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1. 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...
2. 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...
3. 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 +...
4. 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...
5. 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 +...
6. 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...
7. 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...
8. 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...
9. 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...
10. Another coordinate conversions.

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...
11. Changing from rectangular coordinate to sperical

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 +...
12. Help Rectangle to Cylindrical coordinate question

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)...
13. Rectangle to Cylindrical coordinate question

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...
14. Finding Capacitance/Indutance

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...
15. Double Polar integral

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...
16. Double Integral

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 ...
17. What is the magnetic field strength on Earth's surface at either pole?

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...
18. Larange multiplier

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...
19. Lagrange Mulltipliers

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 =...
20. Easy V = IR problem, just help understand it.

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...
21. Finding max and min of a function of several variables( 1 more time )

Homework Statement Find min/max/saddle point of the function : F(x,y) = y^2 - 2*y*cos(x) ; 1 <= x <= 7 F_x = 2y*sin(x) F_xx = 2y*cos(x) F_xy = 2cos(x) F_y = 2y - 2cos(x) F_yy = 2 Finding its critical points : F_x = 2y*sin(x) = 0 F_y = 2y - 2cos(x) = 0...
22. Finding max and min of a function of several variables

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 =...
23. Finding max and min of a function of several variables

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 +...
24. Finding the rate of change of the distance between 2 cars

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...
25. Using differentials to estimate the amount of tin

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...
26. Check work on finding max error of Surface Area

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...
27. Finding capacitance per unit length

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...
28. Implicit derivative of function, calc 3

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...
29. Check work on capacitance.

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...
30. Help, with finding electron radius for a given condition

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...