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...
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 +...
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...
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...
Homework Statement
The actual question is to evaluate the integral. All I need help on is the setting up part.
Instead of making a thread for each, I will post 3 integral question with my attempts.
Just tell me if you see something wrong from rectangular to spherical conversion...
Homework Statement
change from rectangle to spherical coordinate :
z^2 = x^2 + y^2
I know that :
z = pcos(phi)
x = psin(phi)cos(theta)
y = psin(phi)sin(theta)
there fore
z^2 = x^2 + y^2 in spherical coordinate is
p^2cos(phi)^2 = (psin(phi)cos(theta))^2 +...
Homework Statement
evaluate : \int\int\int_{E} e^z DV
where E is enclosed by the paraboloid z = 1 + x^2 + y^2 , the cylinder x^2 + r^2 = 5
I just need help setting this up.
I know that theta is between 0 and 2pi
Now is z between 0 and 1 + r ? and r is between 0 and sqrt(5)...
Homework Statement
can you explain this conversion, I am not sure.
Rectangle coord :
\int^{2}_{-2}\int^{sqrt(4-x^2)}_{-sqrt(4-x^2)}\int^{2}_{sqrt(x^2 + y^2 )} F(x) dzdydx
=
cylindrical coord :
\int^{2\pi}_{0}\int^{2}_{0}\int^{2i}_{r} r*dzdrd\theta
I see that x^2 + y^2...
Homework Statement
Your professor tells you about pre-digital computer days when engineers used electric circuits to model mechanical systems. They could modify parameters of the circuit elements and see the effect on the circuit's behavior. Suppose a 5.0kg mass is connected to a spring...
Homework Statement
Convert to polar integral and integrate.
\int_{D}\int xy dA
where D is the disk with the center origin and radius 3.
I am not sure about the limits. I know that x = rcos(\theta), y = rsin(\theta), dA = rdr*d\theta
Homework Statement
Homework...
Homework Statement
\int_{D}\int y^2
where D = {(x,y) | -1 \leq y \leq1, -y-2\leq x\leq y
The integral I set up is below :
\int^{1}_{-1} \int^{y}_{-y-2} y^2 dx dy
From that I get the answer 0, but the book says its 4/3.
I get 0 because It reduces to this integral ...
Homework Statement
What is the magnetic field strength on Earth's surface at either pole?
Earth's magnetic dipole moment is D_0
What is the magnetic field strength on Earth's surface at either pole?
B = ____ G
Homework Equations
_u = NIA ; N is the number of turns I is current, A...
Homework Statement
Find mix/max
2x + 6y + 10Z bounded by x^2 + y^2 + z^2 = 35
After finding the partial derivative and letting it equal to the bounding equation * C
2 = C * 2x
6 = C * 2y
10 = C * 2z
x^2 + y^2 + z^2 = 35
x = 1/C
y = 3C
z = 5C
inputting this into the...
Homework Statement
Find max/min using L.M of the function :
F(x,y) = x^2 + y^2 ; xy = 1
let G(x,y) = xy - 1
F_x = 2x
F_y = 2y
G_x = y
G_y = x
F_x = L*G_x
F_y = L*G_y
G(x,y) = 1
1) 2x = L * y
2) 2y = L * x
3 ) xy = 1
Now I need to solve those equations.
so x =...
Homework Statement
When a 9.0V - battery is temporarily short-circuited, a 400mA- current flows.
What is the internal resistance of the battery?
Ans :R_int = 9/(400*10^-3)
Can someone explain why this is the answer, I understand its just V/I, but what exactly
does this mean? I am...
Finding max and min of a function
Homework Statement
Find min , max , and saddle points of the function :
f(x,y) = e^x*cos(y)
f_x = e^x*cos(y)
f_xx = e^x*cos(y)
f_xy = -e^x * sin(y)
f_y = -e^x * sin(y)
f_y = -e^x * cos(y)
First finding the critical points :
f_x =...
Homework Statement
Find max/min/saddle point of the function :
F(x,y) = (1+xy)(x+y)
= x^2*y + y^2*x + x + y
F_x = 2xy + y^2 + 1
F_xx = 2y
F_y = x^2 + 2yx + 1
F_yy = 2x
Need help on finding the critical points :
So I have to solve this equations :
F_y = x^2 + 2yx +...
Homework Statement
Car A is traveling north on Highway 16 and car B is traveling west on Highway 83. Each car is approaching the intersection of these highways. At a certain moment, car A is 0.3 km from the intersection and traveling at 90km/h while car B is 0.4km from the intersection and...
Homework Statement
Use differentials to estimate the amount of tin in a closed tin can with diameter 8cm, and height 12cm, if the tin is 0.04 cm thick.
The way I did this was to subtract the Max volume by the Enclosed volume.
Max Volume is pi(4)(12)
Enclosed Volume is pi ( 8 - 2(0.04) )/2...
Homework Statement
The dimensions of a closed rectangular box are measured as 80cm, 60cm, and 50cm,respectively,
with a possible error of 0.2cm in each dimension. Use differentials to estimate the maximum error
in calculating the surface area of the box
The Attempt at a Solution
I...
Homework Statement
You are planning to install a home video studio. A very important piece of information is missing from the specifications. You must find the capacitance per unit length for a coaxial cable. The cable has an inner radius of 2.0mm and an outer conductor 4.0mm in radius...
Homework Statement
Find dy/dx ;
sqrt(xy) = 1 + yx^2
or
0 = 1 + yx^2 - sqrt(xy)
Definition :
dy/dx = - F_x / F_y;
A = F_x = 2xy - 1/2 (xy)^-0.5 * y
B = F_y = x^2 - 1/2(xy)^-0.5 * x
Then dy/dx = -A / B
But the answer according to the book, is this :
4(xy)^-1.5 - y...
Homework Statement
Your home video studio will use a TV antenna cable often known as "twin lead." Two 0.50mm--diameter wires are spaced 12mm apart. Your equipment requires that the total capacitance of the cable not exceed 1000 pF. The cable is 30m long. A technical paper on the cable gives...
Homework Statement
A classical view of the electron pictures it as a purely electric entity, whose Einstein rest mass energy,E = mc^2 is the energy stored in its electric field.
If the electron were a sphere with charge distributed uniformly over its surface, what radius would it have...