Wednesday

April 16, 2014

April 16, 2014

Number of results: 27,433

**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...
*Tuesday, June 26, 2007 at 1:17am 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 ...
*Sunday, January 2, 2011 at 11:12am by Melissa*

**Calculus**

The normals of the two planes are (5, -3, 1) and (1 , 4, 7) Since one is not a multiple of the other, the two planes cannot be parallel if they are orthogonal (perpendicular) then their dot product must be zero so (5,-3,1)∙(1,4,7) = 5 -12 + 7 = 0 YEs, they are orthogonal
*Monday, April 8, 2013 at 10:47pm by Reiny*

**Calculus**

is this a) First see that the two vectors are orthogonal: [4,8,-4].[-1,2,3]=-4+16-12=0 => orthogonal Next solve for s and t for each coordinate direction (x,y,z) 4+4t=1-s 7+8t=5+2s => s=-1, t=-1/2 and this b) Substitute into original equation: <4,7,-1>-<2,4,-2&...
*Sunday, May 6, 2012 at 1:56am by J*

**Calculus**

First see that the two vectors are orthogonal: [4,8,-4].[-1,2,3]=-4+16-12=0 => orthogonal Next solve for s and t for each coordinate direction (x,y,z) 4+4t=1-s 7+8t=5+2s => s=-1, t=-1/2 Substitute into original equation: <4,7,-1>-<2,4,-2>=<2,3,1> <1,...
*Sunday, May 6, 2012 at 1:56am by MathMate*

**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
*Tuesday, November 15, 2011 at 4:59pm by Anonymous*

**Calculus**

If the plane is orthogonal to (5,-6,-1) + t(3,10,-3), then it is also orthogonal to the parallel line t(3,10,-3) which moves through the origin. Consider first the plane orthogonal to this line which contains the origin. If the point (x,y,z) is on that plane, then: (x,y,z) dot...
*Monday, September 10, 2007 at 8:40pm by Count Iblis*

**Calculus**

What is the orthogonal trajectory of y^2 - x^2 = C ??
*Monday, December 14, 2009 at 9:03am by Nadine*

**Calculus**

u•w = v•w u•w - v•w = 0 (u-v)•w = 0 so u-v is orthogonal to w u×w = v×w u×w - v×w = 0 (u-v)×w = 0 so u-v is parallel to w so, u-v = 0 u=v
*Tuesday, November 29, 2011 at 4:37pm by Steve*

**Math - Vectors**

Prove that vector i,j and k are mutually orthogonal using the dot product. What is actually meant by mutually orthogonal?
*Tuesday, August 10, 2010 at 3:39am 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^...
*Saturday, June 28, 2008 at 9:44pm by Kelly*

**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?
*Monday, March 5, 2012 at 10:43am by Hannah*

**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
*Monday, December 13, 2010 at 10:59am by Kay*

**Calculus **

Resolve u=[3,4,7] into two orthogonal vectors, one of which is collinear with v=[1,2,3].
*Sunday, May 23, 2010 at 2:12pm by Arima *

**Calculus **

Resolve u=[3,4,7] into two orthogonal vectors, one of which is collinear with v=[1,2,3].
*Sunday, May 23, 2010 at 2:43pm by Arima *

**math**

Mystery: What text are you using? These are unusual questions for a HS text. This wording sounds very much like linear algebra. Remember the definition of orthogonal: Two vectors are orthogonal when their dot product is zero.
*Monday, June 17, 2013 at 4:53pm by bobpursley*

**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.
*Thursday, March 4, 2010 at 11:50am by zama*

**Math**

Two vectors are orthogonal to each other when their inner product equals zero. For example, (1,-3) and (3,1) are orthogonal because (1,-3).(3,1)=1*3+(-3)*1=0 If we are looking for a vector, (p,q,r,s) which is orthogonal to the given vectors (1,4,4,1) and (2,9,8,2), we just ...
*Wednesday, December 8, 2010 at 8:37am by MathMate*

**Linear Algebra**

Define proj(u, v) to be the projection of u onto v. proj(u, v) = v*(u dot v)/(v dot v) ||u|| = norm u From the 3 given vectors, we want to form a basis such that each basis vector is orthogonal to every other and an unit vector. Take e1 = ||[1,0,1]|| = (1/sqrt(2))[1,0,1]. The ...
*Sunday, January 2, 2011 at 11:04am by Marth*

**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?
*Tuesday, December 4, 2012 at 4:40pm by A.*

**calculus (vectors)**

Determine a vector that is orthogonal to the vector e = [3, -1, 4]
*Saturday, October 20, 2012 at 12:42pm by KnowsNothing*

**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.
*Monday, April 8, 2013 at 10:47pm by Krista*

**Calculus-PLZ help!**

v-u x w-u is a vector perpendicular to the plane containing u,v,w. Divide by its magnitude to get a unit vector uxv•w is the volume desired check u•v u•w v•w for orthogonal
*Monday, May 13, 2013 at 6:58pm by Steve*

**science**

since gravity affects each bomb equally, their trajectories are the same.
*Thursday, June 28, 2012 at 9:52am by Steve*

**Trigonometry**

Calculate the dot product of the three pairs of vectors. If the dot product is zero, the vectors are orthogonal. For example, (i)<18,-3>.<-1,-6>=-18+18=0 So pair (i) is orthogonal. Post your answer for checking if you wish.
*Wednesday, August 1, 2012 at 4:32pm by MathMate*

**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...
*Monday, September 10, 2007 at 8:40pm by Vectors and Planes*

**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?
*Monday, May 13, 2013 at 6:58pm by Liz*

**Physics**

No, #1 and #3 would be different trajectories. Note that they are asking about position vs. time, not about the shape of the trajectory
*Wednesday, June 4, 2008 at 6:48pm by drwls*

**Linear Algebra**

The dimension of vector space R3 is 3. n=(2,3,2) occupies one of the three dimensions, so the subspace orthogonal to n has a dimension of two, i.e. two vectors span the remaining subspace. The basis of the remaining subspace can be in many forms. One way is to start with an ...
*Sunday, November 20, 2011 at 3:09pm by MathMate*

**calculus**

By inspection, the curves intersect at (1,1) and (1,-1) ellipse: 4x + 6yy' = 0 y' = -2x/3y at (1,1) slope = -2/3 at (1,-1) slope = 2/3 semicubical parabola: 2yy' = 3x^2 y' = 3x/2y at (1,1) slope = 3/2 at (1,-1) slope = -3/2 The slopes at the intersections are negative ...
*Tuesday, November 15, 2011 at 4:59pm by Steve*

**Calculus**

express C as a function of x and y: C = ye^-x find y' implicitly y'e^-x - ye^-x = 0 y' = y so, for any point on the curve Ce^x, the slope is just y On a perpendicular trajectory, the slope is -1/y dy/dx = -1/y y*dy = -dx y^2/2 = -x+c Thus parabolas opening to the left are ...
*Monday, March 5, 2012 at 10:43am by Steve*

**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...
*Thursday, July 12, 2007 at 2:55pm by Jeff*

**linear algebra**

Solve for x if the vectors (2, x, 7-x) and (x, 3, -2) are orthogonal
*Saturday, July 27, 2013 at 11:06am by Anonymous*

**Math**

First please confirm the following typographical correction indicated in bold: "How do we know the ith row of an invertible matrix B is orthogonal to the jth column of B^-1 , if i is not equal/unequal to j?" By definition, BB-1=I which by matrix multiplication, the inner ...
*Wednesday, December 8, 2010 at 8:45am by MathMate*

**Vectors **

Determine a unit vector that is orthogonal to both u=[3,-4, 1] and v=[2,3,-4].
*Sunday, May 23, 2010 at 5:41pm by Ariza *

**Linear Algebra**

... and the basis for the subspace orthogonal to n is {A1,A2}.
*Sunday, November 20, 2011 at 3:09pm by MathMate*

**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
*Monday, August 27, 2012 at 8:36pm by Robert*

**Math - Vectors**

mutually orthogonal=the three of them are orthogonal (or perpendicular) to each other,, [angle between them is 90 degrees] first recall the formula for the dot product. for any given vectors A and B, A(dot)B=|A||B|cos(theta) where |A| and |B| are the magnitude of vectors A and...
*Tuesday, August 10, 2010 at 3:39am by jai*

**math**

Show that x^2+y^2-6x+4y+2=0 and x^2+y^2+8x+2y-22=0 are orthogonal.
*Friday, July 9, 2010 at 6:02am by dan*

**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
*Sunday, August 26, 2012 at 4:06pm by Robert*

**calculus (vectors)**

cos 90 = 0 (orthogonal vectors have 90 in between) substitute a vector [x1 , x2, x3] for the second vector and use dot product [3, -1, 4] . [x1, x2, x3] = 0 3x1 - x2 + 4x3 = 0 then solve for xs that would work. an example would be [1, 3, 0]
*Saturday, October 20, 2012 at 12:42pm by JackInTheBox*

**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 ...
*Wednesday, August 24, 2011 at 11:15am by cross product*

**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.....
*Tuesday, April 1, 2008 at 11:35pm by Jessica*

**Math**

If your vectors are orthogonal, then each dimentsion must equal each other. p=3q and qp=1
*Friday, July 31, 2009 at 7:31am by bobpursley*

**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?
*Wednesday, December 8, 2010 at 8:45am by Nolan*

**Math**

Determine whether u and v are orthogonal,parallel, or neither. u=-2i+j v=3i+6j
*Wednesday, February 16, 2011 at 10:28pm by Matt*

**Linear algebra**

Three vectors are linearly independent if the determinant formed by the vectors (in columns) is non-zero. So for u=(1,-1,-1), v=(a,b,c), w=(d,e,f) There are many possible choices of v and w such that the determinant 1 a d -1 b e -1 c f is non-zero. The simplest way is to ...
*Thursday, August 11, 2011 at 7:59am by MathMate*

**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.
*Monday, February 1, 2010 at 7:06pm by Derek*

**Calculus**

Yes, you've got it right. In (a), you see clearly that the equations are different, so they represent different planes. In addition, the coefficients of x, y and z are identical, therefore they are parallel, since the orthogonal vector of both planes are (5,-2,4). For (b), ...
*Saturday, May 5, 2012 at 12:21am by MathMate*

**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...
*Monday, December 14, 2009 at 2:31am by Alvin*

**Algebra**

Determine if the following two planes 2x+3y-z=4 and 3x-4y-6z=1 are parallel, orthogonal or coincidental
*Tuesday, September 21, 2010 at 7:54am by Matthew*

**Math**

You can take the cross-product if you have two vectors, but you only have one so how about this ... let the vector be (a,b,c) then we know that (a,b,c)dot(1,5,2) = 0 a + 5b + 2c = 0 pick any value for any variable, e.g. let b = -1 , c = 2 a - 5 + 4 = 0 a = 1 so (1 , -1 , 2) is...
*Tuesday, December 4, 2012 at 4:40pm by Reiny*

**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
*Wednesday, December 14, 2011 at 12:07pm by Simon*

**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 ...
*Wednesday, March 31, 2010 at 11:46am by pramod*

**science**

I do not understand what you mean by a "frame". If is is "the same particle" in both "frames", why is the time dependence of the position vector different? If you are talking about two different particles following different trajectories, then the problem makes sense. Just ...
*Saturday, November 26, 2011 at 12:23am by drwls*

**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)?
*Saturday, April 27, 2013 at 8:16am by Anonymous*

**math**

Original basis vector u0 = 1 Orthogonal basis vector v0 = 1 Orthonormal basis vector g0 = v0/|v0| |V0|^2 = 2 pi ---> g0 = 1/sqrt(2 pi) Original basis vector u1 = cos x Orthogonal basis vector v1 = u1 - <u1, g0> * g0 = cos x because <cos(x), 1> = 0
*Wednesday, January 16, 2008 at 7:39pm by Count Iblis*

**vectors **

how do you determine if two vectors are a) Collinear b) orthogonal?
*Thursday, June 17, 2010 at 11:05pm by Ariza *

**trig**

The orthogonal projection is (( (2,6) dot (-1,5) ) / ( (-1,5) dot (-1,5) ))*(-1,5)
*Thursday, March 4, 2010 at 12:52pm by Marth*

**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*...
*Sunday, January 26, 2014 at 1:46am by John*

**physics**

Torque is the F x r vector cross product. Do your x, y and z represent unit vectors? It is conventiuonal to use i, j and k for unut vectors along x, y and z orthogonal axes. I am confused by your notation.
*Friday, March 25, 2011 at 7:21pm by drwls*

**Calculus**

The coefficients of the left-hand side determine the vector orthogonal to the plane. Reduce each plane so that the left-hand side are identical (already are for (a)). If the left-hand sides cannot be made identical, the planes are not parallel. If they are parallel, look at ...
*Saturday, May 5, 2012 at 12:21am by MathMate*

**Physics**

That depends upon what information you have. I have no idea what mass you are talking about. The magnitude of a velocity is the square root of the sum of the squares of the orthogonal components.
*Wednesday, October 5, 2011 at 10:43pm by drwls*

**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.
*Wednesday, September 8, 2010 at 7:28pm by VJC*

**Math**

I assume you mean the monkey leaped straight up. Ignoring the fact that free-fall trajectories are parabolas, and not straight lines, we have x = height of leap 300 = hypotenuse (because the distance down the tree and over to the well is 300) √(200^2 + (100+x)^2) = 300 x...
*Sunday, July 15, 2012 at 11:34pm by Steve*

**math**

can an inner product space v have a t invariant subspace U but also have an orthogonal complement that is NOT t-invariant???
*Saturday, March 3, 2007 at 4:52pm by mk*

**Calc**

Determine whether u and v are orthogonal, parallel or neither u= <-4, 7>, v= <-14, 12>
*Monday, February 13, 2012 at 11:34pm by Darius*

**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?
*Tuesday, January 1, 2013 at 6:21am by bhawani*

**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...
*Monday, May 24, 2010 at 11:12pm by Christy*

**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?
*Wednesday, January 2, 2013 at 1:04am by bhawani*

**linear algebra**

if orthogonal, then their dot product is zero (2,x,7-x) . (x , 3, -2) = 0 2x + 3x - 14 + 2x = 0 7x = 14 x = 2 check: (2,2,5).(2,3,-2) = 4 + 6 - 10 = 0
*Saturday, July 27, 2013 at 11:06am by Reiny*

**Math**

that is one way. Pick any other vector, say <1,2,3> then the cross product is orthogonal to both vectors. Then you wind up with some vector u. Take u/|u|*6 to get magnitude 6.
*Tuesday, December 4, 2012 at 4:40pm by Steve*

**math - incomplete**

0 if the segments lie in a straight line. 450, if they are the lengths of the mutually orthogonal edges of a 5-dimensional hypercube. Things will vary, depending on whether you are describing a twisted cube, a prism, a pyramid, or an ellipsoid.
*Saturday, November 26, 2011 at 1:28pm by Steve*

**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)
*Sunday, November 20, 2011 at 3:09pm by Simon*

**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)
*Saturday, May 18, 2013 at 12:09am by Kate*

**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 ...
*Wednesday, October 28, 2009 at 5:47pm by physics studentt*

**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 ...
*Thursday, July 12, 2012 at 8:30pm by Christopher*

**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...
*Friday, January 19, 2007 at 3:50pm by mathstudent*

**Pre-calc**

In general the projection of U onto V is: (U dot V)/|V| = (4,2)dot(1,-2)/|V| = (4-4)/√5 = 0/√5 = 0 makes sense, since the 2 vectors are orthogonal, that is, they form a 90° angle with each other (their dot product is zero)
*Wednesday, May 30, 2012 at 10:14pm by Reiny*

**Calculus**

Find the shortest distance from a point P(2,-1,2) to a line L r= [-1,0,7] + t [4,1,-2]. Assume a point Q on the line such that PQ is the shortest possible distance between them. Then PQ is orthogonal to the line L. Given P(2,-1,2). Let Q(-1+4t, 0+t, 8-2t), then PQ=<-3+4t, t...
*Saturday, May 26, 2012 at 10:07am by MathMate*

**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 ...
*Monday, August 27, 2012 at 12:04am by Robert*

**Calculus**

If the line L: [x,y,z] = [-2,6,5] + t[3,2,-1] lies in the plane P: 3x - 4y + z + 25 = 0 Then both of the following must be true 1. [-2,6,5] must lie in the plane. Check: 3(-2)-4(6)+5+25=0 so [-2,6,5] lies in the plane 2. the vector <3,2,-1> must be orthogonal to the ...
*Saturday, May 5, 2012 at 12:44pm by MathMate*

**Math**

There is indeed a shorter way. What you do is you shift the origin of the coordinate system so that the line moves to the origin. To do that just find a random point that lies on the line, say, the point (-5,0). Then if we translate the entire coordinate system so that this ...
*Saturday, April 25, 2009 at 3:43pm by Count Iblis*

**PHYSICS VECTORS**

The cross product is the determinant of a 3x3 matrix formed by the unit vectors i, j, k, A, and B. (Break A and B into x, y, and z components). i j k 5 2 0 3 -1 0 The result is a vector orthogonal to both A and B; because A and B do not have z components, the result should be ...
*Thursday, September 17, 2009 at 10:18pm by Marth*

**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...
*Sunday, November 20, 2011 at 6:18pm by Jainee*

**Calculus**

sin(x) = sin[2(x/2)] = 2 sin(x/2) cos(x/2) Draw a right triangle with one angle equal to x/2. If you make the length of the side opposite to that angle equal to t = tan(x/2) then the length of the side side orthogonal to it that connects to that angle will be equal to 1, ...
*Thursday, October 31, 2013 at 8:15am by Count Iblis*

**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 ...
*Monday, January 11, 2010 at 8:45pm by Anita*

**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 ...
*Wednesday, January 16, 2008 at 7:39pm by mathstudent*

**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 ...
*Thursday, July 26, 2007 at 3:06am by john*

**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 ...
*Friday, January 18, 2008 at 12:13am by mathstudent*

**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 ...
*Friday, April 13, 2012 at 12:16pm by Scott*

**Calculus**

come on. even without calculus you know that the vertex is at (3,-1). With calculus, f' = 2x-6, and f is increasing where f' > 0
*Sunday, February 12, 2012 at 10:31pm by Anonymous*

**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. ...
*Monday, November 30, 2009 at 9:02pm by poo*

**Sequences**

A+B in a sequence means it is equal to A1+B1, A+d1+B1+d2, .... AxB means several things, but I assume you are working as a orthogonal tensor, which means that each term (like terms) are multliplied: AB, Ar1*Br2, A(r1)^2 B(r2)^2, ...AB (r1*r2)^n, .....
*Sunday, September 30, 2007 at 2:30pm by bobpursley*

**Calculus I**

This post was also placed at freemathhelp, on the calculus board with titled, "Calculus I". No work is shown at either location. Sad.
*Tuesday, September 2, 2008 at 4:53pm by Mark*

**vector physics**

Using the standard orthogonal unit vectors î and ĵ. Momentum of the system: 0.045*9.0 î - 0.145*7 ĵ kg∙m/s Magnitude: √((0.045*9.0)^2 + (0.145*7)^2) kg∙m/s Direction: angle measured off x-axis -arctan((0.145*7)/(0.045*9.0))
*Monday, September 23, 2013 at 12:08am by Graham*

**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).
*Saturday, May 5, 2007 at 9:27pm by Anonymous*

**math**

x^2 + y^2 -6x + 4y +2 = 0 can be rewritten as the equation of a circle, as follows. (x-3)^2 + (y+2)^2 -9 -4 +2 = 0 (x-3)^2 + (y+2)^2 = 11 The center of the circle is (3,-2) and the radius is sqrt(11). The other equation can be rewritten (x+4)^2 + (y+1)^2 = 22 -17 = 5 Its ...
*Friday, July 9, 2010 at 6:02am by drwls*

**Math**

Thanks Reiny!! I understand everything except for the part making the length equal to 6. So I find a vector <1, -1, 2> orthogonal to <1, 5, 2> Then find the unit vector u/lul and get (1/√6, -1/√6, 2/√6) but how did you get (√6/6, -√6/6...
*Tuesday, December 4, 2012 at 4:40pm by A.*

**Calculus**

This is not calculus,it is beginning algebra. What is the point of labeling it calculus?
*Saturday, January 26, 2008 at 10:14pm by bobpursley*

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