Ok, so as I was coming do my comments today, I saw that I totally forgot to do my blog for last week all together, so I'll do it now.
So last week was completley crazy. I forgot to do all my homework and this blog, but last week we did go over a lot. Although we did not learn related rates and angle of elevation last week, we continued on going over it.
Related rates are very similar to optimization; they make optimization look like a piece of cake. Anyway, the steps for related rates are:
1. identify all variables and equations
2. identify what you are looking for
3. make a sketch and lable
4. write an equation involving variables
5. take the derivative with restect to time (dy/dt instead of dy/dx) and solve
This basically helps you solve a problem when something in the problem is changing (a rate; derivatives are rates).
We also went over angle of elevation. I am still pretty bad at these. I can never decide what number in the problem goes with which variable. I particularly have trouble with problems that involve air planes.
EX. When a problem says a plane is flying at 200 mi/hr and starts rising at 20 degrees
I think that's angle of elevation. I'm not completley sure though?
Last week we learned linerization and differentials. Mrs. Robinson described linerization as taking, say, a parabola and streaching it out so it becomes a line. When there is a linerization problem, the key word the problem will say is approximate. The equation for this is:
f(x)=f(c)=f '(c) (x-c)
Differentials are when something is solved for dy or dx.
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if you are given something like the plane is rising at a rate of 200 mi/hr at an angle of 20 degrees, then it asks you to find what's the height, or something like that, im not sure of the wording.
ReplyDeletebut anyways, you would draw out a right triangle. 200 would be your hypotaneuse, and 20 degress is your angle of which 200 is on top (rising).
well, you are looking for the height, which is opposite of the angle given, and you have 200 as your hypotaneuse. you can use sine to figure this out because sin = opp/hyp
you would then plug in sin(20) = y/200
solve for y .... 200sin(20) = y
plug into your calculator and that's your answer.