Mathematics

Mathematics, 01.08.2019 12:30, lauren9261

Describe relative positions of ovals originating from a real algebraic curve and as limit cycles of a polynomial vector field on the plane.

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Mathematics, 27.06.2019 00:20, masseyboy428

Determine if the following statements are true or false. (a) if ∫c vector f · d vector r = 0 for one closed path c, then vector f is path-independent. true false (b) if the total change of a function f along a curve c is zero, then c must be a contour of f. true false (c) line integralc vector f · d vector r = vector f(q) - vector f(p) when p and q are the endpoints of c. true false (d) if vector f is continuous and vector f = gradf, then vector f is path-independent. true false (e) if f(x) and g(y) are continuous one-variable functions, then the vector field vector f = f(x)vector i + g(y)vector j is path-independent. true false (f) the vector field vector f( vector r ) = vector r in 3-space is path-independent.

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Physics, 03.07.2019 03:10, nestor59

Let f (3x - 4y +22)i+(4x +2y 3z2)j + (2xz moving once around an 4y zk be a vector field. consider a particle ellipse c given by parametrization r= 4 cos ti +3 sin tj. find the work done. 3 3 = 3, y=-- and 2 1 2. let d be the region in the first quadrant bounded by the lines y=-r1, y 4 + 1. use the transformation u 3 2y, v r + 4y to evaluate the integral y= (3x2 +14ry +82) dax dy a field f p(a, y)i + q(x, y)j in the ry-plane such that at each point (r, y) (0,0), f is a unit vector pointing to the origin. 3. find #2 da +2y dy+2xz dz does not depend 4. show that the value of on the path taken from a to b ja 5. what can be said about the curl of a conservative two-dimensional vector field? explain as best you can i+ (e + tan over the cardioid a + a cos 0, 6. find the outward flux of the field f 3ry = 1 + 1/2 a > 0 7.

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Physics, 05.07.2019 19:30, RiddleMeThis

An infinite plane of charge occupies the x − y plane with surface charge density σ = −1.8 × 10−6c/m2 . an infinite line charge with charge density λ = 2.2 × 10−6c/m runs parallel to the y axis through the point (20.0cm)ˆz. a negative point charge, q = −8.3×10−7c, is located at the point (10.0cm)ˆz. consider the electric field at a point p at (20.0cm, 0.00, 20.0cm). you must show the symbolic formula you use before substitution and place appropriate english description in the solution to this problem. do not even consider reporting an electric field that is not a vector or a number without appropriate units. (a)draw the electric field vectors of the three objects at point p and label them e~ plane,p , e~ line,p , and e~ point,p for the electric field of the plane, line, and point charge respectively. get the directions correct, you have no way to figure out relative magnitudes. (b)compute the electric field of the plane at point p, e~ plane,p . (c)compute the electric field of the line charge at point p, e~ line,p . (d)compute the electric field of the point charge at point p, e~ point,p . (e)compute the total electric field at point p, e~ p .

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Mathematics, 30.07.2019 17:20, anna8352

In the following questions, do not evaluate surds (e.g. ? 2). leave them in your answer in that form (e.g. ? ? = 1 ± ? 2). 1. (a) find the vector and cartesian equations of the plane which contains the point a=(2,3,-1) and is perpendicular to the vector n =(1,2,2). what is the perpendicular distance of the plane from the origin? ? (b) a plane has a normal = ? + 2? ? and is a perpendicular distance of 2 from the origin. what are the vector and cartesian equations of the plane? what is the perpendicular distance of the plane from the point b = (3,1,-1)? 2. if ? ? 1 = 1 + 3? ? and ? ? 2 = 1 ? 2? ? express each of the following complex numbers in the form ? ? + where a and b are real numbers (standard form / cartesian form) (a) (2? ? 1 + 1) (b) (3? ? 2 ? 2) (c) ? ? 1? ? 2 (d) , (complex conjugates of ? ? and ? ? )1212 (e) |? ? 1| , |? ? 2| (magnitudes of ? ? 1 and ? ? 2) (f) 1z1 (g) ? ? 1? ? 2 3. if ? ? 1 =2+4? ? and ? ? 2 =4+? ? determine the complex number ? ? 3 =? ? 1? ? 2 . sketch the complex plane to show the positions of all three of these complex numbers. determine the modulus ? ? and (principal value) of the argument ? ? of each of these three complex). 4. solve ? ? 4 = ? 1?

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