Expression Definition and 999 Threads

Is the statement "if you are a comedian then you are funny." equivalent to what is defined in part (a)?

How to go about solving this one? (1-i)-1+i so far i have tries using the famous Uv=ev(ln(U) im stuck where i get e-1/2ln(2)+(pi/4)-2kpi*ei(-1/2ln(2)+(pi/4)-2kpi)

Find all possible Values of: 2(-i)

Homework Statement Simplify: (sin t + cos t)2 / sin t cos t Homework Equations tan t = sin t/cos t cot t = cos t/sin t cot t = 1/tan t The Attempt at a Solution (sin t + cos t)2 / sin t cos tsin2 t + 2sin t cos t + cos2 t / sin t cos t(sin t/cos t) + 2 + (cos t/sin t) tan t + cot t + 2...

Homework Statement Simplify: [(sec x)(sec2 x) - (tan x - 1)(sec x tan x)] / sec2 x Homework Equations none The Attempt at a Solution [(sec x)(sec2 x) - (tan x - 1)(sec x tan x)] / sec2 x [(sec x)(sec2 x) - tan x (1 -1) sec x ] / sec2 x [(sec x)(sec2 x) - 0 ] /...

Homework Statement Eliminate the denominator on the RHS of the following expression sin(\alpha)-sin(\beta) = -\frac{-v(sin(\alpha) cos(\alpha) + sin(\alpha) cos(\beta)}{c-vcos(\alpha)} and from it, derive sin(\alpha)-sin(\beta) = -\frac{v}{c}(sin(\alpha)cos(\beta)+sin(\beta)cos(\alpha))...

How exactly might one go about showing that \left| \frac{1 - e^{-iy}}{-iy} \right| is bounded by 1 for y\in \mathbb R? I thought this would be easy to show using the series expansion of e^{-iy} in some way: \left| \frac{1 - e^{-iy}}{-iy} \right| = \left| 1 - \frac{iy}{2} -...

Homework Statement Find the Inverse Laplace Transform of \frac{1}{(s^{2} + 1)^{2}} Homework Equations The Attempt at a Solution I tried using partial fractions but it didn't work. It looks like a cosine transform, but I don't know what else to do. Help please :(

Homework Statement I am attempting the problem below, I might have the correct answer but would appreciate if someone could confirm this (or tell me where I'm going wrong). Consider a statement having 2 states, one at energy 0 and one at energy ε. Find an expression for the Helmholtz free...

What is the units digit of $$\left\lfloor \frac{10^{20000}}{10^{100}+3} \right\rfloor$$?

How to write something similar to the following Or is it better to write $$\sum_{n=k ,m=1}^{k+1}$$

I tried to check x²-1 = (x+1)(x--1) So I did the following: Matlab returns 0. Any suggestions? :) (Matlab beginner by the way)

Hello, I'm trying to solve this equation. (4-4cos(∏*0.16*4)) - (4-4cos(∏*0.16*3)) It seems like it should be so easy. First I start with the left hand side (∏*0.16*4). Then I take the cosine of that, and then multiply it by 4. Then I do 4 - [answer] to get a value for the full left side...

Find the value of $$z = \frac 1{\cos x} + \tan x$$ given $$\frac 1{\cos x} - \tan x = 2$$. By squaring and using trigonometric identities on the given equation, one can arrive at $$\frac {1- \sin x}{1 + \sin x} = 4$$ The unknown expression $$z$$ can, by squaring, be written as $$z^2 = \frac...

Evaluate $$\tan\frac{\pi}{13}\tan\frac{2\pi}{13}\tan\frac{3 \pi}{13}\tan\frac{4\pi}{13}\tan\frac{5\pi}{13} \tan \frac{6\pi}{13}$$.

Homework Statement - 1/[cosx(cos(x-90))] The Attempt at a Solution = - 1/[cosx(-cos(90-x))] //so first I take the negative sign out from (x-90) to make it (90-x) = +1/[cosx(cos(90-x))] // negative sign from outside the cos and outside the entire fraction combine to...

Suppose we have $$[Q^a,Q^b]=if^c_{ab}Q^c$$ where Q's are generators of a Lie algebra associated a SU(N) group. So Q's are traceless. Also we have $$[P^a,P^b]=0$$ where P's are generators of a Lie algebra associated to an Abelian group. We have the following relation between these generators...

Homework Statement If ##\displaystyle \tan\left(\frac{\pi}{4}+\frac{y}{2}\right)=\tan^3\left( \frac{\pi}{4}+\frac {x}{2} \right)##, prove that $$\frac{\sin y}{\sin x}=\frac{3+\sin^2 x}{1+3\sin^2x}$$Homework Equations The Attempt at a Solution...

Homework Statement Find the exact value, without using a calculator. \ cos(\frac{\pi}{15}) \ cos(\frac{\pi}{45}) The Attempt at a Solution I started off using a product to sum formula- \frac{1}{2}[cos(\frac{4\pi}{45})+ \ cos(\frac{2\pi}{45})] Now I don't know where to...

Is there a way to express ##{n\choose k}{n\choose r}## in another form without n as the "top" of the binomial coefficient? I remember seeing it once but I forgot what it was.

how would you simplify this $\displaystyle \frac{1}{5}\ln|\sin5x|+\frac{1}{5}\ln|\csc5x-\cot5x|$ please explain.

Without the use of a calculator, evaluate $$\tan^2 20^{\circ}+\tan^2 40^{\circ}+\tan^2 80^{\circ}$$.

Homework Statement If ##\beta## is such that ##\sin 2\beta≠0##, then show that the expression ##\displaystyle \frac{x^2+2x\cos\alpha+1}{x^2+2x\cos\beta+1}## (x real) always lies between ##\cos^2\alpha/\cos^2\beta## and ##\sin^2\alpha/\sin^2\beta##. Homework Equations The Attempt at...

Homework Statement An electric dipole is located along the y-axis as shown in (picture attached). The magnitude of its electric dipole moment is defined as p=2aq. (a) At a point P, which is far from the dipole (r>>a), show that the electric potential is V=\frac{k_{e}pcosθ}{r^{2}} (b)...

As shown, I must derive a formula to find work. http://i.imgur.com/0U0eLqm.jpg I proceeded as follows. W= F * D = (B * I * L) * D V = BA/T I = V/R = (BA/t)/R = BA/tR F = B * (BA/tR) * A W = ((B^2*A^2)/tR) * A W = (B^2 * A^3)/tR Does that seem right? IIRC, the B*I*L formula is only...

Homework Statement Hi, I want to calculate the residue of this expression: Homework Equations I know that the residue of a function with a pole of k-th order is given by this: The Attempt at a Solution I know that the function has infinite number of poles at k*∏, for k=-∞ to...

Hi I am trying to find a smart way to write the following fraction, $$ F = \frac{a_1}{1+\frac{a_2}{1+\frac{a_3}{1+a_4}}} $$ Here we can just take a_n= n for simplicity. My fraction is in principle infinite, but I am trying to construct a function which can find F for a given n recursively. I...

Homework Statement \dfrac{tan\left( \theta + 2\pi /3 \right) - tan\left( \theta + \pi /6 \right) + cos\left( \theta + \pi /6 \right)}{\sqrt{3}} \\ \theta \in \left( -5 \pi /12, - \pi /3 \right) The Attempt at a Solution At maximum, f'(x)=0 sin(θ+∏/6)=0 But there is no theta in...

Heather Jean's of Facebook writes: Simplify, \[-(6y-\gamma)-5(-\gamma+6y)\]

Hey, What are the steps to follow to draw a truth table and create canonical expression from a given expression A? Lets say I have A= B'.(C'+D) 1) first I have to draw the truth table for the expression above, but How could I do that since I only have one expression? 2)Then I...

Rewriting an expression...what math operation did my teacher do? I'm trying to see how did my teacher rewrite this expression in the following manner: What mathametical operation did he do? I really can't see it...

My basic math is failing me again :( My attempt to simply: My teacher's attempt: Ignore the difference in notation. He writes || which signifies (A x B) / (A + B) = A || B And yes I'm aware there is more to simplify but I fail to follow him on the first step

Homework Statement What is the pH of a buffer solution created by combining 100 mL of 0.2 M acetic acid and 400 mL of 0.10 M sodium acetate? Ka= 1.8 x 10^(-5)Homework Equations 1.8 x 10-5=([C2H3O2-][H+])/([HC2H3O2]) The Attempt at a Solution I know what I'm supposed to do to solve this...

for which value of a the expression write a*m*b+15*m+11*n+8 can be written into a product of something(with m)*something (with n) i can think how to find the product of this expression

I'm currently working out the Schrödinger equation for a proton in a constant magnetic field for a research project, and while computing the Hamiltonian I came across this expression: (\vec{A}\cdot\nabla)\Psi where \Psi is a scalar function of r, theta, and phi. How do you evaluate this...

Hey Guys I am Currently doing my degree in information systems. At the moment the subject is PLC(Processing and Logic Concepts) I understand all of it, I am not sertain on how to start reducing a boolean expression. Once the first step is done I normally get it and can complete the...

I need help figuring out what the little 2 next to an equation means this is what my problem looks like I have the answer but I can't figure out how it was found out. (3)(-4)2 - (3)(-5) so the 2 next to the 4 in parentheses is little.

Hi, I am trying to incorporate the following equation into Matlab in the red: http://http://www.radikal.ru][PLAIN]http://s018.radikal.ru/i518/1305/16/1cc0d2a72d38.jpg The following data is to be used: t=3000000 nr=nx=161 q=0.02 k=5e-13 mu=0.00035 c=1.5e-8 phi=0.25 rw=0.1 h=4.5...

Homework Statement ((a^3-b^3)/(a^2-2ab+b^2))/((2a^2+2ab+2b^2)/(9a^2-9b^2)) Not using complex number system. Not concerned with domain. Find the quotient and put it in simplest terms. Homework Equations The Attempt at a Solution Too many to transcribe. Apparently I'm missing...

So, energy is simply a mathematical expression of how much work is done in the system? Since energy is not a "physical" object that has mass. It's not matter at all. If so, the laws of conservation makes sense, it can't be created nor destroyed. But I can't imagine how a mathematical...

Evaluate $$\cos \left(\frac{\pi}{65}\right)\cdot\cos \left(\frac{2\pi}{65}\right)\cdot\cos \left(\frac{4\pi}{65}\right)\cdot\cos \left(\frac{8\pi}{65}\right)\cdot\cos \left(\frac{16\pi}{65}\right)\cdot\cos \left(\frac{32\pi}{65}\right)$$.

I have 17 elements, and I want to put them in 3 sets. This makes 2 sets with 6 elements, and 1 set with 5 elements. Now I want to find an algorithm to partition n elements in k sets. Can anyone give me an algorithm, or a math expression for me to implement in a algorithm? Thanks

Factor the expression $$30(a^2+b^2+c^2+d^2)+68ab-75ac-156ad-61bc-100bd+87cd$$

Homework Statement Reduce the Expression: 15sin(wt-45°) + 5cos(wt-30°) + 10cos(wt-120°) to the form Vmcos(wt+θ) Homework Equations The Attempt at a Solution My theta value at the end isn't coming out right. My first step was to put make sure each term was in terms...

I have a 9 input to 9 output truth table I constructed using Python. I am trying to find a program that can deduce the (hopefully minimized) Boolean expression for my outputs. I tried Logisim already, but when I try to paste the enormous data (512 rows), my Logisim crashes. Can anyone recommend...

Decompose the expression below into real factors: $$1-\sin^5 x-\cos^5 x$$

Hii All, $ \sum_{i=1}^{x}i^{N}:N>2 $. Is there any approximated lower bound for the above summation? Is it > $ \frac{1}{N+1}x^{(N+1)}$ ? If yes, how to prove that?regards, Bincy

The Laguerre polynomials, L_n^{(\alpha)} = \frac{x^{-\alpha}e^x}{n!}\frac{d^n}{dx^n}\left(e^{-x}x^{n+\alpha} \right) have n real, strictly positive roots in the interval \left( 0, n+\alpha+(n-1)\sqrt{n+\alpha} \right] I am interested in a closed form expression of these roots...

Can someone please show me how to simplify this expression? I have no clue of how it's done so any help would be appreciated. Thank you! x'y'+xz'+yz+x'yz'+xy'z

Homework Statement Let z = 2 + i and u = -3-3i. Calculate the value of |z/u|. Homework Equations None. The Attempt at a Solution |z/u|=|(2 + i)/(-3-3i)| = |(2 + i)/(-3-3i)*(-3+3i/(-3+3i)| --- if it is not clear, I'm multiplying by the conjugate. = |(-6+6i-3i+3i^2)/(9-9i+9i-9i^2)|...