Is it ONLY the 10th week of school? I feel as if I should be getting ready for finals! Not Halloween! v.v
This week was relatively easy! I actually got some of it! I couldn't come up with anything that looked right for the 2nd Implicit Derivatives, so I just took it from the notes. I might need a little bit of help with that if I ddin't get it right. I think I confused myself when I was typing it somehow.
Implicit Derivatives:
What you do for these is
1. Take the derivative like normal.
2. For each y-term, you put y' or dy/dx behind it.
3. Solve for dy/dy or y'.
3x^2 + 4y = 9
1. 6x + 4(dy/dx) = 0
2. 4(dy/dx) = -6x
3. dy/dx = -6x/4
Second Implicit Derivatives:
1. Take the derivative of the first derivative
2. Put d^2y/dx^2 for dy/dx
3. Simplify
4. Plug in values
First Imp. Deriv:
x^2+y^2=25
2x + 2y(dy/dx) = 0
dy/dx = -x/y
Second Imp. Deriv:
d^2y/dx^2 = -[(y(1)-{(x)(dy/dx)}] / y^2
d^2y/dx^2 = (y-(x)(-x/y)) / y^2
d^2y/dx^2 = y+x^2/y/y^2/1
d^2y/dx^2 = (y^2 + x^2) / y^3
OR
d^2y/dx^2 = 25/y^3 (because (Y^2+x^2) = 25 in the orignal problem)
Now, as for what I don't understand:
Angle of Elevation!
When she's going over it, I can somewhat get it, but I don't think I'll ever be able to figure out what to do first second third etc. CAn someone help explain thise please? :) It's kinda like optimization: I knew how to do it somewhat when she was going over it, but I'm lost as a sigh in a windstorm when I'm trying to do it at home. I'll probably have homework questions so but I'm doing that tomorrow. :)
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First thing is to write down your given just like related rates, and for angle of elevation it would be best to draw the picture just so you have an idea of what you are looking for in your head.
ReplyDeleteNext, you have to find a missing angle that you need in the problem, one way to do this is to use tan(theta)=opposite/adjacent. Once you have that, take the derivative and solve. Next whatever that gives you into the original formula they give you in the problem. When everything is solved for that will give you your answer.
hope this helps girl!!