Find the velocity, acceleration, and speed of a particle with position function r(t) = <-7tsin(t), -7tcos(t), 4t^2> v(t) = <?, ?, ?> a(t) = <?, ?, ?>...

Find the velocity, acceleration, and speed of a particle with position function r(t) = <-7tsin(t), -7tcos(t), 4t^2> v(t) = <?, ?, ?> a(t) = <?, ?, ?>...

Find two unit vectors orthogonal to a = <4,-1, 2> and b = <3, 3, 1> First vector = <?, ?, ?> Second vector = <?, ?, ?>

The answer needs to be simplified and written in the form of ai+bj.

A weight of 100 pounds is suspended by two ropes A and B. Rope A makes an angle of 30 degrees with the ceiling and rope B makes an angle of 45 degrees with the ceiling. What are the magnitudes of...

MX=pMC and OX=qOB, if OABC is a parallelogram in which vectors OA= a and OC=b and M is the midpoint of AB and MC meets OB at X

Considering that a and b are scalar to each other

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...

If not, when would linear dependency imply coplanarity?

Find all of the extrema of g(x,y,z)=xyz on the surface z=e^(-x^2-y^2).

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...

Let C be the curve given by the equation, R(t)= sin t i + cos t j + log sec t k (0≤t<π/2) Find: a.) the element of arc length, ds, along C, in terms of...

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 +...

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 the extrema of f subject to the given conditions. f(x,y,z) = x+ y + z x^2-y^2=1 2x+z=1

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...

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...

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...

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