# Search results

1. ### Vector Proof

Can anyone help me?
2. ### 3 Orthogonal Vectors Problem

Yes, but since the vectors have to be unit vectors and both vectors a and c are orthogonal to b, |v| is going to be the same regardless. You can rotate a vector by a specific angle and the others have to stay orthogonal so they will move as well by the angle maintaining |v|. That's why I chose...
3. ### 3 Orthogonal Vectors Problem

Homework Statement A. Given unit vectors a, b, c in the x, y-plane such that a · b = b · c = 0, let v = a + b + c; what are the possible values of |v|? B. Repeat, except a, b, and c are unit vectors in 3-space Homework Equations The Attempt at a Solution I have solutions for both that I'm...
4. ### Vector Proof

I can replace the c\bulletb side with what you've suggested but then how am I supposed to include that it is twice the angle. I loose this ability without the trigonometric function.
5. ### Vector Proof

I'm not quite sure what you are suggesting. I can draw the relationship |a||b|cos \theta = |c||b| cos 2\theta I can eliminate the |b| from both sides, but I don't know where to go from there, since |c| doesn't seem to help when substituting.
6. ### Drawing a Collection Of vectors Satisfying Cross Products

Homework Statement Given a = <1,2,3> and b = <1,-1,-1>, sketch the collection of all position vectors c satisfying a x b = a x c Homework Equations The Attempt at a Solution I've calculated a x b = <1,4,-3> and Defining c = <x,y,z> I found a x c = <2z-3y, z-3x, y-2x>. I want to...
7. ### Vector Proof

Homework Statement If c=|a|b+|b|a where a,b, and c are all non zero vectors, show that c bisects the angle between a and b Homework Equations The Attempt at a Solution I'm taking the approach to prove that the angle between b and c= the angle between c and a I have written...
8. ### Finding the Intersection Of 2 Equations (difficult)

hmm. Interesting. I'll bet If you wanted to take this even further you could use the series expansion for the lambert w function. w(x)=\sum^{\infty}_{n=1}\frac{(-1)^{n-1}n^{n-2}x^{n}}{(n-1)!} -w(\frac{-1}{\sqrt{3}})=-\sum^{\infty}_{n=1}\frac{(-1)^{n-1}n^{n-2}(\frac{-1}{\sqrt{3}})^{n}}{(n-1)!}...
9. ### Finding the Intersection Of 2 Equations (difficult)

Homework Statement Solve the following equation: e^{2x}=3x^2 Homework Equations The Attempt at a Solution I can find an approximate solution with a graphing calculator easily, but I am interested how you would find the exact solution. I can take the natural log of both sides...
10. ### Cancellation Limit

No I dont, I'm just starting calculus, but that looks interesting. I'm sure I'll learn it later. Thanks, that works perfectly. I know where I went wrong.
11. ### Cancellation Limit

Homework Statement Find the limit. \lim_{x\rightarrow0}\frac{\frac{1}{x+1}-1}{x} Homework Equations The Attempt at a Solution I have to do this analytically. Although, I know that the limit is supposed to be -1 from a graphing approach. When you substitute in 0 for x you get 0/0. How do I...
12. ### Polar Form of the Equation of a Conic

Homework Statement The planets travel in an elliptical orbit with the sun as a focus. Assume that the focus is at the pole, the major axis lies on the polar axis and the length of the major axis is 2a. Show that the polar equation of orbit is given by r=\frac{(1-e^2)a}{1-e\cos\theta} here's...
13. ### Converting A Polar Equation to Rectangular Form; Equation of a Circle

Hmm. Ok, I think I know what you mean. x^2+y^2=2hx+2ky bring it over to the other side and complete the square and you get (x-h)^2+(y-k)^2=0 How would you get the h^2+k^2 on the RHS of the equation?
14. ### Converting A Polar Equation to Rectangular Form; Equation of a Circle

Homework Statement Convert the polar equation r = 2(h cos θ + k sin θ) to rectangular form and verify that it is the equation of a circle. Find the radius and the rectangular coordinates of the center of the circle. Homework Equations The Attempt at a Solution First, I...
15. ### Converting A Polar Equation to Rectangular Form

Ahhh.. yes. Thank you, that was a big help. Cant believe I didn't see that before.
16. ### Converting A Polar Equation to Rectangular Form

Homework Statement Convert the polar equation to rectangular form. r=2sin(3θ) Homework Equations The Attempt at a Solution I can expand this out to r=2(\sin\theta\cos2\theta+\cos\theta\sin2\theta) multiply both sides by r...
17. ### Parametric Equations Word Problem

Ok, now I see how to do it. Thanks!
18. ### Parametric Equations Word Problem

Yeah, its suppose to be 3. sorry. so I'd have 10=3+(146.67\sin\theta)(\frac{400}{146.67\cos\theta})-16(\frac{400}{146.67\cos\theta})^2 7=(\frac{(400\sin\theta)}{\cos\theta})-(\frac{16(400)^2}{146.67^2\cos^2\theta}) 7=400\tan\theta-\frac{16(400)^2\sec^2\theta}{146.67^2} Then...
19. ### Parametric Equations Word Problem

Homework Statement Consider a projectile launched at a height of h feet above the ground at an angle θ with the horizontal. If the initial velocity is v0 feet per second, the path of the projectile is modled by the parametric equations x=(v[SUB]0cos θ)t and y=h + (v[SUB]0 sin θ)t-16t2. The...
20. ### Finding Points of Intersection by Substitution

Ok, so. x=\frac{2y-3}{y+1} You can sub that into the other equation and get y(4y^3-8y^2-y+6)=0 Using rational roots test you can find that the root of (4y^3-8y^2-y+6) is 3/2 and of course y= 0 as well. \frac{\pm1,2,3,6}{1,2,4} Is this what you had in mind? It is easier than having to do...
21. ### Finding Points of Intersection by Substitution

Homework Statement Find any points of intersection of the graphs by the method of substitution. xy+x-2y+3=0 x^2+4y^2-9=0 Homework Equations The Attempt at a Solution From the second equation I can solve for y: y=\frac{\sqrt{9-x^2}}{2} Plug it into the first equation and...
22. ### Graphing a Rotated Conic on a Graphing Calculator

Thanks for all your help. It works fine now.
23. ### Graphing a Rotated Conic on a Graphing Calculator

I did that and I wind up getting an imaginary answer. My calculator comes up with errors. x=\frac{-x\pm\sqrt{-3x^2-40}}{2}
24. ### Graphing a Rotated Conic on a Graphing Calculator

Homework Statement Use a graphing utility to graph the conic. Determine the angle through which the axis are rotated. x^2+xy+y^2=10 Homework Equations \cot2\theta=\frac{A-C}{B} x=x'\cos\theta-y'\sin\theta y=x'\sin\theta+y'\cos\theta The Attempt at a Solution I can find the angle of rotation...
25. ### Rotating a Parabola

Ok, Now I see where I went wrong. Thanks.
26. ### Rotating a Parabola

I saw how I was wrong before and used the angle \frac{1}{\sqrt{3}} and it worked out fine. However, looking back at it again I cant find why I took the square root. Because 3\cot\theta-1=0 \cot\theta=\frac{1}{3}
27. ### Rotating a Parabola

Homework Statement Rotate the axis to eliminate the xy-term. 3x^2-2\sqrt{3}xy+y^2+2x+2\sqrt{3}y=0 Homework Equations \cot2\theta=\frac{A-C}{B} x=x'\cos\theta-y'\sin\theta y=x'\sin\theta+y'\cos\theta The Attempt at a Solution Find the Angle of Rotation...
28. ### Rotating a Hyperbola

Never mind. I found my problem.
29. ### Rotating a Hyperbola

Homework Statement Rotate the axis to eliminate the xy-term. Sketch the graph of the equation showing both sets of axis. xy-2y-4x=0 Homework Equations \cot2\theta=\frac{A-C}{B} x=x'\cos\theta-y'\sin\theta y=x'\sin\theta+y'\cos\theta The Attempt at a Solution xy-2y-4x=0 First I find the...
30. ### Approximating ∏ With a Coin!

Arrgg. I cant believe I did that. *slaps forehead* Ok so \frac{1}{4}\pi is the projected probability it should land hitting a vertex. So the closer my actual experiment probability comes out to %78.54 the more accurate my approximation of pi will be. All I would need to do is calculate the...