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    RC circuit formula question

    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...
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    Mathematic Inductive Proof question

    Well (n+1)^2 - 3(n+1) + 2 simplifies to n^2 - n. How do I show that n^2 - n > 0 ?
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    Mathematic Inductive Proof question

    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...
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    How to determine a basis given a set of vectors?

    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...
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    Is {a0 + a1x + a2x^2 + a3x^3 | a0a3 - a1a2 = 0} a subspace of P3?

    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?
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    Is {a0 + a1x + a2x^2 + a3x^3 | a0a3 - a1a2 = 0} a subspace of P3?

    Do I need to do anything with the conditions a0a3 – a1a2 = 0?
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    Show that all 2x2 matrices with real entries is a vector space under these conditions

    Would that be a single column matrix like: [a] [b] [c] [d] ?
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    Is {a0 + a1x + a2x^2 + a3x^3 | a0a3 - a1a2 = 0} a subspace of P3?

    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?
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    Show that all 2x2 matrices with real entries is a vector space under these conditions

    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...
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    Show that all 2x2 matrices with real entries is a vector space under these conditions

    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...
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    At which points on the x-axis (not at infinity) is the electric potential zero?

    Would this be correct: k(-2)/L + k(+3)/L = 0 -2/L + 3/L = 0 -2/L = -3/L Potential is equal to zero at L = -2 and -3?
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    At which points on the x-axis (not at infinity) is the electric potential zero?

    That's what I was thinking, that zero potential would be directly at the origin. How would I express this in terms of L and Q?
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    At which points on the x-axis (not at infinity) is the electric potential zero?

    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...
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    Generic linear algebra echelon form question

    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...
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    Cathode Ray Tube Questions

    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...
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    Cathode Ray Tube Questions

    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...
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    Cathode Ray Tube Questions

    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...
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    Linear Algebra Proof

    Is it because with an equation with an infinite number of solutions, at least one of those solutions must be a rational number?
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    Simple Linear Algebra problem

    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
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    Linear Algebra Proof

    Because the solutions have to equal a rational number?
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    Simple Linear Algebra problem

    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...
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    Simple Linear Algebra problem

    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.
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    Linear Algebra Proof

    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...
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    Simple Linear Algebra problem

    So how do I take the solutions that I have to show a homogeneous system? My equations do not equal to zero. Is there a conversion process to do this?
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    Simple Linear Algebra problem

    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...
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    Need help with a series (radius, convergence)

    Doing the ratio test and checking for the limit I found the limit to be x/4. Where do I go from there?
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    Need help with a series (radius, convergence)

    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...
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    Help with infinite series

    I know using a calculator that the sum is a little over 2, but I would like to know how to do this on my own.
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