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Consider the vector field: V = exi + sin y2 j + cos z5 k.
a. What is the divergence of the vector field? Is it vector or scalar quantity?
b. Find the divergence of the vector field at the point P = (1, √π/2, 5√π).
c. What is the curl of the vector field? Is it vector or scalar quantity?
d. Find the curl of the vector field at the same point P = (1, √π/2, 5√π).
Which conclusion can be made about the vector-field?
Suppose G is an abelian group of order m. Let m, n be relatively prime. Show that for every element g in G, there exists an element x in G such that x^m=g. Abelian Groups and Relatively Prime Order
Five hundred feet of fencing is available for a rectangular pasture alongside a river, the river is serving as one side of the rectangle. Find the dimensions for the greatest area.
find the equation of the tangent line to the curve f(x)=4/(5x + 7) at the point (-1.2). (use the definition of derivative (not short cut) to find f'(x))
The measure of three of the angles of a quadrilateral are 67, 112, and 55 degree. What is the measure of the fourth angle?
Anthony Brett and Charles run a small business and made a profit of $x in a month. They decided to share the profit so that Anthony received one-sixth of the profit, Brett received one-third of the profit and Charles received one-half of the profi..
A closed rectangular box having a volume of 7 ft3 is to be constructed. If the material for the sides costs $1.2/ft2 and the material for the top and bottom costs $1.3/ft2, find the dimensions of the box that can be constructed with minimum cost. ..
assume that all of the cadburys dairy milk bars bought in england were the standard length of 11.4cm. when laid
Find each of the following for the given inner product defined in R^2 =3u(subscript 1)v(subscript 1) + u(subscript 2)v(subscript 2)
the length of the rectangular playing field is 3 yards longer then double the length. If the perimeter is 252 yards, what are the dimensions?
Let G be a group (finite or infinite) and let a and b in G. Let o(a) represent the order of a. Suppose G is abelian and both a and b are of finite order. Show that ab is of finite order and o(ab) divides o(a)o(b).
1) Rudin, Ch. 1, Problem 1: If r is rational (r not equal to 0) and x is irrational, prove that r+x and rx are irrational.2) If (a_n), (b_n) are rational sequences, and lim a_n = a, lim b_n = b, show that: lim(a_n+b_n) = a+b, and lim(a_n b_n) = ab. 3..
Find a linear model for the cost, of waste collection as a function of the number of kilograms.
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