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...
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...
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
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...
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.
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?
>>"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...
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 +...
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...
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 ?
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...
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 +...
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...
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...
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.
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...
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...