...and 10.5#18

I am having trouble with this problem as well. I must be doing something
wrong in the way I am calculating angles but I don't know what.

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I prefer to be in the business of getting you unstuck rather than doing the problem for you.  If you get back to me and tell me what you're did do, maybe I can help out.

10.5#17

I used the formula cos(theta)=n1(dot)n2/|n1|*|n2|

where n1=(5,-2,3) and n2=(2,-5-5)

in the end I did theta=arccos(5/sqrt(2052))

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everything you did is just fine...except the problem was meant to fool you. Notice the second equation is written 2y - 5x -5z=2.  In order to get the normal vector you should rearrange it so it looks like -5x+2y-5z=2.  The correct normal vector is <-5,2,-5>.

The webwork was slightly broken

I'd be surprised if another student hasn't brought this up already, but our webwork shows 12.4 and 12.8 due Next Monday, with 13.8 and 13.9 due on Wednesday. This seems to be a different order than the syllabus suggests, so I'm guessing it is an error?

If not, I'd better get on it soon.

Thanks for your consideration!

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Yes, that's an error. You should be surprised, though, because you are the first one to bring that particular error to my attention.  Thanks!   I think it's fixed now.

Quadrics Pics

ellipsoid#1 x^2/4+y^2+z^2=1

ellipsoid#2 x^2+y^2/4+z^2/4=1

ellipsoid#3 x^2/4+y^2/9+z^2=1

circular paraboloid z=x^2+y^2

elliptical paraboloid z=2x^2+y^2 

hyperbolic paraboloid or saddle z=x^2 - y^2

hyperboloid of one sheet x^2+y^2-z^2=1

hyperboloid of two sheets x^2+y^2-z^2= -1

Lecture Notes 1/23/17 through 1/27/17 (complete)

Lecture Notes 1/23/17

Lecture Notes 1/25/17

Lecture Notes 1/27/17

Lecture Notes 1/18/17-1/20/17 (complete)

Lecture Notes 1/18/17

Lecture Notes 1/20/17

A slight office hours change

I changed my Thursday office hours. They are now 2:30-3:30PM