Vector analysis

Apply Stroke's theorem to evaluate the integral over C of (ydx + zdy + xdz), where C is the curve of intersection of the unit sphere x^2+y^2+z^2=1 and the plane x+y+z=0, traced anticlockwise viewed from the side of the positive x-axis

Vector analysis

(a) Let F(x,y,z)=(x^2+y-4)i + (3xy)j + (2xy+z^2)k. Evaluate the double integral over S of (curl(F). dS) where S is the surface x^2 + y^2 + z^2 = 16, z >=0 (I) Using Stroke's theorem (II)By direct evaluation (b) Find the flux of the vector field F(x,y,z) = (y-x)i + (x+y)j + y k across the side of the triangle with vert ...continues

Period, amplitude, and viewing rectangle

Determine the period and amplitude of the function.Then describe the viewing rectangle 1-y=3/2cos x/2 2-y=2/3cos pi x/10

Inventory turn over rate/cost

BI:$18,500 (in sales figures)purchases $44,700(at cost)net sales $50,300 (sales figures) markup is 22% based on cost, determine inventory turnover at cost..and at sales price

Probability distributions

1) Suppose Tucker the beagle is working in customs inspecting passengers and luggage for banned substances, and Tucker alerts the handler by sitting next to the location of the banned substance. What would be a reasonable guess for the distribution of each of the following: (a) the number of alerts by Tucker during the next 3 ...continues

Probability density function

) Let X and Y have joint probability density function f(x,y) (s,t) = ce ^ -(s + 2t) for 0 <= s, and 0 <= t. Find (a) c (b) Pr {min (X, Y) 1/3} (c) Pr {X <= Y} (d) The marginal probability density function of X (e) E [XY] 5) Let X and Y be independent uniform (0,1) random variables. Compute (a) Pr {X < Y} (b) Pr {X ...continues

Probability density function

6) Suppose we have a building with a floor shaped like an isosceles right triangle. The two sides adjacent to the right triangle have length 100 feet. Think of the right angle being at the origin, and other two corners at (100, 0) and (0, 100). The overhead crane is located at the origin and needs to travel to a point (X, Y), w ...continues

Correlation

6) Suppose we have a building with a floor shaped like an isosceles right triangle. The two sides adjacent to the right triangle have length 100 feet. Think of the right angle being at the origin, and other two corners at (100, 0) and (0, 100). The overhead crane is located at the origin and needs to travel to a point (X, Y), w ...continues

Mean and variance

7) suppose the average weight of an item labeled 16 ounces actually has mean 17 ounces and variance 4 (ounce^2). What is the approximate probability that the combined weight of 25 items exceeds 445 ounces? What theorem is useful in answering this question?

establishing codomain, r2 to r3, proving onto, constructing inverse

establishing codomain, r2 to r3, proving onto, constructing inverse f(x,y)=(x+y,x-y,xy)