Stuck on Vectors

[aznsushiguy]

3. Find the vector from the origin O to the intersection of the medians of the triangle whose vertices are A = (3,2,2), B = (-1,0,4), C = (5,3,-2)

okay, I have the midpoints of each side
AB (1,1,3)
BC (2, 3/2 , 1)
CA (4, 5/2, 0)
wait, so since i have the medians and it's from the origin.....isn't the median just the vector since the initial point is the origin, and i already found the terminal point?

4. Use the dot product to prove that an angle inscribed in a semicircle is a right angle (Hint: with the notation in fig., calculate (A + B) . (A - B)

I did (A+B) . (A-B) dot product multiplication and got a1^2 - b1^2 + a2^2 - b2^2 + a3^2 - b3^2
(each number after a and b are supposed to be subscripts)

is that correct, and how do I prove that an angle inscribed in a semicircle is a right angle?

5. How may lines through the origin make angles of 45 degrees with both the positive x-axis and the positive y-axis?

one....? I feel like that's too simple.

6. Consider the torus generated by revolving the circle (x-b)^2 + y^2 = A^2 (0<a<b) about the y-axis. Use the shells method to show that the volume of this torus equals the area of the circle times the distance traveled by its center during the revolution

Wow....no idea.

7. The given differential equation is not seperable. Use appropriate substitution and algebraically simplify the equation to the one with variables seperable. Then find the general solution.
dx/dy = xy^3/(2y^4 + x^4 )

I don't know where to start or how to do it =(

any and all help is appreciated, Thanks

 

[Deleted member 4993]

3.

Looks like a take home test!!

duplicate post

http://qaboard.cramster.com/calculus-to ... -cpi0.aspx

http://www.mathhelpforum.com/math-help/ ... ctors.html

http://mathgoodies.com/forums/topic.asp?TOPIC_ID=33605

6. Consider the torus generated by revolving the circle (x-b)^2 + y^2 = A^2 (0<a<b) about the y-axis. Use the shells method to show that the volume of this torus equals the area of the circle times the distance traveled by its center during the revolution[/b]

Wow....no idea.

Begin with drawing the circle on a 2-D plane

You must have been taught how to calculate volume of revolution of a curve (around a fixed axis).

Look into your textbook for solved example problems - and do some google search.

If you are still stuck, write back showing your work - so that we know where to begin to help you.



7. The given differential equation is not seperable. Use appropriate substitution and algebraically simplify the equation to the one with variables seperable. Then find the general solution.
dx/dy = xy^3/(2y^4 + x^4 )

This is a homogeneous equation - so after substitution you can have seperable variable.

\(\displaystyle \frac{dx}{dy} \, = \, \frac{(\frac{x}{y})}{2 + (\frac{x}{y})^4}\)

I am assuming you have been taught how to solve first-order homogeneous differential equations.

If you forgot - look it up in your text book and do a google search.

Then write back showing your work - so that we know where to begin to help you.
I don't know where to start or how to do it =(

any and all help is appreciated, Thanks