Absolute Definition and 1000 Threads

Solve |x^2-5|=4|x|. I tried to rewrite it as: (sqrt(x^2-5))^2=4*(sqrt(x))^2 Is this the right way to solve the equation?

We all know that there four fundamental forces in nature, viz. The gravitational force The electromagnetic force The strong nuclear force The weak nuclear force Now also we know that temperature of any system is the average kinetic energy possessed by the particles of the system Now...

Let R be a sigma algebra and let $f$ be a real value function on R such that for a sequence ($A_{n}$) of disjoint members of R, we have that the sum of $f$($A_{n}$) over all n is equal to the image of the countable union under $f$. Prove that the sum of $f$($A_{n}$) is in fact absolutely...

Homework Statement A container is filled to a depth of 20.0 cm with water. On top of the water floats a 29.0-cm-thick layer of oil with specific gravity 0.800. What is the absolute pressure at the bottom of the container? (Answer in Pa) Homework Equations P= ρgh+ P(atmospheric) The...

Suppose I have a variable separable ODE, e.g., \frac{dy}{dx} = 3y. We all know that the solution is y=Ae^{3x} where A is a constant. My question is as follows. To actually find this solution we rearrange the equation and integrate to get \int \frac{dy}{y} = 3 \int dx, which gives \ln...

Homework Statement Find absolute extrema of the function over the region R. f(x,y) = 3x2 +2y2 -4y, R: the region in the xy plane bounded by the graphs of y=x^2 and y=4Homework Equations second partial derivative test d=fxxfyy-fxy2The Attempt at a Solution This is my practice test for the final...

∫tan(x) dx = -ln lcos(x)l + C = f(x) So is f'(x) = -sin(x)/lcos(x)l ? When taking the derivative, do we only consider f'(x) to only exist on the intervals where cos(x) > 0 instead?

Homework Statement Find the CDF of f(x) = |\frac{x}{4}| if -2<x<2 \\ 0 otherwise Homework Equations The Attempt at a Solution I have to integrate the pdf and to do so, I have to split it into two parts \int_{-x}^{0}\frac{-t}{4}dt + \int_{0}{x}\frac{t}{4}dt integrating I get \frac{x^2}{8} +...

Given [a,b] a bounded interval, and f \in L^{p} ([a,b]) 1 < p < \infty, we define: F(x) = \displaystyle \int_{a}^{x} f(t) dt, x \in [a,b] Prove that exists K \in R such that for every partition: a_{0} = x_{0} < x_{1} < ... < x_{n} = b : \displaystyle \sum_{i=0}^{n-1} \frac{| F(x_{i+1}) -...

Homework Statement Given the function f(x) = (abs(x))*x +6, find f^-1(x) Homework Equations The Attempt at a Solution for x≥ 0, f(x) = x^2 + 6 y=x^2 +6 x = √(y-6) for y≥6 → f^-1(x) = √(x-6) for x≥6 for x< 0, f(x) = -x^2 + 6 y= -x^2 +6 x = √(6-y) for y<6 → f^-1(x) = √(6-x) for x<6 But...

Here's a claim: Assume that a function f:[a,b]\to\mathbb{R} is differentiable at all points in its domain. Then the inequality |f(b) - f(a)| \leq \int\limits_{[a,b]}|f'(x)|dm(x) holds. The integral is the Lebesgue integral. Looks simple, but I don't know if this is true. There exists...

4)Find the absolute minimum and absolute maximum values of f on the given interval. a) f(x) = 2cos (x) + sin (2x) on [0, π/2] b) f(x) = x^2 +16/x on [1, 3] Thanks again in advance!

Homework Statement Problem 2: Find the absolute extreme values of f(x) on the interval (1, infinity). Homework Equations The Attempt at a Solution It seems as if this is an indiscretion by the teacher. Absolute extrema don't occur on open intervals except in the case of (-∞,∞) such as in...

Solve 2x - |x+1| < 4.

Homework Statement Y=abs -4(x+3) +1 Note: the 1 is outside the absolute value Homework Equations Switch y and x The Attempt at a Solution So you subtract the 1 to bring it to the other side After that do I put: x-1= -4(y+3) And x-1= 4(y+3) And solve for y? Am I doing...

Homework Statement abs(x+y+z)≤abs(x)+abs(y)+abs(z) indicate when this equality holds and prove this statement Homework Equations Triangle inequality? The Attempt at a Solution I have nothing :/

When I learned about derivatives I was taught to put the absolute value sign around the argument for ln and log. For example \log{|x|} and \ln{|x|} instead of log(x)ln(x). Does this make a difference? Should both brackets and the straight lines be used? When taking the derivative what is the...

Homework Statement The problem is in the context of a probability problem; however, my question in regards to a computation regarding a particular integral. All that is needed to know is that the probability density function is 1 in the range 0 < y < 1 , y-1 < x < 1 - y, and 0 otherwise. I...

Is the Hayflick limit an absolute limit for the human lifespan or is it just the average limit of the human lifespan just like there are average heights and weights? Based on the maximum number of times the cells divide which is 50 according to Hayflick's experiments, how can the maximum...

Hi! Need help in solving this double integral: 1 1 ∫ ∫ |x-y| dydx 0 0 Thanks in anticipation. Regards, Aby.

## x - |x-|x|| > 2 ## how would I go about solving something like this? my initial thoughts was to consider if x >= 0 I get 2-x < 0 then x > 2 in that case then consider if x < 0 which I get -|x+x| > 2-x then 2x > 2-x then x > 2/3 but I'm having troubles deciding which one is correct, and if...

Hey PF, I'm building a simple math calculator program in C for my Programming class. My problem is Xcode doesn't recognize the absolute value function (abs), even with math.h included: Any ideas on what I can do to fix this? Is there a way for me to define this on my own? Thank...

I have no problem that I am trying to solve but simply a question about the derivative of an absolute value equation. I know that the derivative of and absolute value function is (x*x')/(abs(x)) and I understand the process of reaching this equation through the process shown here...

Is |\vec{a}+\vec{b}|^{2} equal to the same thing as (\vec{a}+\vec{b})^{2}? And when is it equal to √(a^{2}+b^{2})? Thanks.

In the 19th century they believed in the absolute motion and the ether, and they were searching for a scientific proof of the motion of the Earth. When Foucaults experiment was done, people still believing that the Earth was still wasfinally convinced that it moves instead. But it is well...

Homework Statement Here is an alternative approach to handling absolute value terms as the decision variables: abs(x) is the smallest value z that satisfies x \leq z and -x \leq z. Using this,convert the following into a lp Min 2x1 + 3abs(x2) S.T x1 + x2 \geq 6 Homework Equations Here is a...

if you are given $$-6 \leq x \leq 14$$ from this how do you create an abs equation like $$|x-4| \leq 10$$ k

Absolute Vales with fractions HELP PLEASE :) hey everyone, Homework Statement find the solution set: l 1/x -3 l > 6 Homework Equations none The Attempt at a Solution 1/x > 9 or 1/x < -3 1 > 9x or 1 < -3x 1/9 > x or -1/3 > x this answer doesn't seem...

Homework Statement |x| + |y| ≤ 1 What is the region in the plane that solves this inequality? Homework Equations The Attempt at a Solution I first tried graphing it by isolating the y variable |y| ≤ -|x| + 1 Then I looked at the hint we were given, which was to assume that x and y...

Homework Statement Hello, I have solved the problem, but not the way the writer intended. I need help figuring out how they wanted me to do it. Here's the problem: The circumference of a sphere is found to be 0.98 m +/- 0.01 m. Calculate the volume and absolute error with five digits...

$\displaystyle\int|2x-1|dx$ please tell me what is the first step to solve this.

An object above absolute zero radiates energy. This implies that object on Earth too radiate energy(infrared?) My question is, if the Earth were not moving, we would be much slower, so would we radiate in some other wavelength of the spectrum? We are essentially traveling really fast because of...

Solve $||||||| x^2 – x –1 |–3|–5|–7|–9| – 11|–13| = x^2 – 2x – 48$.

How much flux reaches Earth from an unobscured star? ##m_{sun} = -26.83## and ##M_{sun} = +4.74## ##m = +6## and ##M = +4.74## Calculated distance of target star: ##d = 17.86 pc## Now, here I'm trying to find the flux of a star that has the same absolute magnitude as our sun, but has an...

I am trying to get a better understanding of what it means for an atom to vibrate. Let's say there is a chunk of iron in deep space that starts out with a temperature of 50 degrees celsius and is rapidly losing thermal energy. I will make the following assumptions: 1. The iron has thermal...

Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) PART A 9) Solve for all X: |2x-5| + 3 = 18 My Answer: x = 10, x = -5 10) Subtract and simplify: (5x^2 - 3x + 8) - (-4x^2 - x + 10) My Answer: 9x^2 - 2x - 2

Why is the value of PI not absolute mathematically?

The title might be confusing. Anyway while preparing for a seminar I made a statement, " Absolute space does not explain the inertial forces, since they are related to acceleration with respect to anyone of the inertial frame". Is this statement correct? Please explain with few examples, Thank you..

Homework Statement Find the limit of this sequence: (-1)n(2n3)/(n3+1) Homework Equations The Attempt at a Solution At first glance I would attempt to use the absolute value theorem which gives an answer of 2 as n approaches infinite. My question is, when the theorem fails (...

Hi all, I'm trying to calculate the M.A.P.E. using the accuracy() function in SDMtools. I have an output of 10.69. I'm not sure if this is 10.69% or 1069% as previously in a different model I had gotten an output of 0.34. If anyone is familiar with this, I would appreciate any help...

I came across this algebra problem, can someone please help me solve this problem? Please show the steps as well. Much appreciated. |(x-1)| + |(y-3)| = 11 |(x- 3)| + |(y-17)| = 3 Find the nearest/possible x and y

Homework Statement A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinate axes at points P and Q. As L varies, what is the absolute minimum value of OP + OQ? The attempt at a solution Let x and y be two points on the line. Using the slope...

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

Hi all, I was working on a proof that essentially worked because: |x-y|+|y-z| >= |x-y+y-z| I knew this was true because, but I'm looking for a generalization in a way that I could write in a proof. Can you say that when comparing two expressions of addition/subtraction that are...

We have ## ||a+b|-|a|-|b|| ##. The only way I can think to eliminate one pair of absolute value signs is to consider the cases separately and determine which pair(s) can be removed without affecting the final answer. I'm trying to get better at doing these types of problems, so feel free to...

I have been trying to find information on the crystal structure or phase of solid elemental metals at temperatures close to absolute zero, but I can only find information on there ambient structures. Does anyone know of any sources that would have thermodynamic tables for solid metals at low...

Define f(x)= |x+3|-|x-3| without absolute value bars piecewise in the following intervals (-∞,-3);[-3,3);[3,+∞). this is how i do the problem, I removed the absolute value bars first f(x)= x+3-x+3 = 6 now i don't know how to define it piecewise. can you show me how define it correctly. thanks!

Hello! What is the integration of the absolute value of e^ix? That is what is ∫|e^ix|^2 equal to? The whole absolute thing got me lost. Thanks in advance.

The formula for absolute pressure is absolute P=gauge P+atmospheric pressure. So when the gauge is at 0 it's actually 1 atm. So using the gas law if I were to half the volume the pressure would increase to 2 atm. So would the gauge read 1 atm when this happens? So how does the mechanism...

Homework Statement ∫0-->x |t|dt Homework Equations // The Attempt at a Solution 1/2*x^2 for x>= 0 1/2*(-x)^2 for x<= 0 Not sure what to do to be honest. (the answer in the back of the book says 1/2*x|x|).