Inequalities Definition and 329 Threads

Homework Statement The Attempt at a Solution So when I started this question, I knew that 2r +3 > 0 in order for this whole thing to work so r > -3/2, and I know that if the middle term has to be more than 0, than only one more of the others is going to be negative, for the first...

Homework Statement Identify the solution set of the inequality. Homework Equations 5x + 1 / x- 1 ≥ 7 The Attempt at a Solution I multiplied both sides by x - 1 which gave me 5x+1 ≥ 7x - 7 Then I combined like terms together which gave me 8 ≥ 2x I divided both sides by 2 which gave...

Hello, I was looking at Riley's solution manual for this specific problem. Along the way, he ended up with a quadratic inequality: If you looked at the image, he said it is given that λ is real, but he asserted that λ has no real roots because of the inequality. Doesn't that mean λ is...

the random value X has the inequality , -10<=X<=10 and E(X)=2, what is the minimum upper bound of the probability P(X>=5) ? my first thought was to find this P(X>=t)<=E(X)/t which is 2/5 from Markov but its not correct, any ideas?

Hello, could somebody please explain to me how 1-exp(-μt) ≤ μt and similarly (1-exp(-μt))exp(-λt) ≥ μt-μ2t2\2)(1-λt) Thanks a lot

Homework Statement x y and z are real numbers solve in lR (1+4x^2)y=4z^2 (1+4y^2)z=4x^2 (1+4z^2)x=4y^22. The attempt at a solution (1+4x^2)y(1+4y^2)z(1+4z^2)x=64x^2y^2z^2(x and y and z =/=0) (\frac{1}{4}+x^2)(\frac{1}{4}+y^2)(\frac{1}{4}+z^2)=xyz now i can tell from this that...

Homework Statement Solve each inequality without graphing the corresponding function. State the solution algebraically and graph on a number line: x/x2-9≤0 so i factor out the denominator and get (x+3)(x-3) the root here is zero, but for some reason in the chart (for rational/reciprocal...

Given: 1)it is not true that : 2>0 and 2+3 =7 2)if it is not true that 2>0 then 2 is less or equal to zero 3)if 2+3 =7 ,then 3+3 =8 4) but 3+3 is not equal to 8 Then prove: 2 is less or equal to zero

I need help with the second part, I've managed to get through all of the part (i), but I have no idea where to really start with part (ii), any hints to start me off and I'll keep posting how I'm doing. thanks

Homework Statement Hi PF! I am studying from a book - A first course in probability by Sheldon Ross, and I have came across this section whereby the are trying to prove the upper bound (equations 4.1 and 4.3) and lower bound (equation 4.2) of the inclusion-exclusion principle from basic...

So could you please help me demonstrate some inequalities? Please! They want to prove them without calculating the integral. 1/3<=integral from 4 to 7 (x−3)/(x+5)dx<=1Thanks!

I want to show that if f(x) > g(x) \forall x \in (-\infty, \infty) and \displaystyle\lim_{x\to\infty}g(x)=\infty , then \displaystyle \lim_{x\to\infty}f(x)=\infty . This result is true, correct? If so, what theorem should I use or reference to show this result? I wasn't sure if...

Homework Statement Solve the following inequalities. Do each one algebraically then check your answers using your calculator's ability (Casio Classspad 330) to solve the inequalities and/or by viewing a suitable graph on your calculator. Homework Equations SEE IMAGE The Attempt at a...

When I was working on a rather difficult real-life math problem, I nearly found the solution. What I came up with was two inequalities: ##X≥\frac{2b-2}{2a+1}-1## and ##Y≥\frac{2b}{2a+1}-2## and the fact that ##X>Y##. However, ##X## must be an even integer and ##Y## must be an odd integer. Is...

Please vote and if possible state the reasons for holding your belief. As a review here are the two major views with quotes by leading physicists in quantum foundations: 1. Observed violations of Bell's inequalities implies that nature is non-local: 2. Observed violations of Bell's...

Hi, I used to do all this type of inequalities but I have not practice this for almost a year and I have totally forgotten and didn't know why did the sign change. For example: If it's 3x ≤ 9 The answer: x ≥ 3 Is this right? I have actually forgotten in what circumstances we are suppose...

Homework Statement Hi, i have a question regarding inequalities: I have to solve this inequality: 4x^4 +(√2y)^4 ≤64 My first first quess was to cancel out the square root (√2y)^2*(√2y)^2 4x^4 + 4y^2 ≤64 Then take the square root on both sides (here my question is: do you take one...

Hello guys, I am trying hard to understand the reason of the violation, and i hope you give me some help. Here is my understanding so far: Bell's inequalities are based on the measurement of non-commuting quantum observables, e.g. the measurement of the spin in x and z direction. This, to...

Homework Statement (x-2)/(x+3) less than (x+1)/(x) The Attempt at a Solution I broke it up into cases. When x+3 less than 0 and x less than 0 and then when both are positive, when one is positive and the other is negative and then the other way around. I'm not sure if that's the right way...

This might sound an odd/inappropriate request, but could someone post some inequalities that can be proven using calculus?

Question 1: A hospital dietitian wishes to prepare a corn-bean vegetable dish which will provide at least 40 grams of carbs, and cost no more than \$0.36 per serving. 28 grams of corn provide 8 grams of carbs and cost \$.04. 30 grams of beans provide 5 grams of carbs and cost \$.03. For taste...

Hello, I'm having some trouble with a Queuing Networks question, not the networks but solving a system of inqualities based on the network. Homework Statement I have to find the value of α that gives maximum γ, and then use the value. The system is defined by 5\gamma< 1 20\gamma \alpha<1...

Homework Statement (5 + √24)x + (5 - √24)x > 98 Homework Equations inequalities exponential The Attempt at a Solution I don't know how to start...trying to put log to both sides could not take me anywhere because the LHS can't be simplified...

Can anyone help me confirm if I've solved this correctly? Many thanks. Homework Statement Prove that \sqrt{ab}>\frac{2ab}{a+b} if a & b are positive & unequal. Homework Equations The Attempt at a Solution if (\sqrt{ab})^2>(\frac{2ab}{a+b})^2 if ab>\frac{4a^2b^2}{(a+b)^2} if...

find the set of values of x for which 2x > \dfrac{3x + 1}{x+1} done this and got -1<x<-0.5, x > 1 b) find the set of inequalities where 2sint > \dfrac{3sint + 1}{sint + 1} where -\pi < t < \pi first I found the set values of t suitable in the range for -1,-0.5,1 which I got to be as...

I am looking at questions like 1/(x+4)>x-4 or 1/(x+7)>x-7 I have no idea how to solve them, I have simplified to (-x^2+50) /(7+x) however I don't think it is correct and I don't know what do do from there.

My final answer matches that of the textbook, but do I need to change the < to > at any point as I solve this? I ask because, if I assume x is 1 (until I solve for x), then the question statement and parts of the solution are made untrue. Homework Statement Solve the following for x...

Homework Statement The final answer I have of (a+b)(a-b) does not appear to fit the textbook's required "results of inequalities which hold true for all real no.s", i.e. either: 1. (a)^2 or (a-b)^2 or 2. -(a+b)^2. Can anyone confirm if I have solved this correctly, in line with the conditions...

I am not getting anywhere with this problem. Prove the Schwarz's and the triangle inequalities for infinite sequences: If $$ \sum_{n = -\infty}^{\infty}|a_n|^2 < \infty\quad\text{and}\quad \sum_{n = -\infty}^{\infty}|b_n|^2 < \infty $$ then $\displaystyle\left(\sum_{n = -\infty}^{\infty}|a_n +...

Homework Statement Hi, there are several methods to solve an quadratic inequality. 1:by graph 2:if (x-a)(x-b) > 0,(x-a) > 0 and (x-b) > 0 or (x-a) < 0 and (x-b) < 0... 3.Using test value method i.e.Find a and b in the expanded form of (x-a)(x-b) a and b are the critical...

Hi, I am trying to solve x^2 - 10x + 26 < 0 Here are my steps: 1.Find the roots of x by using quadratic formula: x = [10 ± √(100-104)]/2 = 5±i 2.Rewrite x^2 - 10x + 26 into [x-(5+i)][x-(5-i)] 3.Now we have: [x-(5+i)][x-(5-i)]<0 x-(5+i) < 0 and x-(5-i) > 0 or x-(5+i) > 0...

I was hoping someone could give a little more insight, or perhaps enlighten me to a better way of approaching solving these seemingly simple Algebra 2 inequalities. I did some google searching but I was not able to find the answers I seek. The problem came up when a friend of mine had an...

Homework Statement The product of two numbers is less than 340. One of the numbers is 3 less than the other. What are the possible values of the larger number?Homework Equations The Attempt at a Solution Hope this is right... xy < 340 then, because y=x-3 x(x-3) < 340 x^2 -3x -340 < 0...

Homework Statement Question 42 in particular. Homework Equations No idea. The Attempt at a Solution The graph depicts an inequality of sorts, like y >= x and y >= -x as well as y <= x and y <= -x. Beyond these basic deductions (which are probably wrong also), I've not a scintilla of clue...

I have been stuck on two question for sometime, and would appreciate some guidance to where I am going wrong. Here are the two questions I seem to have trouble understanding. 1. 2x+5 < x-1/4 I have had numerous attempts at this equation and seem to get the answer wrong each time. The book...

Hello, I am stuck on something so simple. The problem is i have a great difficulty with the geometric interpretation of things.So if I have a system of linear equations in three unknowns, like for example this: -x - 2y + z = 0 x - 3y - 2z = 0this is just a simple system of homogeneous...

So I was brainstorming:bugeye: trying to find what I did wrong in this chemistry problem: https://www.physicsforums.com/showthread.php?t=627731 (simple algebra no chemistry knowledge required) And I noticed something peculiar about the process of solving inequalities, let me sum up in a phrase...

Homework Statement Prove: If a2+b2=1, and c2+d2=1, then ac+bd ≤1 Homework Equations Maybe triangle inequalities theorem. The Attempt at a Solution

Can we explain the meaning of the modulus(absolute value) with these equations? |x| > a =>x > a or x < -a(if a \in R+ and x \in R if a \in R- |x|<a => -a < x < a if a \in R+ and no solution if a \in R-\cup{0} If yes, then examples please?(for instances in x and a) Blindly apply these...

Homework Statement Prove the following inequalities for all numbers x, y. |x+y| ≥ |x|-|y| [Hint: Write , and apply , together with the fact that Homework Equations These were given as hints in my textbook: x=x+y-y |a+b| ≤ |a| + |b| |-y|=|y| The Attempt at a Solution...

Well suppose for an example of an inequality, |x-1|-|x|+|2x+3| > 2x+4 Well in one of its solutions we were told to apply the method of intervals, rather than taking say what; like 8 combination of signs. For everyone of its intervals(say -3/2 \leqx <0) we are said that 2x+3 \geq 0, x<0...

How do we treat expressions under a sqaure root in inequalities ? Like for ex. x+4< Math.sqrt(-x^2-8x-12) (sorry, using m.physicsforums, so i don't know what to use for a root, so JAVA :p) I request the use of this very example.

Homework Statement Sketch all complex numbers z which satisfy the given condition: |z-i|\geq|z-1| Homework Equations z=a+bi |z|=\sqrt{a^{2}-b^{2}} The Attempt at a Solution First I find the boundary between the regions where the inequality holds and does not hold by...

I know the following |x|-|y| \leq |x+y| \leq |x| + |y| where does |x-y| fit in the above equation?

Homework Statement I'm just having a problem with a step that's part of a larger problem. Specifically, if I have: \sqrt{2}i\leq\sqrt{2} I'm not sure what this actually means. If I ignore the i, each side is the same distance from the origin if I imagine both points on a graph...

I am studying unit on limits and one of the example given to prove and established limit simply doesn't make sense. in the given solution of the example righhand side is simply not making sense to me - please see attached document and anyone can throw some light on this will be great so i can...

It is commonly believed that Bell's inequalities are a theoretical derivation of a condition that must be satisfied by locally causal theories. Therefore, it is often concluded that violation of these inequalities by experiments provides very strong evidence (if not conclusive proof, the only...

Homework Statement [abs(x)]/[abs(x+2)]<2 Homework Equations The Attempt at a Solution case 1: [abs(x)]/[abs(x+2)]<2 case 2: [abs(x)]<2[abs(x+2)] is this right so far? if so, why is there two cases and what do i do next?

Homework Statement Solve x/(x-2) > 2 by first rewriting it in the form P(x)/Q(x)>0 Homework Equations The Attempt at a Solution well... i got up to x/(x - 2) > 2 x/(x - 2) - 2 > 0 x/(x - 2) - 2(x - 2)/(x - 2) > 0 x/(x - 2) - (2x - 4)/(x - 2) > 0 (x - 2x + 4)/(x - 2) > 0 (-x...

The Rushbrooke inequality: H=0, T\rightarrow T_c^- C_H \geq \frac{T\{(\frac{\partial M}{\partial T})_H\}^2}{\chi_T} \epsilon=\frac{T-T_c}{T_c} C_H \sim (-\epsilon)^{-\alpha'} \chi_T \sim (-\epsilon)^{-\gamma'} M \sim (-\epsilon)^{\beta} (\frac{\partial M}{\partial T})_H \sim...