Simply curious as to why it is so important to have linear independence? Is it solely based on the fact that linearly dependent vectors are simply multiples of one another and you receive no insight from their dependence relationship? I understand that LI vectors span a space and are necessary...
How can it be reversible if entropy is generated? Entropy is generated for irreversible processes right? I think I remember this, but correct me if I'm wrong.
ah, but actually in order to use Heun's method, I'll need to evaluate a "preliminary" V which means I'll really need to use a preliminary H in the equation involving V(H) (i.e. solving a cubic polynomial, which does not fly because I have to code this problem into MATLAB shortly...), so I guess...
well, for one you're going to have centripetal acceleration so when you apply the kinetic equation (using a normal-tangential coordinate system) you'll be able to get the answer pretty easily. I got N = 2418, which unlike your answer is positive indicating an upward reaction force (assuming...
The only thing I know that I can say about it is that Bernoulli's doesn't actually apply because of all kinds of viscous effects, but instead you'd have to apply the momentum equation (one of the navier-stokes equations) and also/alternatively you could apply the energy equation, but you...
Homework Statement
I just need to get these eqn's together to form a DE
Homework Equations
Q = CA*sqrt(2gH) = -dV/dt
and
V = pi/3 * H^2 * (3*r - H)
These eqn's refer to a sphere which has a flow Q of fluid out the bottom of said sphere. The radius of the sphere is r, the height H is from...
I am in a numerical methods class, which uses MATLAB and c to do methods like regular falsi and Newton raphson. I should know this, but why do we bother finding the value of x that makes our function evaluate to zero? Is it so that we have some basis as to where to start or stop a certain...
what actually causes polymers, ceramics and metals to fracture in either of these ways? From what I understand, polymers can be either brittle or softer which has to do with whether they are thermoset or thermoplastic, saturated or unsaturated, long chain or short chain, etc. but what makes...
Homework Statement
Describe equilibrium cooling from 1200 C to 200 C of an alloy containing 40 wt% Ag. Draw the schematic equilibrium cooling curve
The Attempt at a Solution
Alloy begins as a liquid, begins to solidify as temperature reaches the liquidus line; alpha accumulates and the...
Homework Statement
I can either use the alternating series estimation thereom (which i don't really know) or Taylor's Inequality to estimate the range of values of x for which the given approximation is accurate to within the stated error.
sin(x) = x - (x^3)/6 (|error| < 0.01)
Do I...
Homework Statement
Find the Taylor polynomial T_n(x) for the function arcsin x at a = 0, n = 3
Homework Equations
Well, I understand the Taylor poly. for sine, but how do i get arcsine?