    Homework Statement A pendulum is made of a rigid rod (mass m, length l) and a small bob of mass M attached at one end. The rod is pivoted on the other end. What should be the minimum speed of the bob at its lowest point so that the pendulum completes a full circle? Homework Equations...
  4. S

    Finding the minimum mass of a star consisting entirely of helium

    Homework Statement Consider a star that consists entirely of helium. Make an estimate of the minimum mass for which such a star can ignite helium using the following assumptions: (i) helium ignites at a temperature of Tc = 10e8 K. (ii) assume that the critical mass can be determined by the...
  5. A

    Finding the minimum value of n

    Find the minimum value of n that satisfies the following equation E(\frac{10^n}{x})=2011 where X and n are natural numbers So first thought was using derivatives we need to obtain an f(n) I can't seem to advance a lot in this exercise All I got so far is 0<10^n /x - 2011<1 I did something...
  6. S

    D/A Communications - Minimum bandwidth of a channel

    Homework Statement Homework Equations The given channel transfer function and PSDs. Note that the capital Pi symbol in the PSD of the message symbolizes the rectangle function so Sm(f) = 8rect(f/8000) The Attempt at a Solution From my understanding, channel noise is not filtered at this...
  7. K

    How to determine minimum required force in an applied context

    Hello, I am a graduate student in psychology and I've encountered an issue in one of my studies that is outside of my expertise, but hopefully within one of yours. Here's my predicament: I recently conducted a study with infant participants that investigated infants' ability to...
  8. M

    Find global minimum of f(x1,x2, xn), with many local minima

    Hi I have some function f = f(x1,x2,...xn) over some domain [0,1]^n, and I'd like to find the global minimum. The function is *highly* non-linear and takes about 1 second to evaluate. I know it's positive because it's the sum of squares of about 1,000,000 arguments, each of which pretty much...
  9. K

    Maths question on using the minimum amount of DVD disc

    this is a practical question I have 14 files to burn on a single layer DVD5 disc in which each of them has a size approximately 4.37GB Those 14 files are of the size (in GB) 2.25 2.25 1.15 3.05 1.16 2.40 0.65 2.05 1.36 1.97 1.11 1.14 2.48 2.65 All values are in GB If...
  10. I

    Minimum force to overcome static friction

    Homework Statement http://postimage.org/image/530mgjivr/ How come the solution states: (20)(9.8)(0.7cos30 - sin 30) isn't sin30 going in the positive direction? shouldn't the solution be Sin30 - .7cos30? Also, when solving these types of problems should I leave the mg part outside of the...
  11. U

    Triangles, what is the minimum amount of data required to

    With triangles, what is the least amount of data I need before I can start working out other data about the triangle such as angles and lengths of sides ect? I think it is at least 1 length and 2 angles or 2 lengths and 1 angle? What about triangles other than right angle triangles?
  12. S

    Why is the normal force included in this plane's minimum radius problem?

    Hi all, Homework Statement My problem is exactly the same as the one here: https://www.physicsforums.com/showthread.php?p=2377784 In the solution that Vykan12 provides (which results in the correct answer according to the textbook), however, there is a normal force included in the...
  13. B

    Tissue Engineering Problem - Find minimum starting cell population

    Homework Statement You want to create a tissue engineered blood vessel using smooth muscle cells. Your plan is to isolate smooth muscle cells from discarded human tissue obtained from heart surgery and grow them for a long time to create cells own ECM. Smooth muscle cells have enormous...
  14. Sneakatone

    What Factors Determine the Trajectory of a Baseball?

    in a baseball game the batter hits the ball and launches it upward at n angle of 52.0 degrees...\ I used V_x=Vocos(/theta)+a_xt to solve for V_x and got 31.6m/s which is wrong. what should I do.
  15. R

    Minimum coefficient of friction to keep cars from sliding off the road

    A banked circular highway curve is designed for traffic moving at 61 km/h. The radius of the curve is 201 m. Traffic is moving along the highway at 44 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to take the turn without sliding off...
  16. Q

    Using entry level physics to calculate minimum velocity required.

    Homework Statement A person is trying to jump over the pit in a car. I need to find what is the minimum speed required to make it over. This speed is calculated not from the start of the ramp, but from the take off. Drawing of all the elements Please excuse my ugly drawing :P. Homework...
  17. Saitama

    Finding time period and minimum length of threads

    Homework Statement (see attachment) An iron rod of length L is hung at a common point with threads of length \ell which are attached to the two ends of the rod. The rod is displaced a bit in the plane of the threads. What is the length of the threads if the period of the swinging of the rod...
  18. F

    Conservation of energy minimum speed

    Homework Statement Gus is at end of rope. He needs to reach roof. His friend fires cannon ball horizontally hitting Gus and get stuck in belt. Find minimum speed of cannon ball for Gus to reach roof. 50m is rope. 99kg is Gus. 1kg is ball. 45° angle in diagram Homework Equations...
  19. C

    MHB Is There a Mathematical Basis for an Infinite Number of Twin Primes?

    I’ve encountered a relationship that, if true, could show that there are an infinite number of twin primes. It involves the minimum number of twin primes to be found between 3 and any higher odd number squared. However, I don’t know if this relationship holds true in all cases. We start with...
  20. K

    Testing Harvard minimum accepted SAT/ACT scores

    It is a well-known fact that Harvard university (arguably the most prestigious college in the United States) only accepts the very top highest-performing high school graduates in the country. What is Harvard's minimum accepted high school GPA, number of AP credits, and SAT/ACT scores? I...
  21. micromass

    Intro Physics The Theoretical Minimum by Susskind and Hrabovsky

    Author: Leonard Susskind, George Hrabovsky Title: The Theoretical Minimum: What You Need to Know to Start Doing Physics Amazon Link: https://www.amazon.com/dp/046502811X/?tag=pfamazon01-20 Prerequisities: Contents:
  22. J

    The Theoretical Minimum, Released today, January 29th 2013

    Leonard Susskind's the Theoretical Minimum was released today to go along with his Stanford Courseware lectures. Has anyone gotten there hands on a copy yet? I am very excited for this publication because I am very pro-self-education (if you could call it that). I am debating whether to order a...
  23. A

    How can I be sure that the action has a minimum?

    When you write an action and then you calculate its minima, how can you be sure that they are minima and not maxima? Thanks
  24. T

    Finding Min Value: 2x^2-36x+175

    Right so, I actually know the math, my problem is that I think, I am getting confused with wording. I will explain better where I show you where my problem lies. Question: Show that 2x^2-36x+175 mat be written in a(x-b)+c where the values a,b,c are to be found. state, with reason, the...
  25. C

    Deriving equation for minimum height in projectile motion with two give me's

    deriving equation for minimum height in projectile motion with two give me's :) Homework Statement A ball is launched at a 45 degree angle and lands 152.4 m away. What is the maximum height the ball will reach during its flight. I Know the answer, what I need is to find a way to derive an...
  26. A

    Static Friction and minimum force

    Homework Statement The coefficient of static friction between the box (6.75 kg) and the ramp (30 degree incline) is 0.500. What is the magnitude of the minimum force, F, that must be applied to the box perpendicularly to the ramp to prevent the box from sliding? Homework Equations...
  27. I

    Minimum table size to contain combinations 000 to 999 in adjacent squares

    Consider an m x n table containing single digits 0 to 9. So each cell contain the digits 0 to 9. My goal is to make sure that all combinations from 000 to 999 can be found in the table in adjacent cells. A cell is adjacent to the cells around it (i.e. above, below, to the left, to the right...
  28. T

    What is the Minimum Velocity to Throw a Ball Over a Pitched Roof?

    Homework Statement What is the minimum velocity required to throw a ball over a house with a pitched roof ( See attachment for the figure) You can choose the throwing point as needed The Attempt at a Solution (Choose throwing point standing near a and facing left) Assuming b is...
  29. D

    Minimum amount of power need to charge a li-ion battery

    What is the minimum amount of power needed to charge a small lithium ion battery of 3.4 V and 2100 mAh?
  30. A

    Minimum of two iid exponential distributions

    Let X_1, X_2 \sim Exp(\mu) and Y = min(X_1, X_2) then find E[Y]. My attempt is as follows: $$E[Y] = E[Y/X_1<X_2]P(X_1<X_2) + E[Y/X_1>X_2]P(X_1>X_2) \\ = \frac{1}{2} (E[X_1/X_1<X_2] + E[X_2/X_1>X_2] ) \\ = \frac{1}{2} (1/\mu + 1/\mu) \\ = 1/\mu$$ But, we know that minimum of two exponentially...
  31. N

    Minimum of Ʃ[itex]^{n}_{i=1}[/itex][itex]\left|x_{i}-z\right|[/itex]

    Homework Statement Hello, I have a question what is What is the minimum of Ʃ^{n}_{i=1}\left|x_{i}-z\right| x_{i} are constants Homework Equations Not Much The Attempt at a Solution I split the sum to 3 sums Ʃ^{}_{x_{i}>z}(x_{i}-z) +...
  32. B

    MHB Expected value of minimum Hamming distance

    The Hamming distance(HD) between two strings of equal length is the number of characters that differ between the two strings at the same position, for example the HD between "gold" and "wolf" is 2; the MHD is between N strings and is equal to the minimum of HD's among all possible combinations...
  33. M

    Mohrs Circle, Von Mises and Minimum Yield Strength Help

    Hi Wasn't sure where to post this, hope it's ok in here! I've gotten myself very confused as to how to find the minimum yield strength for an element. I have used Mohrs circle to find sigma1 and sigma2, then plugged that into the von mises equation to find sigma-von = 636.8MPa. The...
  34. N

    Minimum possible kinetic energy in an interaction

    Homework Statement Object A of mass 10 kg moving at 10 m/s [E] interacts with (but does not touch) Object B of mass 8 kg moving at 12 m/s [N]. What is the minimum possible kinetic energy of the system after the collision? Homework Equations M1V1o + M2V2o = M1V1f + M2V2f KE = (.5)(m)(v2)...
  35. L

    Centripetal Force Minimum Period Question

    Homework Statement A boy ties a 3.00kg rock to a 0.70 m string and begins spinning it around in a horizontal circle at a constant speed. If the string will break if the tension is greater than 80.0 N, what is the minimum period for the rock to spinning in a circle. How do i solve this...
  36. P

    Finding the minimum perimeter.

    Homework Statement I'm stuck on part b) of the question, but this includes the whole thing: A farmer wants to make a rectangular paddock with an area of 4000m^2. However, fencing costs are high and she wants the paddock to have a minimum perimeter. a) Show that the perimeter is given...
  37. D

    X^2=1x=1"Exploring the Minimum of f(x)=1/x

    Homework Statement Explain why f(x) = 1/x must have a minimum on [1,2] but not on [-1,2].Homework Equations The Attempt at a Solution I don't know what to do. First, I took the x values from the given points and plugged them back into the function but the results do not coincide with the y...
  38. phosgene

    Minimum energy of electron bound in nucleus

    Homework Statement An electron is confined to a nucleus of radius 4 femtometres. Estimate its minimum energy. Homework Equations ΔxΔp_x=h/4\pi E^2=p^2c^2 + m^2c^4 As the electron's rest energy will be much less than it's kinetic energy, E=pc The Attempt at a Solution So I...
  39. C

    Ultimate Energy: Exploring the Limits of Mass and Speed in the Universe

    New to this and was thinking about extreme cases to help me get my head around how this all works...need help.. Imagine we have an object with mass moving along. Not that this is possible, but what if all other mass in universe was somehow utilized in some nuclear reaction so ALL energy in...
  40. T

    Minimum Uncertainty in Electron Position: Rectangular Wave in k-space

    Homework Statement In the case of an electron wave packet, the function A(k) has a rectangular shape, i.e. it is equal to A0 if k0-a<k<k0+a, and zero everywhere else. (a) Find the minimal uncertainty of electron position. (b) Find the electron wavefunction. Homework Equations ΔxΔp=h/4pi...
  41. L

    Calculate the density at which the available thrust is equal to the minimum drag

    Calculate the density at which the available thrust of a jet propelled aeroplane is equal to the minimum drag for the full fuel load case. Use the simplest assumption for the variation of engine thrust with density. Wing area, S = 29.5 Weight, W = 88000 CD,0 = 0.02 k = 0.044 Max thrust...
  42. P

    Minimum distance between skew vectors

    Hi, Satellites A and B are traced at a particular moment by a space base located at the origin, with respect to which they move at constant velocities: A0 = (a1,0,a3); B0 = (0,b2,b3) V of satellite A = (Va,0,0); V of satellite B = (Vb,Vb,0) Is the minimum distance between the satellites...
  43. S

    Finding the minimum speed of a loop the loop and finding the height of the hill

    Homework Statement I have a hill with a roller coaster cart on it and it goes down and around a loop-the-loop the radius of the loop is 10m Diameter=20m What is the minimum speed the cart needs to go to keep it on the track? There is no friction, what is the height of the hill...
  44. P

    Minimum distance between two satellites

    A space base has traced stallites A and B at a particular moment at: A0 = (a1,0,a3) B0 = (0,b2,b3) whereas the base itself is located at the origin (0,0,0) and the satellites move at constant velocities with respect to the base: Va = (Va,0,0) Vb = (Vb,Vb,0) The minimum distance...
  45. T

    Minimum angle to prevent sliding (Friction & Forces)

    Homework Statement Suppose a truck is going up a hill and the maximum acceleration while braking is 9 m/s2. Find the minimum angle of the hill such that the driver can brake at maximum rate without the refrigerator on back slipping. (coefficient of static friction between truck and...
  46. C

    Sled being pulled by two people. Minimum tension and acceleration.

    Homework Statement A heavy sled is being pulled by two people as shown in the figure. The coefficient of static friction between the sled and the ground is μs = 0.603, and the kinetic friction coefficient is μk = 0.395. The combined mass of the sled and its load is m = 291 kg. The ropes are...
  47. S

    Prove that for any graph G, the connectivity is less that the minimum degree

    prove that for any graph G, kappa (G) ≤delta (G).
  48. Z

    Minimum Kinetic Energy in a Deuteron: Which Formula Is Correct?

    Homework Statement In a deuteron, a proton and a neutron are very weakly bound by the strong nuclear force with an average distance between the particles of about 5fm. Due to the uncertainty principle, the particles have a minimum momentum and hence a minimum kinetic energy of ...? Which...
  49. V

    Maximum and minimum velocity of a moving object on a bank angle

    Homework Statement A curve of radius 300 m is banked at an angle of 10°. A) At what speed is no friction required? B) If the coefficient of friction is 0.8, what are the maximum and minimum speeds at which the curve can be traveled?Homework Equations F=m*a ac=mv2/r The Attempt at a Solution...
  50. D

    Minimum speed required for charge collision

    Homework Statement A charge of 3.0 μC is distributed uniformly throughout the volume of plastic sphere with a radius of 10.0 cm. An identical plastic sphere with charge 3.0 μC is shot directly at the center of the first sphere, from very far away. The mass of each sphere is 5.0 X 10^-5...
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