Base Definition and 586 Threads

<Moderator's note: Moved from a homework forum.> 1. Homework Statement Given 0 < a < 1, i = √(-1), ei2πa = cos 2πa + i sin 2πa but also, ei2πa = (ei2π)a = 1a = 1 How to resolve the apparent contradiction?Homework Equations eab = (ea)b eix = cos x + i sin xThe Attempt at a Solution No clue...

To start with problem #5 i cut the shape Into 2, a triangle and a square, i know that the additional leg length to the triangle can be found by subtracting base 1 and base 2=4 so i have a triangle with a hypotenuse of 8 inches, 1 leg=4 and now i have to find the length of the other leg. The...

I would think that the use of triple base propellants in hand-held weapons, such as assault rifles or pistols, would be greatly beneficial as its use would remove the muzzle flash. Also, it would decrease wear-and-tear on the weapon itself, I would think. I have found some people saying that...

how can i write 17 x 4^4 with respect to base 4? here is what i did: i divide 17 by 4 twice and get 101 on base 4, and then say 1 x 4^6 + 1 x 4 ^ 4 is it correct?

I was wondering if anyone could point me to a set of rules for finding the base of an exponential function? I can figure out that the base of f(x)=7^x is 7 and the base of f(x)=3^{2x} is 9 but even though I know f(x)=8^{\frac{4}{3}x} has a base of 16, I don't know how that answer was reached.

interested in efficiency metrics with regard to our base-load infrastructure... this information is not readily available. I think that renewable stuff has its place only after we make the most of our base plants with load shifting. The base plants exist, and they waste energy. I simply do not...

Homework Statement The SO(3) representation can be represented as ##3\times 3## matrices with the following form: $$J_1=\frac{1}{\sqrt{2}}\left(\matrix{0&1&0\\1&0&1\\ 0&1&0}\right) \ \ ; \ \ J_2=\frac{1}{\sqrt{2}}\left(\matrix{0&-i&0\\i&0&-i\\ 0&i&0}\right) \ \ ; \ \...

Homework Statement [/B] I am reviewing an example on the basics of the genetic code; this example is listed at the bottom of the following webpage: https://www.atdbio.com/content/14/Transcription-Translation-and-Replication.I have produced the example below and added Roman numbers to better...

Homework Statement Which of the following combinations would act as buffered solutions? a. HCl and NaCl b. CH_3COOH and KCH_3COO c. H_2S and NaHS d. H_2S and Na_2S Homework Equations none really... The acid needs to be weak and the base strong though. The Attempt at a Solution HCl is one...

If we put NaOH in water then it disassociates into ##OH^{-}## ions(hydroxyl ions) but if we put ##C_2H_5OH## in water it does not disassociates into ##OH^{-}## ions. What is the reason that ##NaOH## disassociates into ##OH^{-}## ions(hydroxyl ions) whereas ##C_2H_5OH## does not disassociate...

Homework Statement [/B]Homework Equations For 1st I think answer is B For second I(c) = B I(b) B is beta The Attempt at a Solution For 1st I think it's B But book says answer is D Is book wrong? For second I'm getting: I(c) = 3mA And beta = 200 So I(c) = B I(b) 3mA = 200 I(b) This gives I(b)...

Homework Statement A trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has a height of 50 cm. If the trough is being filled with water at the rate of 0.2m3/min, how fast is the water level rising when the...

Hello. I wanted to discuss an interesting recent article on space.com which talks about a book released on the 14 November talking in incredible detail about a Moon base. The article features an interview with the author describing the book and his intents. Cool.

CRISPR is often used to switch out a length of DNA for a different piece of sequence, which can change several base pairs at once. crispr-derived-base-editors-surgically-alter-dna-or-rna-offering-new-ways-fix?utm_campaign=news_daily_2017-10-25&et_rid=33537079&et_cid=1624006']Here is a Science...

Let ##P## be a ##U(1)## principal bundle over base space ##M##. In physics there are phenomenons related to a loop integration in ##M##, such as the Berry's phase ##\gamma = \oint_C A ## where ##C(t)## is a loop in ##M##, and ##A## is the gauge potential (pull back of connection one-form of...

Why is it that all group 15 element's trihalides except Nitrogen on hydrolysis gives an acid while Nitrogen trichloride give ammonia which is a base on hydrolysis?

I was thinking of a hypothetical waste system that uses nanotechnology to its advantage. At the individual level, waste just passes through into pipes when flushed like it normally does. But once it reaches the water treatment plant there is an initial filter to catch solid waste(in other...

Hello, working on a puzzle and I think this may be what I need to do to solve it. I have a long string of characters,752 total with the range 0-9 and a-f. I believe that the data needs to be aligned based off the processor and memory. The Cpu is at 2800MHz and the memory is 1024MB. Is there a...

Hello Guys, I'm currently entering my final month of my Bachelors in Mechanical Engineering. I've always wanted to learn more about robotics and Artificial Intelligence ,But never really put the time into it during my bachelors. I'm considering taking a break next year and applying for an MS...

I want to plot a function f(x) such that it's domain is from 1 to 10000 but I want the graph to read 1, 10, 100, 1000, 10000 in the x-axis, while the y-axis is normal. ##f(x) = 2\sin^{-1} ( e^{-\frac{60}{x}})##

If y=sin5 + log base 10 x + 2 sec x find dy/dx Please solve the problem

The question: What happens to the extra hydrogen when the base pairs combine? For example the formula for Adenine and Thymine are C5H5N5 & C5H6N2O2. So when combined there should be 11 hydrogen, however in the diagrams for A and T when together only show H9. 2 off. Same with G and C...

I'm kind of new in this. Now, I'm especially talking about npn common emmiter configuration. I've read somewhere that base is made narrower to stop the recombination of minority charge with holes in base. And I assume that if base would broad then electron combine with holes creating strong...

Negative number multiplied by itself an even number of times gives us a positive number. Why does log to -10 base of 100 not equal 2? thanks in advance.

Hello PF friends, My name is Visakhan,and I'm presently pursuing my BE in Mechanical Engineering in India. 3/4 way through the course now,But I feel unsatisfied with my grasp of mathematics and programming. I scored marks and passed the examinations,but i don't get that feeling of satisfaction...

Homework Statement To unclog a drain you add 26g of sodium hydroxide to 150mL of water. Calculate the pH and pOH for the solution you prepared. Can someone tell me if I'm doing it right. Homework EquationsThe Attempt at a Solution n = m/M n = 26/40 n = 0.65mol for 0.15L Does this mean that I...

Which of the following statements about weak acids and weak bases are false? (i) The strength of a weak acid decreases as itspKa decreases. (ii) Weak bases react with water to produce a small amount of a strong base. (iii) The strength of a base decreases as the strength of its conjugate acid...

Homework Statement I conducted a titration experiment in which 0.1g of KHP was dissolved in 50mL of distilled water and placed in an Erlenmeyer flask. I filtered a Ca(OH)2 solution (that was left out open on the lab benches for us to use) and put that into the burette and titrated. Ultimately...

I am hoping someone can assist a non engineering person figure something out and is probably the oddest question you will get. I have built a life size version of Han Solo In Carbonite (HIC). It is 80 inches tall and 32 inches wide at the base. It weighs about 125 pounds with most of the weight...

Homework Statement Show that the moment of inertia of a hollow cone of mass M, radius R, and height h about its base is ##\frac{1}{4}M(R^2+2h^2)## Homework Equations ##I=\int r^2dm## where r is the perpendicular distance from the axis Surface Area of a cone ##= \pi R (R^2+h^2)^{1/2}## The...

Homework Statement In this video , why for the xy plane projection , it's a circle with center = y = 1 , i can understand the r = 2sin theta ? why we can't ∬ r dr dtheta where , r = 1 , and with theta = 0 to 2 pi ? They are the same , right ? since volume = integration of area with z a-xis...

Hey guys, Trying to design a spur gear but I am very confused as the root circle/dedendum ends up being greater than the base circle. What do I do in this case? The gear I'm trying to design has a 68.33mm pitch diameter, 60 teeth, the pressure angle a standard 20 degrees. What am I doing...

Using the regression eqn. Find the base resistance of the thermistor. Find the temp. Of the boiling water using this eqn. Y=1.54e^-0.059x How do I go about solving this problem

Homework Statement I am a little stuck/unsure in an homework question for my signals and systems course. See question sheet attached. I have been able to do question 1 for the first section using FBD, and I have solved the DE using Laplace Transforms (See below for my solution). I am both...

Hi again dear friends. , hope all are doing well. Please could some one evaluate my work and advise me in case any correction is required. Have a good day

what happens in the common base type of a transister,if we interchange the input to output and output to input? i suppose that the current gain >1 .so this would use for amplification...

Homework Statement Given: AD=DC = 9m P=78kN S=25Kn Angle alpha = 35 deg A is static but B is movable I need to solve forces on the bases A and B I do not understand where do I mark the forces if there is a base that can move. Homework EquationsThe Attempt at a Solution My attempt: I am...

Homework Statement We call a seven digit number in base eight X, whose digits are given by ##abcdefg## No digits are zero, and none of them are the same. The following divisibility rules are true: (I)The number ##ab## is divisible by 2 (II) The number ##abc## is divisible by 3 (III)The...

Convert the following expressions to the indicated base using base 14 for a < 0 & a not equal to 1.$a^{5/\log_9a}$ So i been stuck for 1 hour trying to figure out this problem may anyone guide me please

Convert the Following expression to the indicated base, using base 14 for a > 0 & a \ne 1.[MATH]{a}^{\frac{5}{log}_{9{}^{a}}}[MATH]

I do not know why can they classify 5 theories of superstring.Is that correct that they base on different symmetries?

If our base space, B, is Minkowski spacetime and our fibers are circles S^1 are the following constructions ways to put together B and S^1 and have a total space, T, that is considered a fiber bundle. Remove from Minkowski spacetime, M, a timelike line, L. At the remaining points of Minkowski...

Lets suppose in not so far future we want to build a research base on Mercury. What would be the main hardships and benefits? For the later, it could gain lots of information about solar flares and storms, solar panels could give it more than enough energy, and if it is landed on North pole it...

I don't know how to calculate the voltages at the bases of every transistor shown in the lower row of that picture (~3V (2.9..V), ~2V, ~1.8V). Any help would be appreciated! - I'm currently trying to figure that out... The other thing I don't really understand: Why do the transistors in the...

Homework Statement Homework EquationsThe Attempt at a Solution From what I know, to make buffer solutions you need a weak acid or base and it's salt. Non of the options has this. What am I missing? Cheers!

Homework Statement Homework Equations Henderson-Hasselbalch Equation The Attempt at a Solution Sorry for the huge picture, but the number says 0.007558 mol. Is my ICE table correct? Equation: 7.42 = 6.85 + log((0.007558-x)/x) (0.007558-x)/x = 3.715 x = 0.00160 mol H+/(0.07483 L + 0.01339 L)...

Hello all, I have a problem to understand a pnp transistor with base (B) connected to collector (C). When I set the VE (voltage of emitter) at 0 V and the VB, which is the voltage of base and collector nodes, since they are tied together), decrease from 0 V to -1.0 V,the simulation result shows...

Homework Statement In the reaction with NH3, is specy BH3 a Lewis base ? Homework Equations Lewis acid = electron acceptor Lewis base = electron donor The Attempt at a Solution H electronegativity = 2.1 B electronegativity = 2.0 N electronegativity = 3 Since N-H bond is more electronegative...

Just out of curiosity, why is the Ampere a base unit and not the Columb? It seems to me that charge is more fundamental than current. Thanks!

Homework Statement (1/25)^x+3=125^x+3 Homework Equations I have used log on both sides but keep getting an incorrect answer. The Attempt at a Solution How would solve this type of equation. I set the bases both to 5, make them equal to each other and i can't get the right answer.