Recent content by Anabelle37

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    Biological mathematics - trimerisations - law of mass action

    haha all good. that makes more sense. Just wondering though should the rate out for d[A]/dt be 2k1[A]2 + k2[A][B]?
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    Biological mathematics - trimerisations - law of mass action

    how come in your d[A]/dt and d[B]/dt expressions they involve derivatives but in d[C]/dt it does not?? Ok. I will work on that. thank you.
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    Biological mathematics - trimerisations - law of mass action

    Homework Statement In the real world trimolecular reactions are rare, although trimerizations are not. Consider the following trimerization reaction in which three monomers of A combine to form the trimer C, A + A \Updownarrow B, where k1 and k-1 are the forward and reverse rate...
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    What are the eigenvectors for lambda = -1?

    Homework Statement find the general solution to x'=Ax; where A is a 3x3matrix: A=[0 1 1; 1 0 1; 1 1 0] Homework Equations det(A-lambda*I)=0 The Attempt at a Solution i found the eigenvalues to be 2, -1, -1. for lambda=2 i found the corresponding eigenvector to be a 3x1 martrix...
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    How is Power Attenuation in a Rectangular Waveguide Derived?

    think there is a typo in the question it should be P(z)=P(0)exp(2k''z). after squaring the phasor I get: P(z) = exp(2j(wt-k'z))exp(2k''z) then i don't know what to do to get in right form.
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    How is Power Attenuation in a Rectangular Waveguide Derived?

    Homework Statement Show from general considerations that the attenuation of power in the rectangular waveguide (TE10 mode propagating in z-direction) is: P(z)=P(0)exp(-2k''z) where k'' is the imaginary part of the wavevector in the phasor exp(j(wt-kz)) Homework Equations power is...
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    How to Evaluate the Integral of x^2/(1+x^6) from 0 to Infinity?

    Homework Statement Evaluate the integral with respect to x from 0 to infinity when the integrand is x^2/(1+x^6), using complex integration techniques. Homework Equations The Attempt at a Solution I have no idea where to start. Please help!
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    Quantum mechanics - creation and annihilation operators

    Thank you both! Vela I had done it a longer way and then just realized your way would have been so much easier lol oh well. What does self adjoint mean again? I got n+1/2 as my answer which i think is correct!?
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    Quantum mechanics - creation and annihilation operators

    Homework Statement Evaluate <n|p^2|n> where p is the momentum operator for the quantised harmonic oscillator. Homework Equations creation operator: a+|n>=sqrt(n+1)|n+1> annihilation operator: a|n>=sqrt(n)|n-1> The Attempt at a Solution the operator p can be defined in terms of...
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    Rate problem - when should the cow be sold?

    Homework Statement A cow weighing 500kg gains 5kg/day and costs $1 a day to keep. the market price for the cattle is $15 per koliram, but is falling by 10cents per day. when should the cow be sold? Homework Equations The Attempt at a Solution so the 500kg is the initial...
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    Chasing Ducks: Solving a Differential Equation in a Square Pen

    Homework Statement one duck is situated in each of the four corners of a 2mx2m square pen. suddenly, each duck begins to chase its anticlockwise neighbour. all the ducks travel at the same speed. (a) by defining the origin of an x-y coordinate system in the bottom left hand corner of the...
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    Applications of integration - volume of volcanic ash

    Homework Statement After a volcanic eruption, the ash gradually falls to the ground euqally in all directions. the depth of the ash diminishes with the distance from the volcano such that at a distance r metres the depth is exp(-r^2). find the total volume of ash falling within 1 km of the...
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    How do we calculate the rate of water level increase in a sloped swimming pool?

    Thank you Mark. And turbo, it's urgent as I've tried to answer them and can't and don't want to just look them up online, I want to work them out myself and Physics Forums is good like that as it gives you hints but doesn't solve them for you. And it's for an exam in a few days and the lecturer...
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    Minimizing Distance to Origin: Solving an Optimization Problem

    URGENT - optimisation problem Homework Statement Find the point on the line y=4x+7 that is closest to the origin. Homework Equations The Attempt at a Solution I am completely lost on where to start and what to minimise. It's for exam preparation!
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