If not, what is the closest solution that applies to as many degrees of polynomials.
A theorem of Galois states that for every integer n > 4 there is a polynomial of degree n that is not solvable in radicals.
http://en.wikipedia.org/wiki/Solvable_group
For cubics and quartics there are known solution methods but they get pretty hairy.
http://en.wikipedia.org/wiki/Cubic_function
http://en.wikipedia.org/wiki/Quartic_function
Of course if the degree is less than 3 then we have simple methods.
Other than that, in general you can do things like look for rational roots using the rational roots theorem, any obvious factorization, Descartes’ rule of signs, and numerical methods.
You need to make 0.1 M glycine solution at pH 9.3. You have two stock solutions. Stock A is 0.1M glycine at pH 9.0. Stock B is 0.1M glycine pH 10.0. How much of each solution do you need to make the correct buffer of 1L?
How do you go about solving this problem?
"pH approximates but is not equal to p[H], the negative logarithm (base 10) of the molar concentration of dissolved hydronium ions (H3O+)" or "Mathematical Definition
pH is defined as minus the decimal logarithm of the hydrogen ion activity in a solution.[12] By virtue of its logarithmic nature, pH is a dimensionless quantity.
pH = -log10(aH+ = log10(1/aH+)
where aH is the (dimensionless) activity of hydrogen ions"
So Stock A has a concentration of 10^-9
and Stock B a concentration of 10^-10
want a ph of 9.3
9.3 = -log base 10 of (x A + y B) where x and y are the amounts of stock A & B required.
9.3 = -log base 10 (x 10^-9 + y 10^-10)
If you have a set of log tables or a calculator which does log base 10 then you should be able to get the answer.
No Solutions as the solution. Show the steps to solving the equation and explain in words why your work proves that there are No Solutions.
Easiest is 0*x=5. You know that for any x 0*x is 0, so 0=5 has no solutions, because there is no x for which it is true. This is opposed to every x is solution in 0*x=0.
Although all solutions thus far have their problems - what is the most likely solution that is accepted?
I don’t think there is a paradox. The Black Hole is a different Frame of Reference from from the Observer. In the Black Hole FoR time stops at the Event Horizon ==> In that FoR it takes forever for an event to occur. In the Observer’s FoR time passes and the information gets sucked in and is lost.
Basis for this opinion. Black Holes can combine ===> The collision does not take forever when viewed from outside.
http://physics.princeton.edu/~fpretori/STSCI_2009.pdf
OR
The universe is governed by 2 sets of laws that do not agree.” – Brian Greene, The Elegant Universe.
General Relativity, The Macro Universe (Things larger than an atom and high energy/mass)
Quantum Mechanics, The Micro Universe (Things smaller than an atom and low energy/mass)
Neither theory works or can be applied to the other scale.
There is a third case
Objects that are small and massive/high energy (Black Holes)
Quantum Mechanics and General Relativity break-down for this case ===> Neither can be used to Analise the paradox ===> You cannot use a combination of both to Analise the paradox ===> The paradox cannot be resolved with current theory ====> We will resolve the paradox when we have a working Grand Unification Theory.
What’s the best solution for a company that wants to securely receive documents from other business partners electronically. The company in question frequently receives documents containing financial information from other external entities. The company would like to ensure that the documents being received are securely transmitted.
Is this enough reason to set up a VPN or would the use of encrypted files over the internet be a better solution?
A good VPN is secure from point to point and nobody can break into the tunnel. (we’re talking real VPN’s here not the PPTP stuff that comes with Windows) However the 2 end points where there is no encryption can still be compromised. For example you send a document over the VPN via Email. Totally secure over the connection and nobody is going to get that file. But once it enters your network and goes over you local network anyone can packet sniff the network and grab the email.
This is where encryption come into play. Use a good encryption program like PGP, True Crypt etc and secure the document with something like 256 AES and you have no worries until it lands on your desktop and you decrypt it.
Using both and VPN and encryption is still a good idea since if someone forgets to encrypt a document at some point at least it’s not floating around the internet waiting to be grabbed.
A solution of H2S and a solution of Cl2 of equal volume were mixed together, resulting in a final total volume of 110 mL and a concentration of H2S of 1.1 mol L-1. What was the original concentration of the solution of H2S?
Because Cl2 and H2s wont react with each other the only effect of this mixing is a change in volume and so in concentration of H2s . And because two volumes are equal the new concentration will be half of the original one .
When 3g of KNO3 is added with about 2mL of water in a test tube, and is inserted into a beaker of water that is at 85 degrees celcius until the solid completely dissolves. Then the test tube with the solution is taken out, and stirred until crystals form.
What property of the solution is illustrated at the moment crystals start to form?
The property that is being illustrated here is the saturation of the solution. When the solution starts to form crystals, it indicates the solution is saturated, meaning it has reached its maximum solubilty for KNO3.
No Solutions as the solution. Show the steps to solving the equation and explain in words why your work proves that there are No Solutions.
Thank you.
You are welcome.
I am doing a qualitative analysis lab, and I have only two solutions left; one is aluminum and one is zinc. How can I distinguish them? At my disposal, I have sulfuric acid, hydroxide ions, and all group 1 and 2 metals in solution with various anions.
You can add HCl to both of them; only Zinc Chloride can be produced at room temperature (AlCl3 needs very high T) and you can verify the presence of ZnCl by recrystallization.
A student makes a standard solution of sulfuric acid by taking 100.00 ml of a super-concentrated stock solution and diluting it to 2.50L. He then standardizes the diluted solution by titrating 40.00ml with 28.58 ml of a 0.4050 M solution of KOH. What is the concentration of the standard solution and the stock solution?
moles KOH = 0.4050 M x 0.02858 L=0.01157
H2SO4 + 2 KOH = K2SO4 + 2 H2O
moles H2SO4 = 0.01157/2 = 0.005787 in 40.00 mL
moles H2SO4 in 2.50 L = 0.005787 x 2500/40.00=0.3617
initial concentration = 0.3617 / 0.1000 L = 3.617 M