Unit Definition and 1000 Threads

The position vector is r(t)= \sqrt{2}t\bar{i}+e^{t}\bar{j}+e^{-t}\bar{k} and it is asking for the unit normal vector at the parameter which is t=0. I have tried this problem many times and I guess it is all of the simplifying that is driving me bonkers! [b]2. I know that to find the...

Homework Statement I'm trying to take the laplace transfrom of t H(t) where H(t) is the unit step function. Also, in a separate problem I get e^{-t} H(t) - e^{-t}H(t-1) and I am wondering how to manipulate it properly Homework Equations L \{ f(t-a) H(t-a) \} = e^{as}F(s) The...

Question: Show that if R is an integral domain then R^x=R[x]^x(or that the units in R[x] are precisely the units in R, but viewed as constant polynomials).

Homework Statement Homework Equations Torque is equal to the derivative of angular momentum with respect to time The Attempt at a Solution I took the derivative of each function given in parts a - d and plugged in the value for t to get my answer for the torque. I don't quite...

Homework Statement f is a polynomial with n variables (x1, x2, ... , xn) with real coefficients. Let Sn-1 = {x E Rn | x12 + x22 + ... + xn2 = 1} (n-1 unit sphere). Show that \exists b,c E Sn-1 such that m = f(b) \leq f(x) \leq f(c) \leq = M for all x E Sn-1. If f(x1, ... , xn) = a1x1 + a2x2...

Hey all, I'm working on a project where I'm trying to use the inherent dehumidification ability of air conditioners to remove moisture from a closed environment. I would like to estimate the amount of condensation (and hence moisture removal) that occurs. I don't have access to the air...

I am having a real tough time memorizing the unit circle and it's values. What would you suggest to make easier for me to remember the quadrants, square roots, and radians?

ok letsa say i have d/dt {(u(-2-t) + u(t-2)} I know that d/dt { u(t) } is q(t)... now is it correct to think that d/dt {(u(-2-t) + u(t-2)} = q(-2-t) + q(t-2) ?

I've picked up a 13.56 MHz RF generator from eBay which I plan to use for an ICP plasma project (this is what it was designed for). I need to construct an RF coil and parallel capacitor with a resonant frequency of 13.56 MHz but I also need to construct an AMU as, as I understand it, as soon...

hello there hi everybody just i have been taken my final exam for calculus one CALCULUS I there was one qeustion which i was confouse while i was reading it [SIZE="4"][FONT="Arial Black"]Set up the intgeral area of unit circle?

hello, if i have an integral like: Int( [-u(-t) + u(-t-1)] * a * dt, -Inf, +Inf)... where a is some constant.. what would be the correct initegration limits? the most important here is to determine correctly the integration limits.. if i solve the inequalities: -t > 0 => t < 0 -t-1 > 0...

The 1s radial function of the wave function of H atom is: R10=2 a-3/2e-r/a ,where a = 5.29*10-11 meter but substituting a with its value,we will get R10 = 5.2*1015 *e(-1.89036*1010 r) and that is impossible if r=a and R(r)=1.9*1015 where is the problem ? What's more, the unit...

Hi My textbook states that say 50 amu/atom = 50 g/mol. Which does not really make any sense. I am not sure how to get the atom unit. Since on wikipedia it says u = Molar-mass/Na Molar-mass(g/mol) = u*Na I also know that 1gram/Na = 1u

Homework Statement I am giving .15Mo/pc^3 how can i convert that into g/cm^3 mo is solar mass and its in grams and pc is distance so its in cm so wht would i do to convert it? Homework Equations The Attempt at a Solution would i just mutiply .15 by the solarmass(1.9e33g) than...

Where could I find a webpage or guide on how to write unit vectors in terms of sin and cos? I looked through my textbook and tried searching google, but I can't find anything...I must be using the wrong terminology. edit: Delete me! I had one of those epiphany moments and figured it out...

My book just gives me what each individual piece is but doesn't explain anything.

Hi everyone Consider a 2x2 partitioned matrix as follow: A = [ B1 B2 ; B3 B4 ] I'm sure that all eigenvalues of A are on the unit circle (i.e., abs (all eig) = 1 ). but, I don't know how to prove it. Is there any theorem?

How to explain unit vector visually?

The problem involves a spray drying process in which a liquid containing dissolved or suspended solids is sprayed into a chamber that has air flowing into it which contains water. One outlet stream has the wet air, and the other has dry solids. The Air inlet stream is described as having...

Unit Cell -- Linear Density -- BCC&FCC Homework Statement Calculate the linear density for the most densely packed directions in BCC and FCC. Note the difference in linear density. Note the difference in linear density. Homework Equations LD = #of atoms/length The Attempt at a...

Homework Statement The difference between structural unit and repeating unit Homework Equations The Attempt at a Solution http://en.wikipedia.org/wiki/Structural_unit wikipedia gives an example with polyethylene terephthalate but I can't figure it out based on the slight...

Homework Statement Find the unit vector e at P=(0,0,1) pointing in the direction along which f(x,y,z)=xz+e-x2+y increases most rapidly. The Attempt at a Solution In order to find the direction where f increases most rapidly, I found the second derivative of f. I don't know how to put the...

Homework Statement Need help with some unit conversion. The problem asks to find mass of a star. p=1.58e9 seconds a=7.61" d=8.15e18 cm +-.001 Homework Equations M=(4pie^2 d^3 a^3)/Gp^2 The Attempt at a Solution My problem is with " arcsecond i think it is. The mass should be...

Homework Statement Consider the points (x, y) = (0,0) and (100,10). Calculate the unit vector u pointing from the first to second. If each coordinate has an uncertainty of +/-2, calculate the uncertainty in u using propagation of error, but making reasonable approximations based on the values...

Homework Statement The area in the region inside the unit circle and above the graph of f(x) = x^5 Homework Equations I don't know how to type the equation in here but the area is the integral between two integration points of the higher curve minus the lower curve. The Attempt at a...

OK here's the problem. I am completely unsure how to solve it my teacher never even did an example like this before. The total force exerted on the top of the mast B by the sailboat's forestay AB and backstay BC is 180i- 820j (N). What are the magnitudes of the forces exerted at B by the...

OK here's the problem. I am completely unsure how to solve it my teacher never even did an example like this before. The total force exerted on the top of the mast B by the sailboat's forestay AB and backstay BC is 180i- 820j (N). What are the magnitudes of the forces exerted at B by the...

Homework Statement We are given the unit circle and the point (5,2). There are two lines that are tangent to the unit circle and they both intersect at the point (5,2). What are the points where these lines are tangent with the unit circle. Homework Equations Tangent line of a circle at...

OK here's the problem. I am completely unsure how to solve it my teacher never even did an example like this before. The total force exerted on the top of the mast B by the sailboat's forestay AB and backstay BC is 180i- 820j (N). What are the magnitudes of the forces exerted at B by the...

The question is: The total force exerted on the top of the mast B by the sail boats forestay AB and backstay BC is 180i-820j (N). What are the magnitudes of the forces exerted at B by the cables AB and AC? I need some serious help with this question. Any help.

Hello all, I already have the answer to my question, but what I would like to know is why. My question is: why in the question below is the plane 111 used to find ao and not another plane? An ordered compound of NiAl has a cubic structure with one formula unit/cell. One Al atom at...

Can somebody give me an example whereby I use the inversion with respect to a circle (unit circle or otherwise) and the problem becomes easier. I guess I am asking: how do I make use of this notion. Or a problem that involves inversion, period. Thank you

I need certain stopping criterion for approximating one unit vector with another. In case there is a perfect match (after a number of iterations), the dot product of the vectors is 1. I need to know (and have a reasoning for) whether in any other case the dot product of the original unit vector...

Homework Statement 4. Let w = f(z) = i(\frac{1-z}{1+z}). Show that f maps the open unit disk {z \in C | z < 1} into the upper half-plane {w\in C|Im(w) >0}, and maps the unit circle {z\in C||z|=1} to the real line. Homework Equations I was given this hint: "set w=i(\frac{1-z}{1+z}) and...

the quantum unit of LUE is umolco2m-2s-1 how can i change it to energy unit ,like gC/MJ i have been puzzle for many days Can somebody help me

Homework Statement The frequency of a vibrating string is set to 15, 20, 25, 30, or 35 Hz and the length needed to attain a standing wave (mode 1) is recorded. A graph of frequency versus 1/L is recorded. Calculate the mass per unit length of the string. The resulting graph has the...

Prove that if a(t) is a unit vector whose components are functions of t, then the vector b(t) = da(t)/dt is perpendicular to a(t) here i have the parameters that make a(t) a unit vector: 1 = f(t)^2 + g(t)^2 i know of the example sinxi + cosxj = a(t) but that is the only one i can get to work. I...

The ideal gas law states that pressure (P) is equal to the product of density (N), the ideal gas constant (R) and temperature (T): P = N x R x T I can't figure out which unit the pressure is actually in, although it does seems to work out as the figure I'm supposed to get with a 11706.85°...

If someone could assist me with some information re: the following it would be very much appreciated. I am planning to build an energy system for my home to address the drastically increasing power bills we have been getting as a result of the unusually hot weather lately. Problem is I am not...

Homework Statement I've got a radius of 22.69kpc, and a velocity of 180km/s. I wish to find the angular rotation speed in units of arcsec/year. I'm stuck at the moment The Attempt at a Solution Starting with the basic v=r\omega, I transpose to get \omega=v/r. For now, I'm going...

Homework Statement Pressures up to 3000 atm are measured with a dead-weight gauge. The piston diameter is 0.17 (in). What is the approximate mass in (lbm) of the weights required? The Attempt at a Solution Abs. pressure = Gauge pressure + Atmospheric pressure = 3000 atm + 1...

what does the u(-t) mean in unit step funtion in basic function of signal and system?how can be time taken as -ve?

Consider a positive charge +q placed at the origin. Let A and b be two points in the space with position vectors rA and rB respectively. What will be the work done by an external force equal and opposite to the Coulumbic force, in moving a unit positive charge from A to B, irrespctive of the...

Homework Statement Show that the curve γ(t)=(t²-t+1,t³-t) has exactly one self-intersection point and finnd the two unit tangent vectors (in the direction of increasing t) at this point. I have found the self intersection. I know that a unit tangent vector is the derivative of each...

Hello frnds! Can anybody convert the following factors? V/(lx-s) to V/(um/cm2) at 555nm ?? Thank you.

I have to spec a sensor to monitor the magnetic field of a DC solenoid element. The specification for the solenoid includes its length, DC resistance, current at the applied supply voltage, and most importantly, the expected Dipole Moment of the unit, as 42 Am^2. I plan to attach a solid...

Homework Statement See first figure. Homework Equations The Attempt at a Solution See second figure. When I set t = 0 in \vec{r(t)} I get 0\hat{i} +2\hat{j} + 1\hat{k}. I know this is a vector and not a point but it has the same "coordinates" as the point they are asking us...

In doing some research, I cam across an equation for instantaneous radiated power, with the CGS units "erg/(sec rad cm)", rad being radians (not rad the unit for radiation exposure). Try as I might, I'm not able to come up with a way to convert it to the SI units for watts. Does anyone know...

Given the formula for an ellipse in x and y and centered on the origin, I need a formula for the x and y components of the normal unit vector at any point (x,y) on the ellipse (y>0). My calculus skills are rusty, and I haven't been able to figure this out. Thanks in advance for any help.

Which of these have higher output per square unit*, phototransistors, photodiodes or APD photodiodes.?