Homework Statement
I'm trying to use fmincon to find the optimal mass ratios for the rocket equation. The only variables are m2/m1 and m3/m2 (R1 and R2 respectively).
The Attempt at a Solution
function [ velocity ] = rocketEqn( MR )
% Calculates the velocity that a rocket can attain...
Homework Statement
I need to create an orbit propagator for the orbit of a specified body and graph it. I've written a code that works and correctly gives me a circular orbit for a satellite in geosynchronous orbit and it appears to correctly display the orbit of the Earth for one year. I'm...
Homework Statement
I need to resolve this network and find the equation for voltage at some time, t'>0. I know how to find the equation, but I'm having trouble finding the value for tau because I'm not sure what the equivalent resistance is.
Homework Equations
tau = R*C
R1 = 4 k...
Homework Statement
X and Y are random variables with the joint density:
fXY(x,y) = k*e^(-lambda * x) if 0 < y < x < infinity
= 0, otherwise
Find P(X + 2*Y <= 3)
Homework Equations
I found k = lambda^2
The Attempt at a Solution
I'm not sure exactly how to solve this, but...
Homework Statement
Let D be the image of R = [1; 3] x [1; 4]. under the map
T(u; v) = (u^2/v , v^2/u)
(a) Compute the Jacobian of T.
(b) Compute the area of D.
The Attempt at a Solution
I'm pretty sure I found the Jacobian (I got -2v/u + 2u/v), but I am confused on the next part...
So the rank = 2 since rank = # columns (4 in this case) - dimNul A (in this case 2). So if the rank is to equal 2 then I will need another free variable, or I need to remove a pivot position. So since h-6 is in a pivot position I can easily make it a nonpivot column by setting h=6. This would...
Homework Statement
Find h in the matrix A such that the eigenspace for lambda=5 is two-dimensional.
A= [5,-2,6,-1] [0,3,h,0] [0,0,5,4] [0,0,0,1]
A-lambda*I(n) = [0,-2,6,-1] [0,-2,h,0] [0,0,0,4] [0,0,0,-4]
Homework Equations
The Attempt at a Solution
I'm not really sure how to...
Homework Statement
A thin wire has the shape of the first quadrant part of the circle with center at the origin and radius a. If the density function is rho(x,y)=kxy, find the mass and center of mass of the wire.
Homework Equations
My parametric equation of the circle was x=a*cos(t) and...
Homework Statement
Assume for the solidification of nickel that nucleation is homogeneous, and the number of stable nuclei is 10^6 nuclei per cubic meter. Calculate the critical radius and the number of stable nuclei that exist at the following degrees of supercooling: 200 K and 300 K...
Homework Statement
So I'm trying to find a basis for the space that is spanned by the given vectors.
{(1,0,0,1) (-2,1,-1,1) (6,-1,2,-1) (5,-3,3,-4) (0,3,-1,1)} These are written as column vectors.
Homework Equations
None really (that I know of)
The Attempt at a Solution
So I...
Okay so here is what I did:
Using the above equation, E=kq/r^2
kq(1)/r^2 + kq(2)/r^2 where q(1) = 2x10^-6 and q(2) = -2x10^-6.
Then the distance from P to q(1) is 13 cm and the distance from P to q(2) is 34 cm (the 21 cm between charges and the 13 cm from q(1) to P)
So it becomes...