Calculators, exams, quizzes

1)  This is an engineering calculus class. You should plan to give a numerical answer to all quiz and exam problems unless instructed otherwise. Come prepared to do so. You should expect to get less than full credit for less than a numerical answer, unless instructed otherwise.

2)  Quiz and exam problems should be presented legibly. If I can't easily read your answers, I won't give you credit for them.

3) I grade in red ink.  If I have to get up to get a different color pen because you wrote your exam problem in red the score I will give you is 0 (zero).

Lecture Notes 9/5/18 and 9/7/18

Lecture Notes 9/5/18

Lecture Notes 9/7/18

10.9#8

I assume this attached the list of all of the answers that I've put in so far. Here's the rest of what was in the email:

For part B, I was able to solve the magnitude of the force by using rotational formulas from the physics class I took last semester. I found that to be 17.55 N.

Back to part A, looking in the textbook, I found what I believe the relevant equation to be:
F(t) = - m * w^2 * (a * cos(w * t) i + a * sin(w * t) j)

I have tried plugging in everything, leaving t in the expression, and I also tried plugging in 12 for t. WeBWork says I'm wrong for both. Here's my work for the x-component:
w = 2pi / 12 = pi/6
a = w^2 / r
F(t) = - 8 * (pi/6)^2 * ((pi/6)^2 / 8) * cos(pi/6 * t)
F(t) = - (pi/6)^2 * (pi/6)^2 * cos(pi/6 * t)
F(t) = - (pi/6)^4 * cos(pi/6 * t)
Is there something else I'm supposed to do after this point?

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(nope, it doesn't attach everything you've done, I just get to see that last thing you did)

Ok, looks like you started off sort of in the right direction, in that you start with a correct vector equation for F=-mw^2(a*cos(wt) i + a sin(wt)j),  but then a) got yourself tangled up figuring out what to put in for w and a (and it looks like you kind of got some of that stuff correct but were insecure about it and kept going when you should have stopped) and then b) you forgot that F is a vector and only kept the i component.

And if not for those confusions you could have worked it out that way.  But I propose that you take a step back and remember Newton's Law, which is covered in the textbook and says that F=ma; note that these are vector equations. And we talked in class about the fact that the acceleration vector a is the second derivative of the position r.  So the basic thing for you to know is: what does it take for you to make r(t) travel around a circle of radius 8 in 12 seconds?  (the w=2pi/12 you have is correct and plays into it).  Once you have that, take the derivative of it twice correctly, using the chain rule of differentiation, and multiply by the mass to get the force. Note that the force will have two nonzero components, and that they will both depend on time through the parameterization r(t)  you  used.

10.5#19

Dear professor,

For Question 19, it asked to "Find an equation of the plane consisting of all points that are equidistant from A(4,−5,−4) and B(0,−4,−4)."

What I tried to do was first find the mid-point between the two points, which I got (2, -9/2, -4). Then I tried to find the vector from A to B, which i got <-4,1,0>. Then I used equation for a plane <-4,1,0>dot<x-2,y+(9/2), z+4>. I got -4x +y +8 + (9/2) = 0. I move the 12.5 to the other side. -4x +y = -12.5.

Professor i don't know what i'm doing wrong. Is this not the formula to solve for this?

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Notice the minus sign that you have in your email that you don't have in the answer you entered?

10.5#17

Dr. Taylor

So i did my dot product and got -26 my magnitude that was calculated were 24 and 20 respectively in the order received from the problem. for theta = arccos (-26/sqrt(24*20)) gives me an error why is that ?

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Ok, I believe we talked about this in class today but here goes.  Your computation is correct--sort of--but also sort of incorrect.  Here's a picture of two lines intersecting:

This intersection makes some angles, I've drawn two of them, one in green, the other in blue.  Which of the angles pictured is the angle between the two lines?  Your calculation gives the other one. 

10.5#10

Hello, Dr. Taylor.
I have repeatedly crunched numbers for this problem but it has not been working out.

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1) You're not asking a question. Often the reason for this is that people don't know enough to ask a question, so I'm a little suspicious that *maybe* you haven't done your diligence.  So, this is just a hunch, but I'm guessing if you read the text book section 10.5 things will be a lot more clear.

2) When you write back to me to tell me *how* you crunched your numbers, I can get lot more helpful, and I'll know that you're prepared to learn how to do this problem.  At that point I'll update this blog post with additional information.

10.4: Problem 9 (updated)

Dr.Taylor
In class we talked about finding the volume of a paralelipiped for a couple minutes and I tried to find the scalar triple product but the answer I got was wrong and I don't know if it has to do with the ordering of the vectors or if it doesn't matter. Thank you for any help you can give.

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Well, it's hard to help without doing the problem for you, because you didn't tell me what you did, your didn't tell me what you tried to do, not to mention also that you didn't actually ask a question. However, taking a stab in the dark, you might want to pay attention to the fact that the scalar triple product is the scalar triple product, while you have four points. What do you make of that?

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I read the blog post and I realize where I went wrong with my wording. I'm taking the scalar triple product of the 3 vectors PQ, PR, and PS in that order. I've tried using different orders as well but none of them seem to work. I wanted to know if the order of the vectors matters and if it does, how do I know which order to put them in.
Sincerely,
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Ok, got it. It sounds like you mostly know what you're doing.  The order matters only in the sign of the determinant.  And since you're taking the absolute value of the scalar triple product in order to get a positive number for the volume,  remember, the order doesn't affect your answer at all.  So...a few thoughts:
1) if, as it sounds like, you're getting different answers for different orders you're doing one of the operations wrong, either the dot product or the cross product but you might also have made a mistake in computing the three vectors PQ, PR and PS.
2) the true answer is smaller than either of the two answers I've seen you try.
3) there are a lot of minus signs in those vectors, a common source of arithmetic mistakes is forgetting that two minuses is a plus. I'd guess that the mistake is most likely in the cross product (but I wouldn't bet even money on it).

PS: if you wrote up your computations LEGIBLY you could take a photo with your phone and email it to me