10.9#3

This problem won't work. the integral of -25sin(5t) is 5cos(5t). But it keeps saying that is the incorrect answer, and therefore I can't get the antiderivative of that either.

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Well, you say that "the integral of -25sin(5t) is 5cos(5t)" , but this isn't true.  AN integral is 5cos(5t), but so is 5cos(5t)+K where K is any constant.  You've reflexively chosen K=0, but any other constant will also be an integral of -25sin(5t).  But this value of K gives the wrong value for v(0), as you can check for yourself.  Which is the right value?

10.9#4

I have attempted to solve this problem many times by 1) finding the velocity vector 2) finding the magnitude of the velocity vector (speed) 3) taking the derivative of the velocity vector and equaling it to zero 4) solving for t. I have gotten 3/52 seconds every time, but I am incorrect. What am I doing wrong? My original position vector is: <-5t^2,-2t,t^2-6t>



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So first a meta-analysis. solving a problem incorrectly many times is frustrating, but it's also a sign post that you missed: when you solve something incorrectly its important to figure out what you don't understand that caused your mistake. Just doing it over again usually won't help.

Secondly, you haven't told me enough of what you did that I can tell you exactly what you did wrong, but I can see that you're off by a factor of 2. Maybe this is because you're getting tangled up in the square root or maybe you incorrectly used FOIL when you multiplied out d/dt (t^2-6t). 

I guess you correctly computed that r'(t) = <-10t, -2, 2t - 6 >, did you get 
s(t) = √(100t^2 + 4 + (2t-6)^2) = √(104t^2 - 24t + 40)?

At this point you could use the chain rule, or you could recognize that s(t) and s(t)^2 are minimum at the same time; the latter is a little tidier to minimize because it's a polynomial.















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Lecture Notes 9-25-19 through .... (to be updated)

Lecture Notes 9/25/19

Lecture Notes 9/27/19

Extra credit assignment

The rules:
1) Research how vector calculus applies in your chosen discipline of engineering.
This means actually research it. This is not meant to be easy or something you can just imagine.
2) Write *about* what you discovered in your own words. Two pages double spaced,
2) Cite your references, with a number referring to the references section, in your writing. This insures that you actually did research something.
3) Document your references, page number and/or section, in a separate reference section. There should be at least four *distinct* references. At most one should be wikipedia.
4) No plagiarism. I.e. no copy-pasta, no using other peoples words or ideas without crediting them.

The value to you: UP TO 66% of the points you lost on Exam 1. You will have to earn your points, though.

Due Date: October 25 at 11:59 PM. 

Firefox browser is giving trouble

As has been pointed out to me, and I've verified for myself: The latest update of Firefox shows a File Not Found error when trying to load the syllabus or the blog.  I recommend that you view the syllabus or blog using Chrome, which still seems to function as normal.

Lecture Notes 9-16-19 through 9-23-19

Lecture Notes 9/16/19

Lecture Notes 9/20/19

Lecture Notes 9/23/19

The test...

It looks like some people don't bother to read the instructions. It looks like some of them are smart in other ways, but since they didn't show their work I can't really tell whether they might have just copied from their neighbors. I bet they'll be unhappy with their scores.

The exam today

Prof. Taylor,

I had a question regarding the topics on our first MAT267 Exam tomorrow. Should we only expect the subjects covered on the practice exam? Are there any topics that we should prepare for that weren't on the practice exam?

Thank you for your time,

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1) Anything in sections 10.1-10.7 is fair game, and anything that we've covered in the lectures is fair game.

2) Of course. We've covered many topics, but only have about ten questions on any practice exam.

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Hello,

I’ve looked for info about the exam but I’m not sure where to find it. Will it be in class tomorrow or another time and location? 

Thanks, 

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All of the midterms will be in the classroom.  The final exam may be somewhere else.

10.7#1

I know the domain for sqrt(t-2) should be 2-> infinity but the value seems so be broken. Plugging this into a graphing calculator with the other functions shows this. What is wrong?

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uh, it looks like you figured it out. Maybe the part about the interval notation and open and closed endpoints is what confused you?

10.5#17

Hi Dr. Taylor. I am having trouble with getting the correct answer on this problem. I took the dot product of the two normal vectors and got -6. I took the magnitude of the two vectors and got the square root of 21 and the square root of 26. I then took the inverse cosine of -6 divided by the magnitudes. I checked my answer with multiple people and said that my calculations were correct. I am not sure what I am doing wrong. Let me know if you can help! Thank you!

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yes, that's a confusing and frustrating situation, and you're doing the right calculation--almost!
Let's imaging you're looking at the two planes edge on. You should see two lines, something like this:

and note that there are two angles between these two lines, one acute labeled as 𝛂 and the other one obtuse, and labeled as 𝛃.  They satisfy 𝛂+𝛃=π radians or 180 degrees. By convention, the angle between the two planes is take to be the acute angle 𝛂.  Similarly, let's look at the normal vectors for these planes. I've drawn the two normal vectors you've used in black, but for every normal vector n the vector -n is also a normal vector, which I've drawn in red.  The angles 𝛂 and 𝛃 show up between these normal vectors again, and you've computed 𝛃. What you need though is 𝛂, which you can compute as cos^(-1)(6/(√21√26)).

A worry about the homework

On Fri, Sep 13, 2019 at 5:15 PM ***************** wrote:

Hello Professor Taylor,

The 10.6 homework is set to close today at 11:59, but we have not covered all of the material in class yet. Could you please extend this homework?

Thank you for your time,

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Oh, yes.  Fixed.

Lecture Notes 9/9/19 through 9/13/19 (UPDATED 9/15/19)

Lecture Notes 9/9/19

Lecture Notes 9/11/19

Lecture Notes 9/13/19

Lecture Notes 9/4/19 through 9/6/19

Lecture Notes 9/4/19

Lecture Notes 9/6/19