sysD

Okay, I think I understand. I'm still trying to wrap my head around orienting structures in three dimensions. Also, we don't cover planes until the next chapter . I have a related problem - mind checking to see if my answer is correct? A parallelepiped is defined by the following vectors: a=(2,-5,-1) b=(2,0,-1) c=(-1,0,1) Calculate the volume. My answer: (a x b)dot c =(5,0,10) dot (-1,0,1) =(-5+0+10) =5 The volume is 5 units cubed. I checked my cross product answer using the dot product check method... I don't know of any methods to check the answer yielded by a dot product... so I'm posting here

Thanks, that helped a lot. Would the volume of the parallelepiped be calculated by: V= | (a x b)dot w | ? I tried graphing out those vectors but it doesn't look like the typical basis of a parallelepiped... the angle between A and C is obtuse.

Three vectors: Vector A = (2,-5,-1) Vector B = (2,0,-1) Vector C = (-1,0,1) What does it mean to have an entire vector represented by cartesian coordinates? Do those points represent the head of the arrow? I know that squaring the components and rooting the entirety yields the magnitude of the vector, but can someone explain what these points represent? BTW Vector A can also be written as (a) with a right-facing arrow on top. In context, these three vectors are going to be used to define the volume of a parallelepiped.

These questions are simple compared to the questions in the preceeding unit of the course... I just wanted to make sure it wasn't a trick :/ Thanks!

Hi, Question: A radioactive substance has a half-life of 20 days. i) How much time is required so that only 1/32 of the initial amount remains? ii) Find the rate of decay at this time. My Answer: i) Let "A" represent the initial amount. Let "t" represent the time in days. (1/32)A = A(.5)^(t/20) (1/32) = (.5)^(t/20) log_.5(1/32) = t/20 5 = t/20 t = 100 days ii) Let "A" represent the initial amount. Let "t" represent the time in days. f(t) = A(.5)^(t/20) f ' (t) = A (ln(.5)) ((.5)^(t/20)) (1/20) f ' (100) = A (ln(.5)) ((.5)^(100/20)) (1/20) = A (ln(.5)) ((.5)^(5)) (1/20) = A (-0.001083042) The rate of decay at 100 days is equivilant to [ -A(0.001083042) ]. Are these answers correct?

Ahhhh, excellent. Thanks for the help!

Sorry, doesn't help. I don't see how the natural log and the base10 log can be used interchangably if they clearly give different answers. eg ln(3) = 1.0908612289~ log(3) = 0.477121255~

Here's the question I was given: Differentiate: f(x) = 3x +x3 my answer: f'(x)= (ln(3))(1)(3x) + 3x2 = (ln(3))(3x) + 3x2 However, wolfram gives me a slightly different answer: f'(x) = 3x2 + 3x(log(3)) Confirmed with two different widgets: http://www.wolframal...7197a484f4257c0 http://www.wolframal...a4fac87af8b07b2 _________________ This goes against the rule I've been taught for deriving exponential functions: f(x) = a^(g(x)) f'(x) = (ln(a))(a^g(x))(g'x) I don't really have any reference to understand why wolfram threw in the base10 log instead of the natural (base(e)) logarithm. [p.s. - i tried to throw in the math script but it returned with a bunch of garbled text and syntax errors]

Awesome, thanks for the replies.

thanks for the replies guys. maybe i should ask a different question: for one seeking an A+ in university ochem (aka orgo)... which concepts would be useful to master BEFORE starting the semester? (even if they are only intro'd once in ochem)

What concepts should one have completely locked down before attempting orgo?

You're close, but that's not it. I promise you its something very simple and every day - yet I don't think many would think to apply it here. Try it out, as a thought experiment. You may be surprised.

that's the one, thanks cap'n.

I'm serious guys. Its very counter-intuitive. I can't give out any hints though; I know someone here is smart enough to prove it. OH Crap. Sorry, I posted the wrong equation. I can't edit the OP so here it is: ________________________________________________________________________ Prove that: x=/=x x is in the set of Real Numbers [couldnt figure out the math script notation for "does not equal..." if a mod would like to help me out i'd appreciate it.]

incorrect. any takers? EDIT: its not what you think

prove that : [math]x=x[/math]

thanks, thetree

Thanks capnI was hoping to get two more answers checked and didn't want to start another topic... 1) Find the points on the curve [math]y=2/(3x-2)[/math] where tangent is parallel to the line [math]y=-(3/2)x-1[/math] my answer coordinates: (0,-1), (4/3, 1) 2) find the equation of the tangent to [math]y=x^2-3x-4[/math] that's parallel to [math]y=7x+3[/math] My answer: y = 7x - 29

[math]f(x)=3x(x^2+4)^-1[/math] . [math]f'(x)=3(x^2+4)^power-1 + (3x)(-1)(2x)(x^2+4)^power-2[/math] [math]f'(x)=(3(x^2+4)^2-6x^2(x^2+4))/((x^2+4)(x^2+4)^2[/math] Sorry, the math script doesn't seem to be working for negative exponents. Reduce: [math]3(x^2+4)^2-6x^2)/(x^2+4)^2[/math] Is that correct? note: (further simplification & factoring) [math](3(x^2+4-2x^2)) / ((x^2+4)^2[/math] . [math]3(4-x^2)/(x^2+4)^2[/math]

Hi, I want to find the derivative of this but I can't use the quotient rule. So I figure I'll use the chain/product rule. I'm new to calc though.Do I use both? Or just one? This is the chain rule I think. Do I go on to use the product rule?

Hi, [math]3x/(x^2+4)[/math] I want to find the derivative of this but I can't use the quotient rule. So I figure I'll use the chain/product rule. I'm new to calc though. Do I use both? Or just one? [math]= 3x(x^2 +4)^-1[/math] [math]=-3x(2x(x^2+4)^-2[/math] That's the chain rule I think. Do I go on to use the product rule?

hiya. ok, so i've got an assignment that's due around 9AM EST on the 13th of Sept (this morning). If anyone could help me out before then, I'd be forever grateful =p Here's the first question: Solve for "x" 2x^3 + 6x^2 -x = 3 and so far, i have: (x+3)(2x^2-1)=0 Its a four mark question, so I have to be missing something here. The other question is: When (ax^3 - 4x^2 +5x -3) is divided by (x+2) and (x-1), the remainders are equal. Find "a" How would I go about doing this?

damn, thanks. that was an awesome response.

dag I'll read that over when I get a few minutes. I'm slowly becoming faster with practice. For the moment, though... I'm also having troulbe factoring: 2x^2 + 4x -3 there has to be a better way than trial and error though

I've uploaded a rough sketch of the graph. http://www.megaupload.com/?d=4OMOS0T9