Vector differential calculus: velocity and acceleration

Here is the problem as it is printed in the book (kreyszig: Advanced Engineering Mathematics. sec. 8.6. Problem 10): ----- (Elliptical Orbit) Consider the motion r(t) = cos t i + 2sin t j. Find the points of maximum speed and acceleration. Find the tangential and normal acceleration. ------ Here is where I am in the problem: Velocity = r' = -sin t i + 2cos t j acceleration=r" = -cos t i + -2sin t j (where i represents the x vector component and j the y component).

Vector fields that are gradients of scalar fields

This question is#24 in Kreyszig's book Adavanced engineering mathmatics 8th ed.. (this section deals with gradients of scalar fields. Q: Potential fields. We can handle potential fields f more easily than vector fields v (v is a vector) =grad f . Find f for given v or state that v has no potential. #24. v=[ye^x,e^x,1] I got a feeling this is actually a pretty simple problem and I am just missing something. Thanks for the help.

Finding center of gravity using double intergral

This question is #14, section 9.3 in kreyszig's book advanced engineering mathmatics. The question is as follows: Find the coordinates x*,y* of the center of gravity of a mass of density f(x,y)=1 in a region R, where R is a triangle with verticies (0,0), (b,0), (b,h). The answer I am looking for involves the use of double intergrals.

Managerial Accounting Problem

Tarheel Furniture Company is planning to establish a wholly owned subsidiary to manufacture upholstery fabrics. Tarheel expects to earn $1 million after taxes on the venture during the first year. The president of Tarheel wants to know what the subsidiary's balance sheet would look like. The president believes that it would be advisable to begin the new venture with ratios that are similar to the industry average. Tarheel plans to make all sales on credit. All calculations assume a 365-day year. In your computations, you should round all numbers to the nearest $1,000. Based upon the industry average financial ratios presented here, complete the projected balance sheet for Tarheel'... click for more

Solve rigid body problem using Newtons second law of motion

Can you correct this from question 1 b? (See attached file for full problem description)