Minimum Definition and 1000 Threads

Hi, I am not sure how to solve the following high school algebra problem. As shown in the attached file, I have plotted the first three equations, but I don't know what to do with the fourth equation. Find the minimum and maximum values of the objective quantity. 2X + Y ≤ -8 3X - 2Y...

Homework Statement Let f(x) be a non-constant twice differentiable function defined on R such that f(x)=f(1-x) and f'(1/4) =0 then what is the minimum number of real roots of the equation (f"(x))^2+f'(x)f'''(x)=0. The Attempt at a Solution f'(x)=-f'(1-x) f"(x)=f"(1-x)...

I'm working on a project where I know that force will be applied by a bolt pulled through a hole in the center of an aluminum plate for load testing purposes (2200 lbs, actual worst case max force around 1500 with a 1.5 times safety factor), the dimensions (27"x6.25"x?), and the material (5052...

Homework Statement "Figure 1 shows two wedge blocks A and B, weighing 1000 N and 50 N, respectively, in contact. The coefficient of friction between all contacting surfaces is 0.1 . What would be the smallest value of P required to push the block A upwards? What would be its value if there...

Homework Statement The floor on a dance hall can take a pressure of 3.5 MPa before getting damaged. A lady of mass 60kg wears high heeled shoes. What is the smallest area of the sole of a heel she could wear such that it won't permanently damage the floor? Homework Equations Area =...

Homework Statement Suppose that f is a continuous function on (a,b) and lim_{x \rightarrow a^{+}} f(x) = lim_{x \rightarrow b^{-}} f(x) = \infty. prove that f has a minimum on all of (a,b) The Attempt at a Solution I have not tried an actual attempt yet. The only think I can...

Homework Statement A hanging 2.00-kg (19.6N) block begins to accelerate a 4.28-kg (41.94N) block on a horizontal surface. But a rope connected to the wall at 26.9 degrees brings the block to an equilibrium position. The coefficient of friction between the surface and the 4.28-kg (41.94N) block...

Hi MHB, I've found an interesting and difficult (at least for me) problem which asks us to find the minimum value of $xy$ and no matter how serious that I tried, I couldn't get myself out of the misery of finding what the question wanted. Could anyone help? Problem: Find the minimum...

Homework Statement A 76-kg petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg.Determine the magnitude of the minimum acceleration at which the thief can descend using the rope. Homework...

Homework Statement A boy throws a rock at speed v_0 at angle α from a balcony of height h. When the ball hits the ground, its velocity makes an angle θ with the ground. What is the minimum value of θ in terms of h and v_0 Homework Equations basic kinematics equations. The...

Hey everyone! I am on a quest to understand the world in which we live in better. In doing so I'm making a stop at Physics. I was suggested the book "A Theoretical Minimum - What you Need to Know to Start Physics". I am in love with this book and cannot put it down. At the moment I am...

Consider the isosceles triangle circumscribed about the ellipse: Find the altitude of the triangle when its area is minimized.

I'm currently self teaching myself physics and I have never seen physics before this. The book that I'm using is The Theoretical Minimum - What You Need to Know to Start Doing Physics by Leonard Susskind. I plan to be finished with the book by mid next week and my question is what's a good...

Determine the minimum value of $$\frac{\sec^4 a}{\tan^2 b}+\frac{\sec^4 b}{\tan^2 a}$$ over all $a,b \ne \frac{k \pi}{2}$ where $k$ is in $Z$.

If $$\log_4(x+2y)+\log_4(x-2y)=1$$, find the minimum value of $|x|-|y|$.

Homework Statement Hi guys, really stuck on this one. A 1000N black is to be lifted using a chain sling (as shown). If the tension in the chain sling is not to exceed 1300N, find the shortest sling ABC that can be used. A is the most left point, B is the most right point and C is the top...

Homework Statement A periscope is made of two good mirrors. Find the ratio of the minimum widths of the mirrors if the distance between them is L and the distance from the lower mirror to the eye of the observer is l.The objects viewed through the periscope are at a great distance from it...

Homework Statement A motorbike starts from rest at time t=0 and begins to accelerate around a circular track of radius 10m. Eventually, at time t=t1 the motorbike reaches the maximum velocity possible without slipping off the track. What's the minimum length in meters the motorbike must travel...

How do you prove that for a given volume, sphere has the minimum surface area?

Problem: The sum of two real numbers is $$1$$. What is the minimum value of the sum of the squares of the two numbers? I have already managed to solve the problem algebraically (by substitution and completing-the-square we arrive at a minimum value of $$0.5$$), but what I am interested in is a...

Can someone help me as a am racking my brain. I have been given this question; Two oil pipes with circular cross-sections are subject to the constraint that the sum of their diameters is 1m. By using careful reasoning find the diameters that give the maximum and minimum possible combined...

Homework Statement Estimate the minimum proton lifetime from the fact that you haven't yet died from internal radiation. Use the following conditions: 1.) At a dosis of Dmax = 2 Greys per year (Jkg-1 yr-1) you would already be dead. 2.) The human body is made mostly of water. 3.) The total...

Homework Statement You place a 2kg box against the side of a cart. Nothing is used to stick the box to the cart which accelerates to the right. The coefficient of static friction is 0.6. Find the minimum acceleration of the cart needed so that the box does not fall Homework Equations...

Homework Statement Let x, y, z be positive real numbers such that ##x+y+z=1##. Determine the minimum value of \frac{1}{x}+\frac{4}{y}+\frac{9}{z} Homework Equations Cauchy-Schwarz inequality maybe? The Attempt at a Solution Applying the Cauchy Schwarz inequality...

Homework Statement There are 2 small metal balls of radius r1 and r2 and are kept at very large distance , what should be ratio of charges on them for electrostatic energy to be minimum Homework Equations E=Q^2/(8πϵR) Self Energy The Attempt at a Solution In this problem, electric...

I am not able to understand how to go about this problem: Find the minimum mean square estimator for the scalar parameter w based on the scalar observation z = ln w + n where f(w) =1 if 0<=w<=1; 0 else: and f(n) =e^-n if n>= 0; 0 else I did f(z/w) = (f(n))...

Here is the question: Here is a link to the question: The position function of a particle is given by r(t)=<−3t^2, −2t, t^2+4t>? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Question: Suppose I want to measure the polarity of a photon. What is the minimum amount of energy I need to invest? What are the needed forms? (Examples might include rest mass for storage devices, energy in interacting particles, etc.) I'm looking for an ideal device. Background: I have a...

Hi all, I was (superficially) reading about the information loss paradox. Of what i understood it's based on the complete evaporation of the black hole via hawking radiation, so in some sense all the energy of a black hole will eventually become radiation. The following question immediately...

Homework Statement A lens (##\mu##=1.5) is coated with a thin film of refractive index 1.2 in order to reduce the reflection from the surface at ##\lambda=480 nm##. Find the minimum thickness of the film which will minimize the intensity of reflected. [Assume near normal incidence]Homework...

Homework Statement White light is incident normally on a thin soap film (n = 1.33) suspended in air. 1. What is the minimum thickness of the soap film that will constructively reflect light of wavelength 477 nm? 2. What is the next minimum thickness of the soap film that will...

Q: Find a fraction between $$\frac {96}{35}$$ and $$\frac {97}{36}$$ that has the smallest possible denominator. My thoughts: Let's assume this fraction is of the form $$\frac pq$$ where $$\gcd(p,q) = 1$$. Since $$\frac{96}{35} > \frac{97}{36}$$, we can write $$\frac{97}{36} < \frac {p}{q} <...

I don't have a specific question, but was wondering how I would go about solving something like this: How would you calculate the minimum velocity that a bike, for example, would require to become airbourne off a circular ramp, if you are given say the radius of the ramp. Would you need more...

How can i calculate how many months it would take me to pay off a debt if I only make the minimum payment? let say I ow 5000 my interest rate is 6.4% my payment rate is 2% so If i calculate my minimum payment I know it be 100 more or less but I i just pay that minimum how many month it would...

Homework Statement A sodium atom emits a photon with wavelength 818 nm shortly after being struck by an electron. What minimum speed did the electron have before the collision? Homework Equations E_{particle}\geq\Delta E_{atom} The Attempt at a Solution For the minimum energy...

A polymer coating has a n=1.30 and a base of n=1.50. What is the minimum thickness of the coating to reflect 500 nm least strongly?

Homework Statement A polymer coating has a n=1.30 and a base of n=1.50. What is the minimum thickness of the coating to reflect 500 nm least strongly? Homework Equations The Attempt at a Solution

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

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?

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...

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...

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...

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...

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...

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?

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...

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...

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.

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...

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...