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...
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?
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...
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...
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...
Homework Statement
Find the sum of the series:
(1/(4^n))+ (((-1)^n)/(3^n))
from n=0 to infinity
Homework Equations
The Attempt at a Solution
I'm not overly familiar with series and am not sure how to approach this. A lot of help guides online talk about testing for...
Homework Statement
A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 3 hours there are 10,000 bacteria. At the end of 5 hours there are 40,000. How many bacteria were present initially?
Homework...
Homework Statement
(secx)(dy/dx) = e^(y + sinx)
Homework Equations
None
The Attempt at a Solution
Not sure. I know I can do ln of both sides and isolate the y+sinx but then I get stuck with log^(secx)
1)Homework Statement
An astronaut of mass 82.0 kg is taking a space walk to work on the International Space Station. Because of a malfunction with the booster rockets on his spacesuit, he finds himself drifting away from the station with a constant speed of 0.600 m/s. With the booster rockets...