In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, |x| = x if x is positive, and |x| = −x if x is negative (in which case −x is positive), and |0| = 0. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero.
Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.
Homework Statement
Find the absolute max and min of
f(t)=t + cot(t/2) on [pi/4, 7pi/4]
Homework Equations
The Attempt at a Solution
I have attempted to find the derivative which I believe is
1 - csc^2 (t/2) * (t/2) which I can simplify down to cot^2 (t/2) * (t/2)
Even...
Hello!
Can someone explain to me what is relative, and what is non-relative or absolute?
As I understand linear motion at constant velocity is called relative.
Can you give more such examles for me to understand why something is called relative?
Cheers!
Homework Statement
Define sequence \left[ {z_n} \right]} _{n=1}^{\infty} of points in the complex plane with z_1 = 1 and z_{n+1} = (4+3i)z_n - 1. Show that |z_n| \ge 4^{n-1} for all n \ge 1.Homework Equations
The Attempt at a Solution
The base case of induction is true, since |z_1| \ge 4^{1-1}...
Homework Statement
I need to simplify the expression below. The absolute value is throwing me off
\left[\left|(\alpha + k)^{2}e^{-2i \alpha a} - (\alpha - k)^{2}e^{2i \alpha a}\right|\right]^{2}
Homework Equations
I know \left|e^{ix}\right| = 1
The Attempt at a Solution
I...
A University of Rochester student decided to depart from Earth after his graduation to find work on Mars. Before building a shuttle, he conducted careful calculations. A model for the velocity of the shuttle, from liftoff at t = 0 s until the solid rocket boosters were jettisoned at t = 79.2 s...
Homework Statement
1) x^5 > x^2
2) 7| x + 2 | + 5 > 4
3) 3 - | 2x + 4 | <= 1
Homework Equations
The Attempt at a Solution
1)
x5 - x2 > 0
x2(x3 - 1) > 0
x2(x - 1)(x2 + x + 1) > 0
Im not too sure what to do next. I can't factor it any further, at least I don't think so. Which...
Homework Statement
Find f'(x), if
f(x) = [x^2 * (3x + 2)^(1/3)] / [(2x - 3)3]
Where the absolute value symbol surrounds the entire function.
Homework Equations
N/AThe Attempt at a Solution
My attempts don't account for the absolute value of the function. Otherwise, I can still take the...
Homework Statement
I found the local maximum for the equation g(x,y)=3xe^y - x^3 - e^(3y), which is (1, 0)...now I am supposed to show that this is not the absolute maximum for g(x,y). I don't know how to find an absolute maximum without an interval! Could anyonw shed some light on this...
Homework Statement
Find the absolute error for the following function:
f = (xy/z)+5w
Homework Equations
Equation for an error vector:
df = (df/dw)dw + (df/dx)dx + (df/dy)dy + (df/dz)dz
Equation for the absolute error:
(df)^2 = (df/dw)^2(dw)^2 + (df/dx)^2(dx)^2 +...
Homework Statement
Consider a function of one variable, f(x), which is continuous on an interval I. If f has a single critical point, x = a, in I, then if that point is a local maximum (or minimum) it must also be an absolute maximum. Explain why this is.Homework Equations
Intermediate Value...
I am working on a lab report related to Ideal Gases at the moment, and I can't quite grasp how you would go about finding the temperature for absolute zero. Here's a brief synopsis of our experiment: We inserted a piston into a cylinder of water to keep the piston at a steady temperature of 23...
Homework Statement
The cylinder C is being lifted using the cable and pulley system shown. If point A on the cable is being drawn toward the drum with a speed of 2 m/s, determine the speed of the cylinder.
Homework Equations
2s_{A} + s_{b} = l
The Attempt at a Solution
I...
Hi! I've got a problem that's got me a bit.. well, in the end I guess the proper word is sceptic, because it feels a bit like I've made the answer up, which is why I'm taking it up here at all. Anyway:
Homework Statement
Determine the domain for f(x) and the asymptotes to the curve y=f(x) for...
First order linear ODE-integrating factor with absolute value?!
Homework Statement
Solve the ODE y' + (3/t) y = t3.
2. Homework Equations /concepts
1st order linear ODE
The Attempt at a Solution
Integrating factor
=exp ∫(3/t)dt
=exp (3ln|t| + k)
=exp (ln|t|3) (take constant of...
Homework Statement
So I've got two problems I'm struggling a bit with. One of them I've solved (I think), but I'm definitely not sure. The other one is bugging me a bit. Anyway:
i] Determine all z∈C so that |z - 1| = 5 and |z - 4| = 4
ii] Determine all z∈C so that |4 - z2| = z...
Homework Statement
You measure the mass of a physics textbook to be 2.97±0.07 kg, and use this value to estimate the total mass of 800 identical physics textbooks in the bookstore. What is the absolute uncertainty in your estimate of the total mass?
I have been working on this for a...
I'm looking at this problem below:
http://apthtml.com/images/deriv.png
The first part I understand - a derivative of some vectors, not a big deal - but the second part is where I'm confused. I can't even come up with a name for it. First I thought magnitude, but I don't really see how...
I'm not sure if this is the proper location for this thread, but its for a math course and I think my issues concern the math portion of the problems. If it should be moved please do so.
Note: I know the post is quite long, so I'll just pull out my few main issues from all the junk.
1)...
My understanding is that, while at a macroscopic level, my skin may seem like an absolute boundary between my interior and exterior, at a microscopic level, it is full of wholes--we cannot draw a line or arc that represents and absolute boundary between my interior and exterior at a given point...
State the Problem
A gage is connected to a tank in which the pressure of the fluid is 42 psi above atmospheric. If the absolute pressure of the fluid remains unchanged but the gage is in a chamber where the air pressure is reduced to a vacuum of 25 inHg, what reading in psi will then be...
Energy is considered a relative quantity.
Is there any measure of energy that is absolute?
If temperature is measured by measuring the frequency of the emitted photons then observers with different velocities would measure different temperatures.
But a body at absolute zero would not...
Homework Statement
http://img3.imageshack.us/i/0902091724.jpg/
http://img3.imageshack.us/i/0902091724.jpg/Homework Equations
The Attempt at a Solution
My problem is that I don't even know where to start on this! My first problem is always forgetting what I can and can't use, because we can...
[b]1. Solve:
l2x^2+7x-15l<10
[b]3.
I split it up into two cases and got:
2x^2+7x-25<0 and 2x^2+7x-5>0
With the quadratic formula I got:
x= [-7+/- (249)^(1/2)]/4 and x= [-7+/- (89)^(1/2)]/4
These clearly are the answers, but I am confused about the inequality from this...
I've heard it said that it is impossible to determine an objects absolute velocity, all one can do is find it relative to some other object...
but, if the CMB is everywhere, why could you not just measure the doppler shift in all directions, and adjust your velocity so the CMB has no doppler...
According to Special Theory of Relativity nothing is absolute in this universe, but relative to each other. as we know that Einstein told me that speed of light is max. Now I'm little bit confuse if speed of light is absolute or relative i.e it may be max. for initial reference frame but for any...
I'm calculating absolute relative error at the moment for a practical I did. However, I've hit a brick when attempting to find a general relative error I can use because I need to gradient to find something else which also requires a relative error calculation.
I have frequency (+/- 0.0005)...
Absolute value of acceleration Help!
Homework Statement
I am getting a value of -1.94 m/s^2 for my acceleraton. An it wants to know the absolute value of acceleration what do I put down. It also state that the plus or minus is just to indicate direction. But the way the problems is computed...
"Absolute Position"
This is a bit of a contrived scenario, but I wonder how it might be solved..
Say you have two highly advanced civilizations that want to meet each other, but in order to do so the trip will take billions of years.
Now, in this time, solar systems collapse, orbits change...
I'm having a difficult time rationalizing the description that a book I'm currently reading has given of Newton's idea of acceleration relative to absolute space.
As I understand this description, it states that acceleration occurs relative to the whole of absolute space. I don't understand...
Here's the thing. I have 4,7 nF capacitor and AC: 1 kHz < f < 10 MHz.
I measure real and imaginary part of capacitance C*=C'+iC" (C'=C'(f) and C"=C"(f)).
I did 2 measurements - in first capacitor is directly attached to measuring device, in second I use 1 m coaxial cables to attach it.
I...
Well, I am an absolute beginner at astronomy, but I'm really very interested..I want to start stargazing and observing space and studying space and stuff. can anybody help me? I don't have a telescope or any written material or guides or anything related to space...so any suggestions will be of...
This is either a topic that is so blatantly obvious that it's ridiculous I'm saying it, or I'm missing something. From my limited physics knowledge, I know that absolute zero is a temperature in which the molecules are not moving whatsoever. In other words, it's the lowest possible...
Hi all, this is my first post to the forum.
I've been thinking about a mechanism that can't work, but I can't figure out why not. Here is the idea:
1) If I have two wires parallel to each other on a table and I run a current through them, they will be attracted to each other. I believe...
Quadratic equation and absolute value...
Consider equation |x2-2x-3|=m, m belongs to R
If the given equation has no solution then find the interval in which the m lies.
2. Homework Equations -Given in question
3.
Since this equation is in modulus there would be two equations...
What are the advantages of using the absolute mean deviation over the standard deviation. Is it possible to show a simple example where the former is more (or less) appropriate?
Also, related to the mean deviation is my own variation. Does it have a name? Instead of calculating the absolute...
I'm in grade 8, but this website looked really helpful
Im doing my science fair project on time dilation, and I am wondering how to prove that the speed of light is absolute.
Can anyone help me?
Homework Statement
i just want to know one value that i can't find anywhere, and would love some help
Homework Equations
\lim_{x\rightarrow\ -\infty}|x|}
The Attempt at a Solution
thanks
hi guys,
(i) By comparing with the luminosity of the Sun, calculate the absolute magnitude of a 60W light bulb.
[The absolute magnitude of the Sun is +4:75; you may ignore colour differences
between the bulb and the Sun.]
(ii) The Hubble Space Telescope (HST) can detect objects as faint...
Sirius A has an apperant magnitude of -1.5, and his distance from us is 2.6 pc. the sun has an apperent magnitude of -26.8 and a distance of 1 AU.
what is Sirius's absolute magnitude?
how meny times is Sirius brighter then the sun?
m1-m2=-2.5lg(f1/f2)
this is the equation I'm supposed...
find the absolute maximum and absolute minimum (if any) for the given function :
f(x)= 2x + 32/x ; when x > 0
I tried to solve it but I'm not sure if its a maxima or minima, here are my try :
f(x)= 2x + 32/x
f'(x)= 2-32/x^2
2-32/x^2=0
2u^2=32
u^2=16
u=4 or - 4
-4 is not included...
Hi ,
Please help me to solve following problem.
If 20 KJ are added to a carnot cycle at a temperature 100 degree Celsius and 14.6 KJ are rejected at 0 degree Celsius,determine the location of absolute zero on celsius scale?
Ans -270.16 C
Please tell me how to solve it
Thanks in...
This problem seems straightforward and easy enough, but I still want to check my answers.
Suppose the pressure of the bulb (light bulb I'm guessing used in experiment) is 20 psi (absolute) at 20C. What would you predict the pressure to be at 0C? What would you predict would be at 100C?
I...
Homework Statement
|1/(x-1)|<1
The Attempt at a Solution
is that the same as this -1<1/(x-1)<1
can i do each side by it self then take the values at which they intersect
so i subtracted the 1 then got (-x+2)/(x-1) then made a sign chart with 2 and 1 on it
then took the less than...
Homework Statement
Find the absolute maximum and absolute minimum of f(x,y)=12xy-x^2 y-2xy^2 on the region bounded by x=1, y=1, and y=4/x
Homework Equations
The Attempt at a Solution
For x=1
f(1,y)= 12y-y-2y^2
= 11y-2y^2
f'(1,y)= -4y+11=0
= -4y=-11
=...
Homework Statement
Find \frac{d}{dx} \sin^{-1}(\sin x)
Homework Equations
The Attempt at a Solution
Now, I know that the above expression simplifies directly to \frac{d}{dx} x = 1, but I attempted it the long way. Here it is:
\frac{d}{dx} \sin^{-1}(\sin x)
= \frac{\cos...
1. I understand that it is impossible to say if something is absolutely stationary, for example wrt the universe, and that there is no such thing as absolute movement
now
2. if you place a point source of light at the origin, “O”, of a Cartesian coordinate system. At t1 the point source of...
Homework Statement
FIND THE ABSOLUTE MINIMUM AND ABSOLUTE MAXIMUM OF:
f(x) = 9x + 1/x
on the interval [1,3]
Homework Equations
The Attempt at a Solution
I don't know how to get started!