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December 20, 2014

Search: Calculus - Orthogonal Trajectories

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Calculus - Orthogonal Trajectories
Find the orthogonal trajectories of the family of curves: y = k*(e^-x) --------------- so k = y/(e^-x) differentiating we get: 1 = -k(e^-x)*(dx/dy) 1/(dx/dy) = -k(e^-x) dy/dx = -k(e^-x)...substituting for k: dy/dx = -(y/(e^-x))*(e^-x) dy/dx = -y Integral(1/=y)dy = Integral dx...
June 26, 2007 by COFFEE

Math
Mark each of the following True or False. ___ a. All vectors in an orthogonal basis have length 1. ___ b. A square matrix is orthogonal if its column vectors are orthogonal. ___ c. If A^T is orthogonal, then A is orthogonal. ___ d. If A is an n*n symmetric orthogonal matrix ...
January 2, 2011 by Melissa

calculus
two curves are orthogonal at a point of intersection of their tangents at that point cross at right angles. Show that the curves 2x^2+3y^2=5 and y^2=x^3 are orthogonal at (1,1) and (1,-1). Use parametric mode to draw the curves and to show the tangent lines
November 15, 2011 by Anonymous

Calculus
What is the orthogonal trajectory of y^2 - x^2 = C ??
December 14, 2009 by Nadine

Math - Vectors
Prove that vector i,j and k are mutually orthogonal using the dot product. What is actually meant by mutually orthogonal?
August 10, 2010 by Shaila

calculus
if the tangent of two intersecting circles, at their points of intersection are perpendicular, the circles are said to be orthogonal. Show that the circles x^2+y^2-6x+4y+2=0 and x^2+y^2+8x+2y-22=0 are orthogonal. find the equation of the tangent to the ellipse x^2/a^2 + y^2/b^...
June 28, 2008 by Kelly

Linear Algebra, orthogonal
The vector v lies in the subspace of R^3 and is spanned by the set B = {u1, u2}. Making use of the fact that the set B is orthogonal, express v in terms of B where, v = 1 -2 -13 B = 1 1 2 , 1 3 -1 v is a matrix and B is a set of 2 matrices
December 13, 2010 by Kay

Calculus
Resolve u=[3,4,7] into two orthogonal vectors, one of which is collinear with v=[1,2,3].
May 23, 2010 by Arima

Calculus
Resolve u=[3,4,7] into two orthogonal vectors, one of which is collinear with v=[1,2,3].
May 23, 2010 by Arima

Math
I'm doing a bunch of practice finals and I don't know how to approach this problem. Find a vector a such that a is orthogonal to < 1, 5, 2 > and has length equal to 6. If I want to find a vector that is orthogonal to <1,5,2>, I must take the cross product?
December 4, 2012 by A.

Calculus
Find the orthoganal trajectories of the family. Use a graphing utility to graph several members of each family. y = Ce^x What am I supposed to do here? Can someone point me in the right direction?
March 5, 2012 by Hannah

calculus
Find an equation of the plane orthogonal to the line (x,y,z)=(-4,-9,9)+t(-8,-1,5) which passes through the point (-9,9,-4). Give your answer in the form ax+by+cz=d.
March 4, 2010 by zama

Calculus
Determine whether the planes are parallel or orthogonal. Equations given: 5x - 3y + z = 4 x + 4y + 7z = 1 How exactly do I solve this? It wasn't covered completely in class.
April 8, 2013 by Krista

Calculus
Find an equation of the plane orthogonal to the line: (x,y,z) = (5,-6,-1) + t(3,10,-3) which passes through the point (-6,-1,5). so i got so far: x=5+3t y=-6+10t z=-1-3t Should be in form ax+by+cz+d=d Not sure where to go from there...
September 10, 2007 by Vectors and Planes

calculus (vectors)
Determine a vector that is orthogonal to the vector e = [3, -1, 4]
October 20, 2012 by KnowsNothing

Calculus-PLZ help!
Given u=3i-2j+k,v=2i-4j-3k, w=-i+2j+2k, 1 Find a unit vector normal to the plane containing v and w. 2 Find the volume of the parallelepiped formed by u, v, and w. 3 Are any of these vectors parallel? Orthogonal? Why or why not?
May 13, 2013 by Liz

calculus
I have 3 points: P(-3, 1, 2), Q(-1, 2, 3), R(2, 1, 0) and I need to find a nonzero vector orthogonal to the plane through these three points. I seem to recall this having something to do with the cross product, so I mad vectors PQ <2,1,1> & PR <5,0,-2> calculated ...
August 24, 2011 by cross product

math
Show that x^2+y^2-6x+4y+2=0 and x^2+y^2+8x+2y-22=0 are orthogonal.
July 9, 2010 by dan

linear algebra
Solve for x if the vectors (2, x, 7-x) and (x, 3, -2) are orthogonal
July 27, 2013 by Anonymous

Diagonalize
construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible. Just write down a diagonal matrix with one zero on the diagonal and then apply an orthogonal transformation. E.g. if you start with the matrix: A = [1 ,0 0,1] And take the orthogonal transformation...
July 12, 2007 by Jeff

Vectors
Determine a unit vector that is orthogonal to both u=[3,-4, 1] and v=[2,3,-4].
May 23, 2010 by Ariza

Math
Determine whether u and v are orthogonal,parallel, or neither. u=-2i+j v=3i+6j
February 16, 2011 by Matt

Calc
Determine whether u and v are orthogonal, parallel or neither u= <-4, 7>, v= <-14, 12>
February 13, 2012 by Darius

Math
Knowing u = (4,0,-3), v = (x,3,2) and that the orthogonal projection of v on u is a vector of norm 6, determine x. Thank you
August 27, 2012 by Robert

math
Determine all values of k for which each pair of vectors is orthogonal. a) (1,2) and (k,k) b) (1,2,1) and (k,2k,4)
September 23, 2014 by Kyle

Math
Determine all values of k for which each pair of vectors is orthogonal. a) (1,2) and (k,k) b) (1,2,1) and (k,2k,4)
September 24, 2014 by Kyle

Algebra
Determine all values of k for which each pair of vectors is orthogonal. a) (1,2) and (k,k) b) (1,2,1) and (k,2k,4)
September 24, 2014 by ZZZ Top

Algebra
Determine if the following two planes 2x+3y-z=4 and 3x-4y-6z=1 are parallel, orthogonal or coincidental
September 21, 2010 by Matthew

Linear Algebra
Knowing u = (4,0,-3), v = (x,3,2) and that the orthogonal projection of v on u is a vector of norm 6, determine x. Thank you
August 26, 2012 by Robert

Math
Find an equation of a plane through the point (1, 5, 1) which is orthogonal to the line x=3+5t y=5-1t z=-1+4t in which the coefficient of x is 5.
February 1, 2010 by Derek

Math
How do we know the ith of an invertible matrix B is orthogonal to the jth column of B^-1 , if i is not equal/unequal to j?
December 8, 2010 by Nolan

TRIGONOMETRY
Use the dot product to determine which of the following vector pairs are orthogonal. a. v1 = (-5,5) and v2 = (1,1) b. v1 = (154,169.4) and v2 = (88,64)
May 18, 2013 by Kate

physics
A particle is moving in a circular trajectory because of a magnetic field. Show that regardless of the veolocity of the particle, it will take the same amount of time to complete one revolution. I'm not sure how to prove this. Should i use the formula for circle trajectories.....
April 1, 2008 by Jessica

Linear Algebra
A test Question: Find the parametric equations of the line through the origin that is orthogonal to the plane 2x+4y-z=0
December 14, 2011 by Simon

Geometry/Algebra/Calculus
Why isn't the surface area of a sphere with radius r the following: 2*pi * (pi*r) That comes from the following flow of logic: Doesn't it makes sense to think of the surface area of the sphere with radius r as the the circumference of the semi-circle with radius r, pi*r (2*pi*...
January 26, 2014 by John

Math
The functional determinant of x, e^x, and e^-x is equal to___ The orthogonal trajectory of y^2 - x^2 = C is__ The slope of the normal line to y^2 = x/2 at P(1/8,1/4) is ____ help please...
December 14, 2009 by Alvin

Neurology
Which of the following pairs of terms identify spaces that are roughly PERPENDICULAR (orthogonal) in the human brain (give or take 30 degrees or so)?
April 27, 2013 by Anonymous

math
A trigonmetric polynomial of order n is t(x) = c0 + c1 * cos x + c2 * cos 2x + ... + cn * cos nx + d1 * sin x + d2 * sin 2x + ... + dn * sin nx The output vector space of such a function has the vector basis: { 1, cos x, cos 2x, ..., cos nx, sin x, sin 2x, ..., sin nx } Use ...
January 16, 2008 by mathstudent

vectors
how do you determine if two vectors are a) Collinear b) orthogonal?
June 17, 2010 by Ariza

rotational mechanics
a thin rod of length 2R and mass M is standing vertically on a perfectly smooth floor. the state of equilibrium in which the rod at rest is unstable and the rod falls. FInd the trajectories that the various points of rod describe and velocity with which the upper end of rod ...
March 31, 2010 by pramod

math
Find an orthonormal basis for the subspace of R^3 consisting of all vectors(a, b, c) such that a+b+c = 0. The subspace is two-dimensional, so you can solve the problem by finding one vector that satisfies the equation and then by constructing another solution which is ...
July 26, 2007 by john

Art History
In linear perspective, all parallel lines converge at a(n): A. orthogonal. B. vanishing point. C. horizon line. D. picture plane. OK, my textbook says it both A and C so I am totally confused.
November 22, 2014 by Pat

math
) Determine whether the following two planes x + 4y − z = 7 and 5x − 3y −7z = 11 are parallel, orthogonal, coincident (that is, the same) or none of these.
April 22, 2014 by Carrolyn

physics
Two frisky grasshoppers collide in midair at the top of their respective trajectories and grab onto each other, holding tight thereafter. One is a robust 250 g beast initially moving south at 20.0 cm/s, while the other is a svelte 150 g creature initially moving north at 60.0 ...
October 28, 2009 by physics studentt

math
can an inner product space v have a t invariant subspace U but also have an orthogonal complement that is NOT t-invariant???
March 3, 2007 by mk

math
Find the least squares approximation of x over the interval [0,1] by a polynomial of the form a + b*e^x --------------------------------------------------------- The polynomial produces an output space with two linearly independent basis vectors: u1 = 1, u2 = e^x I believe ...
January 18, 2008 by mathstudent

Linear Algebra
Find the basis for the following vector space. Please state the dimension of the vector space. S consists of all x in R3 such that x is orthogonal to n=(2,3,2)
November 20, 2011 by Simon

math
given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q are the unit vectors,find the dot product of vectors p and q?
January 2, 2013 by bhawani

math
given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q are the unit vectors,find the product of vectors p and q?
January 1, 2013 by bhawani

physics
An electron starting from rest acquires 4.20 keV of kinetic energy in moving from point A to point B. How much kinetic energy would a proton acquire, starting from rest at B and moving to point A? Determine the ratio of their speeds at the end of their respective trajectories.
September 8, 2010 by VJC

math
There is one step in a proof that I don't understand. Could someone please explain? u = any vector in vector space S W = finite dimensional subspace of S with orthonormal basis of vectors {v1, v2, ..., vn} The theorem to prove is: u can be expressed exactly one way as u = w1...
January 5, 2007 by mathstudent

Math
Show that A = [3 2 4 2 0 2 4 2 3] is distinguishable even though one eigenvector has algebraic multiplicity 2. Do this by brute force computation. Why would you expect this to be true, even without calculation? Then, for the A, write A= Q lambda Q^(T) where Q's columns are ...
July 12, 2012 by Christopher

Math
1. P5 is an innerproduct space with an inner product. We applied the Gram Schmidt process tot he basis {1,x,x^2,x^3,x^4} and obtained the following as the result {f1,f2,f3,f4,x^4+2}. a. What is the orthogonal complement of P3 in P5 with erspect to this inner product? b. What ...
April 13, 2012 by Scott

Physics
Two projectiles are launched from ground level at the same angle above the horizontal, and both return to ground level. Projectile A has a launch speed that is twice that of projectile B. (Sketch trajectories of projectiles). Assuming that air resistance is absent, what should...
May 24, 2010 by Christy

math
Prove that if A is a symmetric n x n matrix, then A has a set of n orthonormal eigenvectors. http://ltcconline.net/greenl/courses/203/MatrixOnVectors/symmetricMatrices.htm I've read the entire page and while it's on the correct topic, it doesn't prove what I'm looking to prove...
January 19, 2007 by mathstudent

Linear Algebra
Ok this is the last one I promise! It's from a sample exam and I'm practicing for my finals :) Verify if the following 4 points are consecutive vertices of a parallelogram: A(1,-1,1); B(3,0,2);C(2,3,4);D(0,2,3) (b) Find an orthogonal vector to the plane containing the ...
August 27, 2012 by Robert

ART! URGENT
What shold an artist do first in order to draw a two-point perspective image? A. Use orthogonal lines. B. Use value changes C. Draw all vertical lines D. Draw a horisan line C?
October 6, 2014 by Anonymous

math
The runway of an airfield faces west. An airplane, flying in the direction of north-east at a height of 2km and at a speed of 400km/h, on a path which passes over a point 3km west of the runway end, is spotted sqrt(29)km horizontally(south-western quadrant) from the runway end...
November 20, 2011 by Jainee

Trigonometry
Which of the following pairs of vectors are orthogonal? (i) v = 18i − 3j and w = −i − 6j (ii) v = 15i − 2j and w = −4i + 30j (iii) v = 3i − j and w = i + 3j A. (i) and (ii) B. (i) and (iii) C. (ii) only D. (i) only 17.
August 1, 2012 by Anonymous

Pre-Calculus/Calculus
I am too embarassed to ask this Calculus (really pre-calculus) question in tutoring, because I know I should know. Is the inverse of f(x)=3x-1 actually f(x)=1/3x+1? How do I find it? What if it asks the same equation replaced with f to the -1 power (x)? I think I know how the ...
July 1, 2008 by Molly

Calc 3
Consider the points below. P(2, 0, 2), Q(−2, 1, 4), R(7, 2, 6) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR. * I answered part a and got the correct answer with the vector <0,26,-13> I found...
September 8, 2012 by Backy

Calculus
What is the use of Calculus? How is it use in jobs? What jobs use Calculus? Calculus is used in engineering, economics, any physical science, and in business (e.g., actuary studies and statistics).
May 5, 2007 by Anonymous

linear algebra
3. Suppose A is symmetric positive definite and Q is an orthogonal matrix (square with orthonormal columns). True or false (with a reason or counterexample)? a) (Q^(T))AQ is a diagonal matrix b) (Q^(T))AQ is a symmetric positive definite matrix c) (Q^(T))AQ has the same ...
December 1, 2010 by michael

linear math
Let u=(2,0,k,-1) v=(-4,0,-3,2) and w= (0,1,0,0). Each answer must be justified(there is no answer where k=nothing) a) find all values of k, (if any) for which u is orthogonal to v b) Find all values of k (if any) for which the set {u,v,w} is linearly independent. Find all ...
November 20, 2011 by Simon

math
Can I please get my answers double checked? True or False 1. The tangent function is used to find the angel between two vectors. True 2. If two vectors are orthogonal, then their dot product is -1. False 3. The length of the projected vector is always shorter than the length ...
June 17, 2013 by mysterychicken

Biology
Theme A: Surface anatomy of the brain Of the following pairs of directional terms, which pair contains terms that define PERPENDICULAR (orthogonal) directions when applied to the identified region of the central nervous system? in the brainstem, ventral & anterior in the ...
April 10, 2013 by Anonym

Maths trigonometry
using basic trigonometry derive the following equations, which are used to convert cartesian to polar coordinates and vice versa. why is the cos(phi)in the x term? x = R cos (phi) sin (lamda) y = R sin (phi) they are used in orthogonal projection of a spherical surface to a ...
October 16, 2011 by forest

Algebra
In an interview of 50 math majors, 12 liked calculus and geometry 18 liked calculus but not algebra 4 liked calculus, algebra and geometry 25 liked calculus 15 liked geometry 10 liked algebra but neither calculus nor geometry 2 liked geometry and algebra but not calculus. Of ...
January 11, 2010 by Anita

art history
1. Art enabled new understandings in this field 2. Credited with being the founder of Renaissance painting in the Netherlands 3. his most famous painting depicts sin and redemptionhe 4. brought Germany into the mainstream of Renaissance art 5. objects appear to get smaller ...
June 23, 2014 by bekah

Calculus
What is the simplest solution to the Brachistochrone problem and the Tautochrone problem involving calculus? (I know that the cycloid is the solution but I need a simple calculus proof as to why this is the case)
May 27, 2010 by Sam

math
8. In an interview of 50 math majors, 12 liked calculus and geometry 18 liked calculus but not algebra 4 liked calculus, algebra, and geometry 25 liked calculus 15 liked geometry 10 liked algebra but neither calculus nor geometry 2 liked geometry and algebra but not calculus. ...
November 30, 2009 by poo

Art Please check answers
1. These two technological advancements of the Industrial Revolution helped lead to the development of Impressionism. the railroads and the printing press the railroads and photography photography and electric lighting** the automobile and electric lighting 2. According to ...
December 3, 2012 by Anonymous

Art Please check answers
1. These two technological advancements of the Industrial Revolution helped lead to the development of Impressionism. the railroads and the printing press the railroads and photography photography and electric lighting** the automobile and electric lighting 2. According to ...
June 2, 2013 by Mstv1112

physics
The drawing shows a steel ball rolling along a flat surface at constant velocity from point A to point B. A magnet exerts an attractive force on the ball only for the short time that passes as the ball rolls past point B. Which one of the following trajectories does the ball ...
June 8, 2014 by Sam

physics
he drawing shows a steel ball rolling along a flat surface at constant velocity from point A to point B. A magnet exerts an attractive force on the ball only for the short time that passes as the ball rolls past point B. Which one of the following trajectories does the ball ...
June 8, 2014 by Sam

art history
1. art enabled new understandings in this field (the protestant reformation) 2. credited with being the founder of Renaissance painting in the Netherlands distance 3. his most famous painting depicts sin and redemption (genre) 4. he brought Germany into the mainstream of ...
June 23, 2014 by bekah

Physics (help steve)
Exact solutions for many-body problems are rarely encountered in physics. The following problem deals with a non-trivial motion of four charges. Due to the symmetry of the problem it is possible to determine the trajectories of the charges analytically. Four identical ...
July 9, 2013 by Kay

SCIENCE,PHYSICS
Exact solutions for many-body problems are rarely encountered in physics. The following problem deals with a non-trivial motion of four charges. Due to the symmetry of the problem it is possible to determine the trajectories of the charges analytically. Four identical ...
July 10, 2013 by GT

math
If vector u = [1,-3,-2] and vector v = [4,-5,3] find: a) |vector u + vector v - 5j | b) Find Q, where P (-7,5,-1] and vector PQ=2(vector u) c)find vector w which is orthogonal to both vector u and vector v
October 23, 2014 by Tina

math-calculus
1.For any function y+f(x), express dy/dx using limit notation. Give a clear explanation for your given answer. you probably meant to type y=f(x) By definition dy/dx = Limit (f(x+∆x) - f(x))/∆x as ∆x-->0 The explanation of this equation is the whole basis ...
March 26, 2007 by Chris

calculus
Can someone please tell me what the word "WHOLE" AND "IRRATIONAL" MEAN IN CALCULUS? THANKS
September 2, 2008 by Mike

Math:Calculus
Use the Fundamental Theorem of Calculus to find the derivative of g(x)=1/(1+t^5)dt in the interval 1 to x.
November 22, 2010 by HELP!!!!

Calculus
Use fundamental theorem of calculus: Int(pi/2_pi) of e^(sin(q))*cos(q)dq
April 28, 2011 by Rachel

Calculus Help
Use calculus to find the area A of the triangle with the given vertices. (0, 0), (3, 1), (1, 8) A = ????
May 1, 2014 by Anonymous

Calculus, bobpursley!
This has to do with my last Calculus problem. I need help on it..The part I replied to after you answered the question.
September 21, 2010 by Leanna

Calculus
The area is bounded by y= x^3, x= 2 is rotated around the x-axis. Find the volume using calculus.
July 24, 2012 by Ted

math, calculus 2
Use part 1 of the Fundamental Theorem of Calculus to find the derivative of g(x)= integrate from 9x to 4x of ((u+4)/(u-1))du
August 29, 2012 by bobby

Calculus Precalculus
Answer the calculus question about Point P, 45 mph, etc. It is ALREADY posted on here.
August 27, 2011 by Zach

COLLEGE CALCULUS. HELP!
the fundamental theorem of calculus, f(x)=∫(0,x) t^3+2t^2+2dt, and find f"(x). my answer was: f'(x)=x^3+x^2+2 f"(x)=x^4/4 + 2x^3/3 + 2x it said its wrong.
April 15, 2012 by lindsay

calculus
Find the arc length of the graph of y = x from x = 0 to x = 3 using calculus.
September 11, 2010 by Denise

calculus
I need help with this calculus problem. H(S)=S/(1+S) If F 1/2, -1/2 & (a+1)? I can't figure out what this mean /?
May 30, 2011 by Tammy

calculus
Why do we end up with f(x) instead of f(t) on the second fundamental theorem of calculus?
November 7, 2011 by Jose

Calculus 1
Use the fundamental theorem of calculus to find the area bounded by f(x)=3 square root of x+2x and the x-axis between x-=0 and x=1
December 6, 2011 by Ihg

Calculus AP need help!
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. If f(x)= ∫(4,x^3)√(t^2+10) dt then f '(x).
April 17, 2012 by dania

Calculus
I need to take a college calculus class. Can someone direct me to a site which might help me get a good start? Thanks in advance.
July 10, 2008 by jules

calculus
Use the fundamental theorem of calculus to evaluate the following integral ∫^π/2 **the bottom is zeroe. |cosx| dx
December 13, 2011 by Roxy

Calculus
Use any calculus method to determine extrema, intervals where the function is increasing or decreasing, asymptotes,and points of inflection for y = -x^4 + 2x^3 - x + 2
October 20, 2012 by Sissy

Calculus
Find the derivative of the following function using the appropriate form of the Fundamental Theorem of Calculus. intergral s^2/(1+3s^4) ds from sqrtx to 1 F'(x)=?
April 18, 2014 by Brady

Calculus
Integrate e^(-x^2/2) dx What branch of calculus is this? Is this differential equations?
March 7, 2008 by mathstudent

calculus
Find the limit of this calculus problem.? (5x-3)/(ln(5+4e^(x)) x=inf
November 4, 2010 by Zel

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