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From this site: https://www.whitman.edu/mathematics/calculus_online/section06.02.html Exercise 6.2.13: The trough shown in figure 6.2.6 is constructed by fastening together three slabs of wood of dimensions 10 ft × 1 ft, and then attaching the construction to a wooden wall at each end. The...

Hello All, This is from http://math.mit.edu/~jorloff/suppnotes/suppnotes02/v6.pdf F = -y/(r^2) î + x/(r^2) ĵ Page says curl F = 0 and cites a previous example. ....... sp. edited I cannot find the sited previous example But I get curl F = 1/(r^2) - -1/(r^2) = 2/(r^2) I cannot figure out what...

Hello All, I’m reading Axler “Linear Algebra Done Right” I’m still very much a beginner in linear algebra. My other linear algebra sources all only teach, at least so far, using just Real numbers. Axler uses both Real and Complex numbers, using symbols R, C, and F where F is all of both real...

Hello, On this page - http://www.math.umbc.edu/~campbell/Math221/Glossary/ This definition: Codomain The codomain of a linear transformation is the vector space which contains the vectors resulting from the transformation's action. Thus, if T(v) = w, then v is a vector in the domain and w is...

Exercise: Integral from 0 to 1 of 2/((4-x^2)^(1/2)) or 2/sqrt(4-x^2) Book pulls out the 2 in the numerator and calculates arcsin(x/2) from 0 to 1 = pi/6. Then multiplies by the 2 for a final answer of pi/3. I factored out the 4 under the radical which becomes 2 in the denominator which cancels...

Hello All, Given: f : R3→R r : R→ R3represents position of moving object as a function of time g(t) is valueof f at the object’s position at time t Firstquestion: Is all thiscorrect for me to say: w = f(x,y,z)= f(r(t)) = g(t) Secondquestion: Are partialderivatives of w and of f the...

When I evaluated ∫ csc x dx, I used csc x – cot x for mysubstitution instead of csc x + cot x So my final answer is ln│csc x – cot x │ + C The correct answer is -ln│csc x + cot x │ + C My answer seems to also be correct but I cannot prove it sonot sure what I’m missing. Any insight greatly...

HelloAll, Thisis from the document found here: https://math.dartmouth.edu/archive/m12f10/public_html/RepresentingMatrix.pdf (7) (Very importantexample) Let A be any m x n matrix. Then A defines alinear map LA : Rn →Rm (“left-multiplicationby A”) defined by LA(v) = Av for v ϵ Rn. Note that...

Hello All, Book (Linear Algebra by Jim Hefferon) says this set is not asubspace of R2. X 0 1 0 {( ) + ( ) │x ϵ R} Seems to me it contains zerovector and is closed with respect...

Hello All, Working on a physicsproblem regarding an LRC circuit, and more specifically what isthe time required for the charge amplitude to drop to half its starting value? I correctly started withthis equation. ½ Q = Q0e(-Rt/2L)cos(w’t+ɸ) I got stuck trying tofigure out what to do with the...

Proven in book so I know must be true: "In a vector space, the span of any subset is a subspace." Based on these following statements, obviously I am misunderstanding something. If someone could point out all of my errors, wrong statements, etc, I would greatly appreciate it. V = (set of all...

Limit as x becomes much greater than R ie x >> R What does this reduce to when x >> R? ((x^2 + R^2)^(1/2)) – x I factored out the x^2 to get ((x^2)*(1 + (R^2/x^2)))^(1/2)) – x I cannot figure out the step(s) that now get to the correct answer of x*(1 + (R^2/2x^2)) – x Thank you

1180 = 98t + 1080(e^(-0.1t)) Taking the log of both sides doesn't seem to work. Exponentiating both sides doesn't seem to work. I think I am either doing something wrong in taking the natural log or not exponentiating correctly or I am missing something else that I think I should know. Just a...

I need to integrate ∫ ((16 - x^2 - y^2)^(1/2)) dy I cannot figure out how to start, specifically, which method to use.If someone wouldn't mind giving me a method of integration hint, I would appreciate it. Thank you

Hello, I’m working on drawing a free body diagram for a rocket. The book says that the force of gravity is M*g where M is the mass of the rocket. Since dM is the rate of expulsion of mass of fuel, I feel like the force of gravity should be (M-dM)*g Hopefully I am missing something obvious...

I'm working on a problem in the chapter "Surface Integrals of Vector Fields". Problem is to evaluate a vector function over the top half of a sphere. In the solution, the Professor states: "In this case since the surface is a sphere we will need to use the parametric representation of the...

Pulley (vertical disc): r = 0.33m, m = 4.00kg, initially at rest Rope pulling (perpendicularly from side) with Force = F(t) = 3.00t - 0.20(t^2) At t(in seconds) = 8, find linear speed of a point on the rim of the pulley. Torque = R*F = 0.99t - 0.066(t^2) = 3.696 mN From here, I don't know how...

I’m working on Arc Length with Vector Functions where: Arc length is L = ∫ from a to b of magnitude of r’(t) dt Then arc length function is s(t) = ∫ from 0 to t of magnitude of r’(u) du I'm trying to get all the functions and variables and the relationships between them straight in my head...

Section: Conservative Forces and Potential Energy Question: A spring with k=63 N/m hangs vertically next to a ruler. The end of the spring is next to the 15-cm mark on the ruler. If a 2.5-kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler...

Problem section is - Kinetic Energy: Work-Energy Principle A mass "m" is attached to a spring which is held stretched a distance "x" horizontally by a force "F", and then released. The spring compresses, pulling the mass. Assuming there is no friction, determine the speed of the mass "m" when...