Absolute Definition and 1000 Threads

Rewrite each statement using absolute values. 1. The number y is less than one unit from the number t. y < | t - 1 | 2. The sum of the distances of a and b from the origin is greater than or equal to the distance of a + b from the origin. | a + b - 0 | > or = | a + b - 0 | Is this correct...

Rewrite each statement using absolute values. 1. The distance between x and 4 is at least 8. | x - 4 | > or = 8 Can this also be expressed as | 4 - x | > or = 8? If so, why? 2. The distance between x^3 and -1 is at most 0.001. | x^3 -(-1) | < or = 0.001 Can this also be expressed as | - 1...

The | x | = x when x > or = 0. The | x | = - x when x < 0. Rewrite the following expression in a form that does not contain absolute value. | x + 3 | + 4 | x + 3 |, where x < -3 -(x + 3) + 4 -(x + 3) -x - 3 + 4 - x - 3 -2x - 6 + 4 -2x - 2 Correct?

Rewrite each statement using absolute values. 1. The distance between x and 4 is at least 8. Work: | x - 4 | > or = 8 Correct? Why must we write greater than or equal to for AT LEAST statements? 2. The distance between x^3 and -1 is at most 0.001. Work: | x^3 - (-1) | < or = 0.001...

The definition of absolute value states the following: | x | = x when x is > or = 0 | x | = -x when x < 0 I can use the above definition to rewrite expressions that do not contain absolute values. | -sqrt{3} - sqrt{5} | Since the expression in the absolute value is less than 0, we can say...

The definition of absolute value states the following: | x | = x when x is > or = 0 | x | = -x when x < 0 I can use the above definition to rewrite expressions that do not contain absolute values. | x^4 + 1 | Since x^4 + 1 > 0, then the answer is simply the expression itself or x^4 + 1...

The definition of absolute value states the following: | x | = x when x is > or = 0 | x | = -x when x < 0 I can use the above definition to rewrite expressions that do not contain absolute values. | x - 3 |, where x < 3 If x < 3, then we can say that (x - 3) is less than 0. So, -(x - 3) =...

The definition of absolute value states the following: | x | = x when x is > or = 0 | x | = -x when x < 0 I can use the above definition to rewrite expressions that do not contain absolute values. | 1 - sqrt{2} | + 1 The value 1 - sqrt{2} is less than 0. So, we have -(1 - sqrt{2}) + 1. -1...

Is absolute zero nothing? Can a quanta exist in nothing? There could be no quantum fluctuations at absolute zero.

Homework Statement Prove the equation for ΔRC. (See the first attachment with the circuit schematic inside) Homework Equations (The equation for RC, in both attachments) The Attempt at a Solution You can see my attempt at a solution in the second attachment. I'm stuck at the step shown in the...

Suppose that the force needed to push a disc down on top of another disk = weight x g, then the two discs are charged with opposite quantities of electricity, then the weight removed, and still the discs remain together due to the force of attraction between the discs; so then the electric force...

Hello, I'm a student of electrical engineering. This task appeared in one of the past exams. I've been using the procedure I believe should yield the correct result, however, it turns out I was wrong. Could somebody please check out where the mistake lays in my calculations? Homework Statement...

Precalculus by David Cohen 3rd Edition Chapter 1, Section 1.2. Question 68, page 11. Before typing the textbook question, I must say that I have not been able to find a satisfactory answer to absolute value equations that equal a negative number. Question: Explain why there are no real...

Homework Statement A 410kg bluefin tuna rests motionless at a depth of 15m below the ocean's surface. The absolute pressure at this depth is 251,700 Pa. What is the volume of the fish? Homework Equations absolute P=gauge Pressure+atmospheric pressure 1atm=1.03e5Pa P=density x g x height...

This is the problem given at my basic astronomy course. If I turn it in within a month correctly, I get 10 extra points in the finals. Problem: We have binary star system consisting of Star A and Star B. Astronomers have observed it for 11 years, during which it has moved from point A to point...

Homework Statement Hi guys, I am going to calculate the following integral: $$\int_0^{f_c+f_m} |Y(f)|^2\, df$$ where:$$Y(f)=\frac{\pi}{2} \alpha_m \sum_{l=1}^{L} \sqrt{g_l}\left [ e^{-j(\omega \tau_l - \theta_m)} \delta(\omega - \omega_0) + e^{-j(\omega \tau_l + \theta_m)} \delta(\omega +...

1. The problem statement, all variables, and given/known data A car of proper length 12m is being driven at 0.9c through a garage of proper length 6m. The garage has a front and back door. The garage owner, Joe, says that the car will fit inside the garage with no damage to it, albeit for a tiny...

Homework Statement A manometer is used to measure the pressure of a gas in a tank. The fluid used has a the specific gravity of 0.85, and the manometer column height is 55 cm, as shown in figure 3-20. If the local atmospheric pressure is 96 kPa, determine the absolute pressure within the tank...

Ok, so I'm not even bothering with tire friction simulation anymore. What I'm trying to simulate is a tire that has 100% grip at all times (no lateral velocity.) Now you see that the statement I just made has a contradiction in it...If a car has 4 tires, and if a car is rotating, it is...

An absolute value property is $$\lvert a \rvert \geq b \iff a\leq-b \quad \text{ or } \quad a\geq b,$$ for ##b>0##. Is this true for the case ##a=0##? I mean if ##a=0, \lvert a \rvert =0## so ##0 \geq b##. But ##b## is supposed to be ##b>0##, so we have a contradiction. How can this property...

I've 2 questions 1) Why do we take absolute of the power series? 2) I don't get why the interval of convergence is from -inifinity to +infinity. You can find the problem below.

Hi folks, Tell me please why in classical Newtonian physics one can say that the space and time are independent? But we have equations of motion which clearly show this dependence (x=Vt; x=x0+1/2at^2+v0t). Thank you.

Homework Statement Given values and uncertainties of d, find the absolute uncertainty in 1/d^2 (see table attached) Homework Equations I know that if it's a square function the absolute uncertainty will be 2 (delta d) / d but I'm not sure if it's correct for an inverse function. The Attempt...

If we define ##|a| = \sqrt{a^2}##, then why can't we do something like ##\sqrt{a^2} = (\sqrt{a})^2 = a##? Or equivalently ##\sqrt{a^2} = (a^2)^{1/2} = a^{2/2} = a##? Isn't this a contradiction? Also, how would this relate to showing that ##\sqrt{|a|} = |\sqrt{a}|## is true or false?

Find the absolute extrema of the function over the region R. (In this case, R contains the boundaries.) f (x, y) = 12 - 3x - 2y R: The triangular region in the xy-plane with vertices (2, 0), (0, 1), and (1, 2). I need the steps to guide me through this monster question. I am familiar with...

In basic terms, what is the main difference between relative extrema and absolute extrema? I know that absolute extrema is more involved but why is this the case?

I was asked in an exam the following question: Q: How is the absolute Kelvin Thermodynamic temperature scale defined ? My answer is the following: A: The absolute zero kelvin thermodynamic temperature is defined as the temperature for which the entropy of the system is zero, i.e ##S|_{T=0} =...

Find the absolute extrema of the function over the region R. (In this case, R contains the boundaries.) f (x, y) = 12 - 3x - 2y R: The triangular region in the xy-plane with vertices (2, 0), (0, 1), and (1, 2). I need the steps to solve such a problem. I was told to graph the 3 given points...

Is the idea of negative absolute temperature analogous to a virtual image in geometrical optics? I was reading this article about such a negative temperature: http://www.livescience.com/25959-atoms-colder-than-absolute-zero.html It seems to me that since temperature is defined by its...

Homework Statement How to find absolute min/max of f(x)=x^3+3x^2-24x+1 on[-1,4] I need to find the absolute min and absolute max. Homework EquationsThe Attempt at a Solution I first took the derivative, reduced, and set it to equal 0 to find crit numbers. x^2+2x-8=0 Factored. (x+4)(x-2) = 0...

I was reading Bransden's Quantum Mechanics 2nd edition, chapter 2 page 61. There,it says "It should be noted that since E =hv (v for nu), the absolute value of the frequency has no physical significance in Quantum mechanics..." Why is that? Isn't this a contradiction?

GR lacks absolute space, but does Newtonian physics also? If not what does GR lacking absolute space mean? I had thought in Newtonian physics that there existed an absolute space in which Newton's laws are true, and that an inertial frame was a reference frame in relative uniform motion to...

Hello :) I'm struggling a bit on how I can find steps to solve problems like this, because my mind goes all over the place. Find absolute min and max of f(x,y) = 18-3x+6y on a closed triangular region with vertices (0,0), (6,0), and (6,9). I still struggle with partial derivatives and take a...

Let us assume that a spacetime has a global time-displacement symmetry described by a timelike Killing vector field ##\xi^\mu=(1,0,0,0)##. Further assume that we have a particle with four-momentum ##P^\mu=m\ V^\mu##. It is well-known that a stationary observer with four-velocity ##U^\mu##...

Homework Statement In the first 2 notes , i was told that the absolute max moment will occur under the largest force lying nearest the resultant force of system . but , in the example that i have uploaded , i found that the absolute max moment will occur under the 6kN load instead of 8kN p/ s...

Homework Statement For the maximum moment occur under the 1.5k load , why when we consider the left part of the beam, we just need to consider the forces 2k and 1.5k only ? Homework EquationsThe Attempt at a Solution How about FR = 4.5k and also the 1k ? Cant i just consider all of them ...

Understanding Absolute Viscosity - shearing stress Hi everyone, I have found information about Absolute viscosity: Coefficient of absolute viscosity is a measure of internal resistance. Dynamic (absolute) viscosity is the tangential force per unit area required to move one horizontal plane...

Why do all the volume temperature curves of an ideal gas intersect at the same point on the temperature axis ?

I would like to ask you why the author does not use absolute value of y instead of y? Source: Mathematical Methods in the Physical Sciences by Mary L. Boas Thank you.

In one of my problems, I have this set of data. I have to create two best fit lines, and find a value of absolute zero for both. The first best fit line is to be made assuming there is NO uncertainty in P. This is rather straightforward, just use the normal linear regression, find a slope...

$$\sum_{k=1}^{\infty}\left(\frac{k}{k+1}\right)^{2k}$$ $\textsf{how do you use absolute converge test on this?}$ ☕

If I take a spaceship and park it near the event horizon of a black hole and then measure the age of the universe by observing SNe Ia, then travel back out to normal space (no gravitational forces, at rest with respect to CMB), will the dates agree? That is, if the measured age of the universe...

Hello good evening to all, I was studying here and got stuck with this. I solved the integral and got [x+sin(x) -1] and that´s the farthest that I got. I would appreciate the help.

In Mary L. Boas' Mathematical Methods in the Physical Science, 3rd ed, on page 17 it goes over absolute convergence, and defines the test for alternating series as follows: An alternating series converges if the absolute value of the terms decreases steadily to zero, that is, if |an+1| ≤ |an|...

Homework Statement Hi Physics gurus, this question was in my Chem Eng exam, and I can't agree with my lecturer's answer. He makes a LOT of mistakes, so it's hard to know when he's being clever or reallllly dumb. The question I have issue with is: "Is the pressure a manometric or an absolute...

Homework Statement The ammonia molecule (NH3) has a dipole moment of 5.0×10−30C⋅m. Ammonia molecules in the gas phase are placed in a uniform electric field E⃗ with magnitude 1.3×106 N/C . Part A: What is the change in electric potential energy when the dipole moment of a molecule changes...

There are two ways by which absolute motion might be detected: by measuring motion with respect to a beam of light, and by making use of inertial effects that arise when an object is accelerated. So why MichelsonMorley experiment showed the first method to be unworkable? Einstein's special...

I've seen, in the description of a black hole's photon sphere, a mention of a "light-like ds." I was happy to see it because I've been thinking about a photon's physical environment; at the speed of light, it would experience no radial dimension & no time dimension. Might it make more sense to...

When referring to the absolute magnitude ,for example, in the B filter of a distant galaxy(considered point source) what are we talking about? Are we talking about the observed redshifted flux density(luminosity density) hypothetically seen from 10 pc away (1) ; or are we talking about the...

Homework Statement X and Y 2 real numbers / |x| <1 and |y|<1 Prove that |x+y|<|xy+1|Homework EquationsThe Attempt at a Solution |x+y|<2 I couldn't prove that |xy+1| >2 And couldn't find a way to solve the problem Please help