Homework Statement
I'm doing a physics lab and have a question about RC circuits. I'm given four formulas:
1a) dQ/dt = -Q/RC
1b) Q = (Qo)e^(-t/RC)
1c) E - RI - Q/C = 0 ---> R(dQ/dt) + Q/C - E = 0
1d) Q(t) = CE[1 - e^(-t/RC)]
I am told that 1b is the solution to 1a and 1d is the...
Homework Statement
Give a proof by Mathematical Induction of the following:
For all integers n>=3, (n^2 - 3n + 2) is positive.
Homework Equations
The Attempt at a Solution
Hey guys, this is a problem from my discrete mathematics study guide. Here's what I got so far:
Proof: n-initial=3...
Homework Statement
Let V be the subspace spanned by the following vectors:
[ 0]...[ 1 ]...[2]
[ 2]...[ 1 ]...[5]
[-1]...[3/4]...[0]
Determine a basis for V.
The Attempt at a Solution
I'm not quite sure how to start here. Would placing the vectors in a matrix and deriving its...
How do I derive the elements of my set from the equation?
If I select a0=2, a1=3, a2=4, and a3=6, then these numbers meet the requirements of the equation.
Similarly, a0=-2, a1=-3, a2=-4 and a3=-6 would as well. Where do I go from there?
Homework Statement
Is {a0 + a1x + a2x^2 + a3x^3 | a0a3 - a1a2 = 0} a subspace of P3? Why or why not?
*The digits should be in subscript.
How would I go about answering this?
I think I've actually got this figured out. I just test two 2x2 matrices of random values under the various axioms and if they pass then under matrix addition and scalar multiplication then it should show that all 2x2 matrices are a real vector space right?
What other kind of vector space is...
Homework Statement
Show that all 2 x 2 matrices with real entries:
M(2x2) = {
a b | a,b,c,d are real numbers}
c d |
is a vector space under the matrix addition:
|a1 b1| + | a2 b2| = |a1+a2 b1+b2|
|c1 d1| + | c2 d2| = |c1+c2 d1+d2|
and scalar multiplication:
r*| a b | = | ra...
Homework Statement
Two point charges -2Q and +3Q are on the x-axis at the origin and at
x = L. Find all the points on the x-axis (not at infinity) where the electric
potential is zero. Express your answers in terms of L and Q.
Homework Equations
V= k*Q/r
The Attempt at a Solution
I...
Homework Statement
What is the reduced echelon form of a n x n nonsingular matrix? Briefly explain.
Homework Equations
The Attempt at a Solution
I know that a n x n nonsingular matrix will always result in echelon form will always have a diagonal orientation with a single digit in its own...
Sorry, I'm using the perspectives that my lab book uses so I'll correct them for conventional usage.
I've found that the speed of the electron as it leaves the anode can be given as:
Vx = ((2)(e)(Va)/(m))^(1/2) (e=electron charge, Va=accel voltage, m=electron mass)
Once the electron enters...
Thanks for the help, I'm definitely further along now. I have just one more question.
I've found that the speed of the electron as it leaves the anode can be given as:
Vz = ((2)(e)(Va)/(m))^(1/2) (e=electron charge, Va=accel voltage, m=electron mass)
Once the electron enters the...
Homework Statement
Have a few questions on CRT's. If we are given the accelerating voltage (250V) how would I calculate the kinetic energy of the electron as it leaves the positive end of the charge area? What is the formula for the speed of an electron along the tube (vz) as it leaves the...
Ah! That's right! I can just make them any number, and then add the resulting vectors together correct? Thank you so much!
Would I right that as such? :
when z=w=1;
solution vector:
1
-3
1
1
So solving for that homogeneous system produces the following result:
2 4 6 4 = 0
0 1 1 2 = 0
0 0 0 0 = 0
with x=-z+2w and y=-z-2w, solution set is (-z+2w, -z-2w, z, w)
and a solution vector of:
0
0
0
0
Which is not what the problem is asking for. How do I find a solution vector that has no...
What process did you use to arrive at this equation set? I'd like to do so on my own. Thanks for the help!
*edit* I see that you simply took all of the solutions and replaced them with zero's.
Homework Statement
Prove that if a system with rational coeffcients and constants has a solution then it has at least one all-rational solution. If such as system has infinitely many solutions, will it also have infinitely many all-rational solutions ?
Homework Equations
The...
Homework Statement
1. Express the general solution of the following system in vector form.
2x + 4y + 6z + 4w = 4
2x + 5y + 7z + 6w = 3
2x + 3y + 5z + 2w = 5
Clearly identify the particular solution. Also produce a vector with no zero components that satisfies the corresponding homogeneous...
Homework Statement
Find the series' radius and interval of convergence. What what value of x does the series converge absolutely, conditionally?
Sum (n=0 to infinity) (nx^n)/((4^n)((n^2) +1)))
Homework Equations
The Attempt at a Solution
Not quite sure where to start with this...