1. Given f(x,y,z)=x^2y^3z^6, in what direction is F(x,y,z) increasing most rapidly at the point P(1,-1,1). What is the rate of increase? 2. Locate and classify the critical points of the function h(x,y) = x^2 -4x+4xy+y^2-16y.
1 Given a = 9i - 5j and b = 7i-4j, express i and j in terms of a and b 2 Given a=<4,5,-3> and b =<4,-2,2> determine whether a and b are parrallel, perpendicular, or neither. 3 Given F = 4i -2k;..... P(0,1,0) and Q(4,0,1) find the work W done by the force (F)moving a particle in a straight line from P to Q. 4 Given a
I don't understand how you count the degree of the vertices. (See attached file for full problem description) --- 2.- Prove that a tree with Delta(T)=k ( Delta means maximum degree) has at least k vertices of degree 1. Proof. We prove it by contradiction. Suppose that and there are s vertices of degree 1, where s<k.
Please see the attached file for the fully formatted problems.
Please see the attached file for the fully formatted problems.
Two planes left an airport at noon. one flew east at a certain speed and the other flew west at twice the speed. The planes were 2700 mi. apart in 3 hours. how fast was each plane flying? Write an equation and solve.
If V is a vector function, show the following by expansion that the following equality may be maintained: (V.grad)V=(gradxV)xV + grad(V^2/2) Please see the attached file for the fully formatted problems.
Find a subset of the vectors that forms a basis for the span of the vectors; then express each vector which is not in basis as a linear combination of the basis vectors. v1= (1, 1, -1), v2= ( 1, 0, 1), v3= ( 1, -2, 5), v4= ( 5, 3, 2)
I need assistance finding the period of a vector valued function. The function is of the form cos^2(2T)+Sin^2(3t) + cos(2t-pi/2) I remember doing something like this back in pre calc where the period was 2pi/b but the functions were not vectors. How would I proceed from here? Any help is appreciated.
A tree has 11 vertices of degree 3, 12 vertices of degree 2, 10 vertices of degree 4 and the remaining vertices are of degree 1. How many vertices does it have?
Please view the attached files to see the expressions which are in question for parts A and B. 1. A) Determine whether the following sets are vector spaces, in each case giving reasons for your answer. B) Determine whether W is a subspace of the given vector space V.
Find the equilibrium vector for each matrix M1 = .85 .15 M2= 3/5 2/5 .55 .45 1/4 3/4
Each square n*n region of an image yields a vector of length n^2 such that the components of the vector are the grey levels of the pixels in the square. Let u, v be the vectors obtained from two image patches, let a be the average of the entries in u, let b be the average of the entries in V and let e be the vector of length n^
(See attached files for full problem description) For this one you need chapter 2 I think, it is problem number 4 page 57.
Please show in detail how to find the center, vertex, & directrix of parabola, the center, vertices, & foci for the ellipse, the center, vertices, foci, & asymptopes of any hyperbola 1) 9X^2+4y^2-18X-27=0 2) x^2+4X-8y+28=0 3) -3x^2+2y^2+12x-4y+8=0
Please show a detailed solution to this problem. Pleas show the curve and vectors together in a sketch. Thank you! Find the unit vectors that are tangent and normal to the curve at the given point: y = e^x , (ln2,2)
Vectors in the plane and the horizontal/vertical components of force : A kite string exerts a 12-lb pull (F=12) on a kite and makes a 45° angle with the horizontal.
Please find the horizontal and vertical components of F in the problem below: A kite string exerts a 12-lb pull (F=12) on a kite and makes a 45° angle with the horizontal. Find the horizontal and vertical components of F.
Prescribed textbook: Viscous Fluid Flow, 2nd Edition, F. M. White In the attached document. Please show me in detail (use maths) how to obtain the equation 3-149 from 3-148 and how to obtain equation 3-151 from 3-150.
1. Find the component form of the vector representing the velocity of a boat traveling at 8 knots, or nautical miles per hour, with a bearing of N 53-degrees W. 2. A force of 703 pounds is needed to push a stalled car up a hill inclined at an angle of 16-degrees to the horizontal. Find the weight of the car. Ignore fric
Let vector r(t) = t i + t^2 j represent a plane curve. Find T(t), T(1) and N(1). Sketch the plane curve and graph the vectors T(1) and N(1) at the point t = 1.
A baseball is hit from a height of 3 feet with an initial speed of 120 feet per second at an angle of 30 degrees above the horizon. Find the vector-valued function describing the position of the ball t seconds after it is hit. To be a home run, the ball must clear a wall 385 feet away and 6 feet tall. Determine if this is a home
Given the vector r(t) = t i + t^2 j find T(t), T(1) a dn then N (1). After this I am to sketch the plane curve and graph the vectors T(1) and N(1) at t = 1.
I am asked to find the unit tangent vector at t=2 for the following : vector r(t) = t i + t^3 j + 3t k How do I do this problem and what is the final answer?
Find the velocity, speed and acceleration of the vector-valued function: Vector r = cost i + sint j - 16t^2 k at t=pi/4
How do I evaluate the limit of the following vector: lim[(e^2t/t^2-1)i + (1-cost/t)j + sq rt (4-t^2)] t-->0 How do I go about solving this problem and what is the answer that will be obtained. I'm not even certain where I should begin.
Please explain in step by step detail the following: 25. A weight of 850 pounds is suspended by two cables. ONe cable makes an angle of 66 degrees with a vertical line, the other makes an angle of 42 degrees with a vertical line. Find the amount of force exerted by each of the cables. 24. An airplane is scheduled to reac
1. Explain why vectors QR and RQ are not equivalent. 2. Explain in your own words when the elimination method for solving a system of equations is preferable to the substitution method.
The problem asks me to sketch the curve represented by the vector-valued function. The vector-valued function is: r(theta) = cos theta i + 3 sin theta j The solution in the solution manual has the following: x = cos theta y = 3 sin theta Up to here I understand what is being done. T
Vector Fields and Work Done when a Paritcle Moves Along a Curve; Find the Potential of a Conservative Field; Find Curl...
Given...determine if F is conservative. Find its potential. Given...find the potential of this conservative field. Find length of curve... Find curl F... Given the vector field... find work done when a paritcle moves along a curve. Please see the attached file for the fully formatted problems.
Describe the surfaces in R3 of the equation: y^2 = x^2 + z^2