Which of the following equations are dimensionally correct?
463421
KE = mv\nWrong: energy <> momentum\n\n2y = (2 m)cos(kx)\nRight: a lenght =  lenghth x a number between -1 and +1\n\nvf = vi + ax\nWrong: x should be t\n\ndensity = volume/mass\nWrong: fraction should be inverse
1017997
The equations are wrongor insufficient. Post the correct data if you want me to help/ Alternately, you could also message me.
886519
The first one is non-linear (because of the (y')^2 term) and I am not an expert on non-linear differential equations.  Are you sure that is right because if it is only y', then you can simply seperate variables and then solve it.\n\nThe second one, find the integrating factor and then it becomes an exact equation.
361724
The Jacobian matrix will have dimensions depending on what you have constructed the Jacobian for.  You'll need to supply a bit more information.
766444
time to the minus one.\n\nDo a dimensional analaysis on a rate equation to confirm this.
714493
This *is* the way to write it so that x is the input and w is the output. If you want to solve for x in terms of w (i.e. have w the input and x the output), you are better off doing numerical approximations than using the cubic formula (it is really, really nasty).
98990
A system of partial differential equations can be described as an nxn matrix (lets call it A). The eigenvector (X) will be the n dimensional vector which has the property that there exists some real eigenvalue (L) such that AX=LX.
776321
the question is unclear.\nDo you want an explicit formula for Y[n or do you just want to write out the convolution]
569885
This is a good time to learn dimensional analysis.  It will come in handy for all of your physics courses.\n\nFirst, µ x M cancels one another leaving ohms x Farads\n\nOhm = volt/amp\n\ncharge = capacitance x voltage  so capacitance = coluomb/voltage\n\nOhm x Farad = volt/amp X coulomb/volt\n\nso the volt cancels leaving \n\nOhm x Farad = coulomb/amp\n\nAmp = coulomb/sec\n\nOhm x Farad = coulomb/(coulomb/sec)\n\n= (coulomb/1) x (sec/coulomb) = sec\n\nBy the way, Tau = RC is the timeconstant of an RC type circuit.. you remember for a cap charging it is I = V/R[exp (-t/RC)  RC is in units of time = sec\n\nI used to have to do this stuff all the time in my undergrad physics courses.
25791
dimensional analysis is solving a problem by using the units of the terms involved.\n\nfor instance, since volume density has units of mass / volume, you know how to find volume density given a mass and a volume, it would just be: mass/volume = density.\n\na more complicated example force (F) has units of newtons. Newtons can be further broken down into the units (kilogram * meters)/seconds^2\n\nthus, if you know the mass of an object (kilograms), and the acceleration (meters/second^2), you then know how to put the two together to find force, it would just be:\n\nkilograms * (meters/seconds^2)\n\nwhich is mass*acceleration.\n\nthis type of analysis can be strung together to solve more complicated problems.
940602
You're correct. Differentiating them and showing they are equal to zero will indicate that they are constant. The equation\n\nA(w_1)^2 + B(w_2)^2 + C(w_3)^2\n\ndifferentiated with respect to time yields\n\n2*A*w_1*(d/dt w_1) + 2*B*w_2*(d/dt w_2) + 2*C*w_3*(d/dt w_3)\n\nIf you substitute from the system of equations that shows the evolution then\n\n2*w_1*w_2*w_3*(B-C) + 2*w_1*w_2*w_3*(C-A) + 2*w_1*w_2*w_3*(A-B)\n\nyou can see that the terms cancel leaving you with zero.\n\nFollow the same technique for the second equation. It will look similar except you will wind up with an additional constantt, e.g., A*(B-C), etc.
1069671
yep...scalars multiply vectors component by component just like you have shown.  you can also show it by plotting out the original vectors, scaling them appropriately, adding them, and finding the resukltant components.
353301
See p. 541 of Econometric Foundations by Mittelhammer, Judge and Miller.  Will be a bit tough to explain on Yahoo.  Actually, I don't like this book, but none of my other ones have this.
162293
On both equations, you have x^ but don't say what x was raised to. I'm assuming that it is x^2. Is this correct?
140428
x\n\nthe answer below is just for voltage - see my graph above - it is quite accurate. here it is again, larger: X
107932
These are kind of fun if you apply dimensional analysis over and over again.  Lets assume that our years are 365, 365, 365, 366 days, and that we'll experience two leap years in the time span.  This is then 8*365 + 2*366 days, which is our starting point\n\n3652 days\n\nnow we know that there are 24 hours = 1 day, so take this formula and multiply both sides by (1/day) to get 24 hours/day = 1.  Since multiplying by 1, by this equation multiplying by 24 hours/day does not change value\n\n3652 days * 24 hours / day\n\nNow cancel the "day" term in the numerator and denomenator\n\n3652 * 24 hours\n\nNow do the same thing for minutes and then for seconds.  60minutes/hour = 1 so\n\n3652 * 24 * 60 hours * minutes / hour\n\ncancel hour and apply 60 seconds/minute = 1\n\n3652 * 24 * 60 * 60 minutes * seconds / minute\n\nand cancel the minute term and perform the multiplication:\n\n315,532,800 seconds
499903
it the way the math worked out, there are supposedely either 11 or 26 dimensions. this math is way beyond me, but the theory is still unproven so they may be any number.