Base Definition and 586 Threads

Suppose for a given matrix A, Sarah finds the eigenvectors v1 = [1 3 4 5]' and v2 = [5 6 3 4]' form a base for eigenspace of labmda = 2. Now suppose Janie finds the eigenvectors v3 = [1 2 2 3]' and v4 = [7 8 7 6]' form a base for eigenspace of lambda = 4. Is Janie's solution compatible with...

Is there a way to calculate multi digit base 10 logs without a calc or tables? eg.. what is ? log (base 10) of 1381.42?? (without a calulator)??

Hello, everyone. I would like to get some concrete examples of the number of distinct bases of k-dimensional vector space W over a finite field F with q elements. The formula for the number of distinct bases of W is ( p 412 Dummit ) (q^k - 1 )(q^k - q)(q^k - q^2)...(q^k - q ^(k-1) ) I...

Question: Decimal (10-nary) expansions of real numbers were defined by special reference to the number 10. Show that the real numbers have b-nary expansions with analogous properties, where b is any integer greater than 1. Attempt at solution: I think if I show that there is a bijective...

1. A transformation from base S to base T. The three combinations C(x)=(-1/sqrt(2))(C(+) - C(-)), C(y)=(-i/sqrt(2))(C(+) - C(-)) and C(z)=C(0) transform to C'(x), C'(y) and C'(z) just the way that x,y,z transform to x',y' and z'. You can check that this is so by using the transformation laws...

I'm writing an exporter for 3d studio max and i want to export skeletal animation. 3D studio max uses a coordinate system that has the X axis going from left to right, the Z Axis going from bottom to top and the Y axis going from front to back. Opengl uses a left handed coordinate system, whilst...

I was wondering if the Golden ratio base (phinary system) has any use somewhere and if arithmetics with it is easy? I programmed a surprisingly simple algorithm to calculate the logarithm yielding digits in base phi using nothing more than 2 multiplications/divisions per result digit. Can it...

Hi All I have a question that I require an answer to. For the above titration, concentration of A-(conjugate base of acid) is the same as concentration of HA at half equivalence. It is at this point that pka=ph of the solution. I agree to this conclusion, but why is the concentration of A-...

I know that logarithms to the base 1 is undefined, due to the reason that: \log_1{x} = \frac{\log_a{x}}{\log_a{1}} And this leads to divison by zero, which is undefined. There was a question in one of my textbooks that asked describe the graph that results if y = \log_1{x}. Is such a graph...

So I was browsing Wikipedia, and I stumbled across this article: http://en.wikipedia.org/wiki/Conway_base_13_function The article claims that the Conway base 13 function, as a function from (0,1) to the reals is a counter example to the converse of the Intermediate Value Theorem (i.e., that for...

the question is simply to determine the [OH-] and pH of a solution that is .210 M in HCO3- first of all if i can get [OH-] then i can easily get pH by converting [OH-] to [H+] and then doing the -log[H+] so that part is easy. i just cannot get [OH-] what i did was first write the...

Homework Statement Calculate \int_{0}^{4}\sqrt{x} e^{\sqrt{x}) The Attempt at a Solution At first I tried substitution, but this didn't bring me anywhere since the integral is not of the form \int f(g(x))g'(x) My attempt at integration by parts also leads to an endless loop...

http://en.wikipedia.org/wiki/Dot_product" is a Wikipedia about the Dot-Product, which includes the relevant section on Rotation. Given the first example- is it correct where it says "Notice that the rotation matrix R is assembled by using the rotated basis vectors u1, v1, w1 as its rows, and...

i have been trying to solve this problem for about 14 hours and have gotten nowhere, I am trying to figure out the voltage going into the base of an npn transistor, I am trying to build a circuit where i can take the current from the battery and build a circiut from 7npn transistors in a common...

I have been grappling with this one for the past 24 hours. I'll make this baseball related, consisting of three independent events assuming the following: Player A has a 40% chance of stealing a base in "his game" tonight. Player B has a 60% chance of stealing a base in "his game" tonight...

Base heads, or zombies with £5000 worth of mega watt audio in their cars, from now on i am going to carry a spud with me, and it is going right up the next ones exhaust, and i am not joking, they are talking about them on the radio now but they are only going half way in describing how annoying...

i can't understand how it works: i have two bit numbers (x1 x0 ,y1 y0) which are needed to be subtructed i can't understand why x1 x0 y1 y0 | B D1 D2 0 0 0 1 | 1 1 0 0 0 1 0 | 1 0 1 0 0 1 1 | X X X i can't understand these arithmetics the first one is 0-1=-1 so in base 3 the...

First of all, I don't really know if this problem corresponds to this section, but anyway I have this as a probem in my matemathical physics class. The problem is stated something like this: Find the matrix elements of the position and momentum operators in the legendre base (on the...

Homework Statement Titrating .1006M CH3COOH with .2012M NaOH. pKa=4.74, Ka=1.8*10^-5 What is the pH at the equivalence point of the titration? Homework Equations pKa = -log(Ka) pH = -log[H+] The Attempt at a Solution Alright, after setting up an ICE table (in order to find...

In my lab, I'm trying to identify an unknown compound. So I did a solubility test of the unknown into 5% NaOH. According to the manual it said that if it appears insoluble,take the supernatant out and add 5% HCl until neutral. If percipitate or turbidity results, it means the unknown is an acid...

Why is the enthalpy of neutralisation of a strong acid mixed with a strong base always the same, no matter what acid and base combination you use, provided they are 'strong' acids and bases? Am I right to say that this value is accepted as -57.35 kJmol-1? Thanks for any help, Isaac.

Homework Statement A buffer is prepared by dissolving 1.00 mole HLac (with a ka=8.0x10-3) and 1.00 mole of sodium lactate (NaLac) in enough water to form one (1) liter of solution. Calculate the [H+] and the pH of the buffer. 36 minutes ago - 3 days left to answer. Additional Details 12...

If The second is currently defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. And The meter is defined as 1⁄299 792 458 of a light-second. Then Why can't we...

Homework Statement We want to make an open box with squared base. Let x be the dimension of one side of the base and y the height of the box. We pay a cost of $1.00 /cm^2 for the base and $0.50/cm^2 for each side. The box must have a volume V = 6400 cm^3. Determine the dimensions x and y...

Homework Statement We did a lab in class about weak acid/strong base titration, but I'm having a bit of trouble. We we only given the molarities of an unknown weak acid and a strong base (NaOH) and the pH of six different mixtures containing different mL of the two, which is below: Test...

Homework Statement There are two groups of bases, one that contains OH- (example : NaOH), and one that forces water to form OH- (example: NH3). Which of these are the stronger bases? Which are the weaker bases? Why? Ok so our class just started learning about acids and bases. I've read...

Hi I have been trying several days to solve this problem. But i can't find the procedure to solve this weak acid and weak base problem. I will really appreciate some help. What is the pH of a soft drink in which the major buffer ingredients are 6.90 g of NaH2PO4 and 5.70 g of Na2HPO4 per...

Hi I have been trying several days to solve this problem. But i can't find the procedure to solve this weak acid and weak base problem. I will really appreciate some help. What is the pH of a soft drink in which the major buffer ingredients are 6.90 g of NaH2PO4 and 5.70 g of Na2HPO4 per...

I am building a robot for a design class. Part of the design includes a wheel base to drive the robot forward. To accomplish this I was going to attach a spur gear system to a wheel axel and drive the input gear with an electric motor. The gears themselves will be made out of acrylic and cut...

Homework Statement A 0.307g sample of an unknown triprotic acid is titrated to its equivilence point using 35.2ml of 0.106 M NaOH. Calculate the molar mass of the acid. Answer is in g/mole. Homework Equations The Attempt at a Solution I just don't know where to start with this...

25 mL of 0.1 M HOAc are titrated with 0.15 M NaOH. What is the pH at equivalence? I know that the pH at start will be greater than 1.0 and the pH at equivalence will be greater than 7 since its a titration of a weak acid and a strong base. But what I don't know is whether or not there is a...

Homework Statement In the binary number system 1100011 is the name for the largest 2 digit palindrome in base ten. What base 10 number does this binary number represent? Homework Equations None The Attempt at a Solution My question about this problem is the 2 digit part is...

1. Homework Statement Every separable metric space has countable base, where base is collection of sets {Vi} such that for any x that belongs to an open set G (as subset of X), there is a Vi such that x belongs to Vi. 2. Homework Equations Hint from the book of Rudin: Center the point...

Homework Statement Every separable metric space has countable base, where base is collection of sets {Vi} such that for any x that belongs to an open set G (as subset of X), there is a Vi such that x belongs to Vi. Homework Equations Hint from the book of Rudin: Center the point in a...

Hey Guys, I seem to be having some problem with this question. Can anybody help me out? Each of the following salts can be prepared from an acid and a base. Write the balanced molecular equation and net ionic equation for the preparation for each. Indicate states of the reactants and the...

Hi. In class, i am required to perform a titration where i am given a solution of sodium carbonate and a solution of hydrochloric acid of known concentration. I am to use the acid to calculate the percentage purity of the sodium carbonate. Im not really sure how to go about doing this. The...

Homework Statement 1) Let D_n-1 D_n-2...D_0 be a n-digit unsigned number with base(radix)=b. How much is it in decimal? 2) How can you convert 301_10 to a number with base b? 3) What is the range of n-digit unsigned integers with base=b? Homework Equations The Attempt at a Solution D_(n-1)...

Homework Statement 2^x=1500. solve for x. I need to know the key strokes on my scientific calculator. If I push log, it assumes log base 10. I need base 2. Homework Equations The Attempt at a Solution

For some reason I'm having issues today figuring out what size base plate to make for a post that has a 30lb wieght at 50" from the floor? Does anyone have a simple formula? I just want to post to not tip over without any outside forces acting on it. Thanks.

Base conversion -- the LOGIC and INTUITION behind it... for example, converting from base 10 to 2, a systematic way is to divide the number by 2's successively and keep track of the remainder. the remainder coefficients represent the binary number. Now why does this work is beyond me but I...

Homework Statement Do not understand the question. 2. My Lab Results Topic : Volumetric analysis - Acid base purpose : To determine the exact concentration of a mineral acid, HXO4, and to determine the relative atomic mass of the element X. Materials : KA1 is a mineral acid, HXO4...

Check this out: In base 2 take all (or the first several hundred thousand) the odd numbers and figure out the mirror image of the bit string for each number. Ex: mirror of 11111 is 11111 mirror of 1011101 is 1011101 mirror of 100000001111 is 111100000001 You can't really mirror an even number...

Hello everybody, I'm having difficulty understanding the rationalization behind the strengths of Bronstend Lowry acids and bases and my textbook isn't too helpful. Can someone please expalin to me: (1) What exactly is effective negative charge density? (2) how does electronegativiy correspond to...

Can somebody tell me the color the following items turn when purple Cabbage Indicator is added: Water Hydrogen peroxide Isopropyl alcohol Saline solution Aspirin Pepto-Bismol Alka-Seltzer Tonic water Vinegar and can you tell me if the items listed above are Acid or Base or Neutral...

does anyone know how to answer this problem? A spaceship ferrying workers to Moon Base I takes a straight-line path from the Earth to the moon, a distance of 384,000 km. Suppose it accelerates at an acceleration 20.6 for the first time interval 16.0 of the trip, then travels at constant speed...

When fractions F1 and F2 are written as base n decimals, F1=(.7373)base n and F2=(.3737)base n. In base m, F1=(.5252)base m and F2=(.2525) base m. Find (m+n). No trial and error please.

Why amonia NH3 in water acts as a base and not an acid? Thanks

The Ph of 0.3mol/l of a weak base is 10.66, calculate kb. I was thinking of using ph and calculate the concentration of H ions and then calculate poh and OH, but don't know what to do next. Any ideas?

please i need your help, this question is from my midterm exam ineed solution very quick, it is due next week! "your finger can provide an (n-1) multiplication table in base n, 2<=n<=10 as follow: hold n fingers in front of you. to multiply (n-1) by k in base n, lower the kth finger from the...

Homework Statement In aqueous base, 97% of 2,2-diphenylethanal is present as a species different from the aldehyde, enol or aldol addition or condensation products. What is this species? Please also try to explain the mechanism. Homework Equations The Attempt at a Solution...