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[Sphere]

f(k)=sqrt(k^2-1) is not defined for -1<k<1 so how do you get those answer?

It is if you use imaginary numbers. Then using this property of absolute value you can make the imaginary term go away.

http://www.mathwarehouse.com/algebra...lex-number.php

[John Doe]

it was clear that k is real from the question

You have the two inequalities, where k is a real number;
.....

@nikitn
so both equation are defined on ]-inf;-1]U[+1;+inf[
there is symmetry as well, if you replace k by -k, equation (1) becomes (2), and (2) becomes (1).

let see for k positive
1=<k (L1)
1=<k^2
0=<k^2-1
0=<sqrt(k^2-1) (L4)
1=<k + sqrt(k^2-1) ((L1)+L(4))
so equation (1) is never true for k>=1

and because that simetry, equation (2) is never true for k=<-1

There isn't a common a k that would satisfy both equation (1) and (2)

EDIT: you'll need be little bit more rigorous because of the absolute values but that's the way to go.

EDIT2: actually, I don't think it's called a symmetry, more of a permutation, it's a long time I did that stuff...

[Sphere]

Yeah, I think you're right. What kind of algebra did you use to get to that result?

Edit: I just redid the problem and I now got the same as you, and I followed all the rules too. but could you show me anyway, just to be sure?

I thought about finding the roots to

k + |rt(k2-1)|(+/-)1 = 0
k - |rt(k2-1)|(+/-)1 = 0

For both they are -1, 0, 1

I tested -2, -.5, +.5, +2 (using the absolute value of a complex number trick) using a spreadsheet.

1.) Is only less than zero at -2 and -.5
2.) Is only less than one at +2 and +.5

That's were I got zero as the dividing line. Missed the fact about -1 & +1.

I am trying to solve it algebraically, but I cannot seem to get that 0 root, only -1 & +1. The zero root, which is obviously there if |i| = 1, doesn't fall out of the algebra as far as I can tell. I do not know why.

[Heavy Weapons Guy]

Need help with this, due tomorrow. If I don't get this done then surely I will fail in math.

There it goes:

Earthquake strength is measured by Richter's scale. They are calculated by this formula ''Mr= 2lg E-3,2'' E is energy.
................................................................................................................................_
...............................................................................................................................3

a) In 1960 22th May in Chile happened an earthquake, which was 9.5 strong by Richter's scale. How big joule energy happened during the Earthquake?

c) How big joule energy happens during 9;9,1;9,2;9,3 strong Earthquake?

d) A guy says that earthquakes of 9 and 9,3 strength by Richter's scale are in the same strength. What would you answer to him? (With proves)

(There's no b)

If something isn't clear, then please let me know. This is really important though and in all show how you got to the result. I will give rep.

[edse]

I'll try.

Mr= (2lg(E-3,2))/3

first step: 3Mr/2=log₁₀(E-3,2) simple

then you take 10^x of both sides. 10^log₁₀(x) takes out each other.

10^(3Mr/2)=E-3,2 and then it's simple again.

then you just have to put in the different Richter values.

[ccllnply]

I was hoping someone could confirm something I did in a test today. Basically we're doing Curve Fitting in Numerical Methods. I got to the linear equation part and since it was a exponential curve, I had to use this equation (E= sum of):

(Ex2)A+(Ex)B=x.log.e.y
(Ex)A+nB=log.e.y

Now on the bottom line, the "n" before the "B" is meant to represent the amount of x values. In this question, it was over 8 weeks so n=8, simples. Or so I thought.

This meant that I had to multiply the bottom line by 4.5 so I could subtract down to get rid of the B values and get A on it's own. However, if I counted in the total in the x values as well, this would bring "n" up to 9 and I would have to multiply the bottom line by 4. This is where I got worried. In all my notes, not once is the total value part of n but in this case the fact that adding it meant that I had to multiply by a whole number (4) made me think that everything I had been taking down in maths class was wrong.

Can someone help me out and confirm this because I can't find it anywhere with Google.

[Gaidin]

There's a few different methods, and I'm not really sure what you're looking for here. But here's a summary from someone's notes that might give you a basic idea: link. Don't you have a textbook going over this method you could look at with an example?

[knight of meh]

why are you all math people -.-

[Gaidin]

We're nutcases.

[ccllnply]

There's a few different methods, and I'm not really sure what you're looking for here. But here's a summary from someone's notes that might give you a basic idea: link. Don't you have a textbook going over this method you could look at with an example?

Basically I just want to know if I was right to not count the "total" as another X value, which would have changed nB from 8B to 9B. I'm almost certain I was but I just want to be sure.

And no, we don't have text books. Everything is online and on worksheets.

[Gaidin]

Well, I don't have my textbooks easily at hand(3 states away), and without you being able to name a specific method(there are many ways to do curve fitting), your best bet is to go back to your worksheets and online notes and work through the numbers you remember.

[Ima Farmathar]

Im sorry to bother you, but i really need help,
I’m trying to integrate the following system
[{x^' [t]==c1x[t](c4x[t]+c3y[t]),y^' [t]==c2y[t](c6x[t]+c5y[t])},{x,y},t]
I tried in wolfram,
DSolve[{x^' [t]==c1x[t](c4x[t]+c3y[t]),y^' [t]==c2y[t](c6x[t]+c5y[t])},{x,y},t]
However it doesn’t give any result, keep in mind that my notation might be a bit of.

Then I tried finding the roots manually, the only roots it can find are (0,0) I tried finding my own roots, with no more luck.

Having only an equilibrium point with derivative 0, I fail to get any solutions.

[napoleon boneaparte]

I'm still not very sure on how to write ionic equations. e.g. CaCO3 + 2HCl -> CaCl2 + CO2 + H2O. The ionic equation is CO3(2-) + H(+) -> CO2 + H20. How does one pick the ions to put in the ionic equation?

[knight of meh]

I'm still not very sure on how to write ionic equations. e.g. CaCO3 + 2HCl -> CaCl2 + CO2 + H2O. The ionic equation is CO3(2-) + H(+) -> CO2 + H20. How does one pick the ions to put in the ionic equation?

it's the ions that react in the equation you need to represent .

how i learnt it:

1) Write out the equation and balance (add state symbols!)
2) If any of the compounds are aqueous, then you can split it up into 2 ions (the +ve and -ve)
3) Look at both sides now - cancel out anything that remains the same
4) You have an ionic equation

There is another example:
MgO(s) + HNO3(aq) ------> Mg(NO3)2(aq) + H2O(l)

Okay lets do step 1..
1) MgO(s) + 2 HNO3(aq) ------> Mg(NO3)2(aq) + H2O(l)
2) MgO(s) + 2H+(aq) + 2NO3(aq) ------> Mg2+ (aq) + 2NO3(aq) + H2O(l)
3) The 2NO3(aq) is common so cancel it out to get:
MgO(s) + 2H+(aq) ------> Mg2+ (aq) + H2O(l)


CaCO3(s) + 2HCl(aq) -> CaCl2(aq) + CO2(g) + H2O(l) run this through the system and get the ions that appear on both sides,


CaCO3(s) + 2(H+) + 2Cl(-) = 2Ca(2+) + 2Cl(-) + CO2(g) + H2O(l)

eliminate what appears on both sides which is the chlorine so the ionic equation is .

CaCO3(s) + 2(H+) -----> 2Ca(2+) + CO2(g) + H2O(l)

i don't know if your wrong or not in your example but your CaCO3 would have to be (aq) to allow it to be split like that in an ionic equation in my experience it's usually solid

[Eugene of Savoy]

Could someone explain the theory of relativity to me in simple terms for a non-scientists?

[knight of meh]

Could someone explain the theory of relativity to me in simple terms for a non-scientists?

i assume you mean Einstein work? first off that encompasses two theories special and general relativity

big things introduced.

1)the speed of light is a constant for all observers
2) space and time can be grouped together or taken in relation to each other i.e spacetime
3)measurements are relative to the velocity of observers



special relativity involves space and time ,it assumes (and then proves) light is a constant and the laws of physics don't change.
it explains how to interpret motion between two things that are moving at a constant speed in relation to each other . the classic example to explain this is if you and an astronaut want to compare your observations all you need to know is your speed in respect to each other .

general relativity is a law of gravitation which states that an observed gravitational effect between masses is a result of the warping of spacetime. It builds on special relativity to include instances where the two things are accelerating in respect to each other. In essence it describes the effect of matter on spacetime (together) as what we now perceive as gravity .

[Nikitn]

Could someone explain the theory of relativity to me in simple terms for a non-scientists?

If in my frame of reference I drive a car at a velocity of 50kph relative to the road, and you drive 30 kph faster than me; then you drive in your frame of reference 80kph relative to the road. Right? OK, now let's say I am in a spaceship travelling at 90% of the speed of light relative to the earth while you are travelling at 80% of the speed of light relative to me. According to classical mechanics you would be travelling at 170% of the speed of light relative to the earth, but this is wrong. In fact, you will be travelling at only 98.84% of the speed of light relative to earth. This is the important thing here: at high velocities classical mechanics are not valid, so to provide accurate predictions you need a new theory to cover this speedy world; Einstein's theory of relativity.

There are two main areas of the theory of relativity: Special Relativity (treats non-accelerating frames of reference), and general (describes accelerating frames of reference and the effects of gravitational fields).

Special Relativity is built on Einstein's two postulates:
1) The speed of light in vacuum is constant in all non-accelerating frames of reference.
2) The laws of physics apply in all non-accelerating frames of reference.

And that's essentially all of SR condensed into two simple sentences. However, when these two claims are taken to their full logical conclusions you will end up with mathematics adjusting the formulas of classical mechanics for very high velocities; you will see that from your point of view time flows slower in another frame of reference moving at a velocity relative to you (yet from the other frame of reference's point of view, time flows slower for YOU); and you will find that if you travel past an observer at a speed close to the speed of light, they will look squeezed (yet from their point of view YOU will be the squeezed one!). In the end you will understand why FTL communication is forbidden and that it does not make sense to speak of point in space without the accompanying time.

General relativity is not known well to me, but suffice to say GR allows frames of references to be affected by acceleration, gravitational fields and so on. One of the results from GR is that gravity both slows time and curves space itself around it.

[Eugene of Savoy]

Thanks guys (+rep)t

[Eugene of Savoy]

How did the beryllium polonium initiator work on the bomb "Fat Man"? If you could use simple terms, I'm not good at this science stuff

[Morkonan]

How did the beryllium polonium initiator work on the bomb "Fat Man"? If you could use simple terms, I'm not good at this science stuff

https://en.wikipedia.org/wiki/Nuclea...on-type_weapon

Basically,

The surrounding shell of explosives detonated and dramatically compressed the plutonium core. That core, due to its "radioactive" element, released enough electrons in enough of a tightly enclosed space to initiate a rapid chain reaction of released energy. Without that compression, the core would have happily sat there for eons, its plutonium slowly decaying, the plutonium not compressed tightly enough to achieve criticality.

Watch this: https://www.youtube.com/watch?v=5BHdsjo-NR4 (Physics for future presidents - Nukes)