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    Diffy-Q question

    Figured it out, thanks for looking.
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    Diffy-Q question

    Homework Statement Consider the population model dP/dt = -P^2/50 + 2P for a species of fish in a lake. Suppose it is decided that fishing will be allowed, but it is unclear how many fishing licenses should be issued. Suppose the average catch of a fisherman with a license is 3 fish per...
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    Affine transformation proof

    Oh, I should have read the question carefully. Thanks a lot.
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    Affine transformation proof

    Homework Statement An affine transformation T : R^n --> R^m has the form T(x) = Ax + y, where x,y are vectors and A is an m x n matrix and y is in R^m. Show that T is not a linear transformation when b != 0. Homework Equations There are couple of useful definitions, but I think this one...
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    Boolean algebra

    Make a truth table to see why. X can equal only 1 or 0 thus the truth table for x*x is below : -------- x x x*x 0 0 0 1 1 1 ------- As you see if X = 0, then X*X = 0 = X, and if X = 1, then X*X = 1 = X. Thus X*X = X
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    Basic Matrix Question

    In the last row you have this : [0 0 0 0 1] which means this in equation form, 0X1 + 0X2 + 0X3 + 0X4 = 1, which means 0 = 1. This is impossible mathematically, right? Because a 0 cannot never equal 1, which means that the system is inconsistent, or no solution. So Yes you are correct as to...
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    Basic Matrix Question

    Its ok, the problem is trying to make you think hard, but I think once you thought about the problem a little, you should then confirm it by solving the matrix.
  8. T

    Basic Matrix Question

    well try to solve it out and see
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    Basic Matrix Question

    Oh, wait see this : The original matrix : [3 -2 0 1 1] [1 2 -3 1 -1] [2 4 -6 2 0] realize that the last row is a multiple of row2. Lets scale the last row3 so we have : [3 -2 0 1 1] [1 2 -3 1 -1] [1 2 -3 1 0] Notice something there?
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    Basic Matrix Question

    Oh wait, there are 3 equation, and 4 variables. Do you think we have enough information to solve this matrix?
  11. T

    Basic Matrix Question

    The key thing is on row3.
  12. T

    Quick question about matrix operations.

    Ok, I will search for it. Thanks.
  13. T

    Quick question about matrix operations.

    >>"What I have done is replace the 2nd equation by itself + 1 times the first equation." See thats the part thats bugging me. From middle school I have took that method as granted. Do you think that there if a formal proof of why that method would work? Or is it just drawn from intuitive reason...
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    Quick question about matrix operations.

    Say there are these systems of equations : x - 2y + z = 0 2y - 8z = 8 -4x + 5y + 9z = -9 In matrix form, it can be represented like this : -- [1 -2 1 0] < -- row 1 [0 2 -8 8] < -- row 2 [-4 5 9 -9] < -- row 3 When we do elementary row operations, say on row3 = row3 +...
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    Findin largest volume

    A*z = 2z(xy+xz+yz) V = xyz x = V/yz P/4 = x+y+z P/4 - x - y = z A*z = 2z(xy+xz+yz) A( P/4 - x - y ) = 2(P/4 - x -y) ( V/z + V/y + yz ) is that right? For a rectangular box, we could compute the area of one size and multiply by its depth to get the volume no? I am...
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    Findin largest volume

    I thought Az was the volume? Since x*y = Area, then V = Az. ? I am not sure about the second question. A = 2(xy+xz+yz ) then A*z = 2z(xy+xz+yz) ?
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    Findin largest volume

    Area times z is also volume no? And what is meant by long-winded ? So V = xyz V = A * z A = 2x(y+z) + 2yz P = 4(x+y+z) ?
  18. T

    Findin largest volume

    Perimeter : 2(2x + 2y) + 2(2z) = 4x + 4y + 4z Area of a rectangle box = 2(xy) + 2(xz) + 2(yz) = 2xy + 2xz + 2yz V = xyz What do you think? Also how do you think we could incorporate the variable P and S ?
  19. T

    Findin largest volume

    Homework Statement Johnny needs to make a rectangular box for his physics class project. He has bought P cm of wire and S cm^2 of special paper. He would like to use all the wire (for the 12 edges) and paper (for the 6 sides) to make the box. What is the largest volume of the box that Johnny...
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    Check calculation on pendulum.

    Can someone check my calculation for pendulum. Its written in C++, but I think it should be understandable. //F = mg*sin(theta) = ma; //a = F/ m //a = mgsin(theta) / m //a = g*sin(theta) ball.accelVec = Vector3D( g * sin( changeInAngle ) ,g * cos(changeInAngle) , 0.0f ); //V = v_0 +...
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    Find base in which the number is a palindrome

    Sorry, this is not a H.W question . But I figure this is the more active section in math, and that maybe some calculus can help. The question is that given a number n, Find which base its a palindrome in. For example, The given number is n = 3. Starting from base 2 to x, we check...
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    Quick question about taking a derivative

    So say for a line integral, the curve C is given by y = sqrt(x), from point (1,1) to (4,2); In my integral I have some integrand* dy. Say I wanted to change the dy to dx. From whats given : y = sqrt(x); dy = 1/(2sqrt(x) ) dx; I could just substitute that instead for dy. But...
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    Jacobian Transformation.

    Since : x = 2u + v , y = u + 2v The jacobian is : |2 1| |1 2| = 2*2 - 1*1 = 3 ; The the answer is -4/5* 3 = -12/5 ? I still did something wrong I guess.
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    I think my problem solving is absurd.

    Let u = e^(-x) + 2 the du = ...
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    Jacobian Transformation.

    Homework Statement Use the given transformation to evaluate the given integral. \int\int(x-3y)DA R. where R is the triangular region with vertices (0,0), (2,1) and (1,2) ; x = 2u + v , y = u + 2v Trial : Using the points given I came up with these equations for the...
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    Finding average value

    so is it just this : 1/2\int^{2}_{0} 4 - x^2 And how about the double integral of it?
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    Finding average value

    Find the average value of y on the region D that is bounded above by the parabola y = 4 - x2 and below by the x-axis. Does this question makes sense? I know the formula for the average values function : 1/(A(x)) * doubleIntegralOf F(x,y)DA But its says above the parabola and below...
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    Setting up a triple integral to find volume of a region

    In what type of coordinates? Spherical coordinates looks good.
  29. T

    Another coordinate conversions.

    There is no way to give reps or something similar, because you earned a million of them. Thanks a lot, as usual.
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    Another coordinate conversions.

    If anyone could help on any of the 3 problems, checking if my conversion is correct, then I would really appreciate.
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