you are on a boat 400 m from the closest point Perpendicular on the beach. you want to visit your friend who is located another 1km along the beach. if you can row pedal boat at a constant speed of...
Vector Calculus Resources
Considering that a and b are scalar to each other
Find a transformation matrix that will turn the triangle with vertices (0,0), (1,0), and (0,1) in the uv-plane into the triangle with vertices (1,0),(0,1), and (2,2) in the xy-plane. Find...
Describe the region bounded by the planes: x = 0, y=0, z=0, x+y=4, and x=z-y-1. Describe as a region (in any order you can) the region inside the ball x^2+y^2+z^2=4 and...
Evaluate ffD(x^2+y^2)dA where D is the region in the first quadrant bounded by y=x, y=3x, and xy=3
Lagrange multipliers work great for finding the minimum value of y-ax, restricted to the curve y^2-x^2=1 for any a with 0<=a<1 (what is it?) but fails quite miserably if a >=1. Use the geometry...
Find all of the extrema of g(x,y,z)=xyz on the surface z=e^(-x^2-y^2).
Find the extrema of f subject to the given conditions. f(x,y,z) = x+ y + z x^2-y^2=1 2x+z=1
Use differentials to find the approximate amount of copper used in the four sides and bottom of a rectangular copper tank that is 6 feet long, 4 feet wide and 3 feet deep inside if the sheet of copper...
Suppose that x^2+y^3-z^4=1 and z^3+zx+xy=3. a.Take the total differential of both these surfaces. b.The two given surfaces intersect in a curve along which y is a function of x...
For each vector field in R4 given below, either find a function for which it is the gradient, or explain why no such function exists. Variables are in the order x, y, z, w. a.(siny +...
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an airplane is heading 040degree with an airspeed of 800 km/h. A wind from the west causes it to have the course 045 degree. Find the resultant ground speed of the airplane and the speed of the wind...
Suppose a body has a force of 10 pounds acting on it to the right, 25 pounds acting on it -135° from the horizontal, and 5 pounds acting on it directed 150° from the horizontal. What single force...
If vector v has an initial point at P1 and a terminal point at P2, write v as multiples of the basis vectors i = <1,0> and j = <0,1> That is, write v in the form v = ai + bj. P1...
Find a unit vector that points in the opposite direction as v. Let .v=-3(pi 2)i-4(pi 2)j A. u= (3/5)i+(4/5)j B. u= -(3/5)i-(4/5)j C. u= -(5/3)i-(5/4)j D...
Find a unit vector in the direction of the vector v=〈√2,√2〉. Please show step by step work to solution and provide final answer. Please and Thank You!
X1 = [ 1 -1 1] x2 = [1 0 -1] create a matrix A having X1 and x2 as its Rows. The null space V of A consist of all vector x such that Ax =0. List all vector in V.
A projectile is fired with an initial speed of 230 m/s and angle of elevation 60°. (Recall g ≈ 9.8 m/s^2. Round your answers to the nearest whole number.) (a) Find the range of the projectile...
We have an empty cardboard box of dimensions breadth = 3 m, length = 4 m, and height = 2 m. An ant and a fly are sitting at one of the 8 corners inside the box and wish to go get some food at the...
At what points does the curve r(t) = ti + (4t − t^2)k intersect the paraboloid z = x^2 + y^2? (If an answer does not exist, enter DNE.) smaller t-value (x, y, z) =...
