Recent content by mill

Thanks!

Where k is a constant. I am trying to simplify a problem but the t has constant in front of it that is not one, and I can't seem to find a chart that verifies it either way.

The instruction says to simplify the differential. So I assumed it was the derivative?

Homework Statement Simplify ##d(log(x^2 + y^2) − z^3)## Homework Equations the derivative? The Attempt at a Solution The instruction says to simplify. In a similar problem I ended up using the d(a(b-c))= da d(b-c). I am not sure how to deal with the log and only found formulas...

http://tutorial.math.lamar.edu/Classes/CalcIII/EqnsOfLines.aspx Symmetric equations of the line

Equation 1 ##\frac {d\vec T} {ds}## 2. s=arc length=∫|v|dt 3. |v|=speed 4. ds/dt = |v| (distance/time)Does the s from the notation of arc length or the notation of speed? derivative of arc length vs derivative of speed I am getting confused because ds was referred to as distance in a...

Got it, thanks.

It's not covered by example in my books, so I was confused about the setup. While looking around, I've seen |r''| and |r'|^2 being thrown around in these types of problems but I'm not sure how they're being used. Ideally to minimize, I would set the chosen equation to 0 to find the critical...

Fixed the two typo. Everything following is the same though. I set the equation to 0 in order to find the min. or is that not what I'm supposed to do?

Homework Statement At what time t does the speed of the particle moving in space with its position function r(t)=##<t^2, 3t, t^2 - 8t>## have its minimum value? Homework Equations Derivative, speed The Attempt at a Solution Found derivative. r'=<2t, 3, 2t-8> Found speed...

u dot u = ##|u|^2## so |u|= ##\sqrt {u dot u} ## ? Possibly, that becomes |2v-w|=sqrt(something?) or would |?|(1/2)=|2v-w| I'm afraid I don't see how things are connecting to the third equation though. 1/2 = (something analogous to u dot v)/|2v-w|?

Homework Statement If |v|=4, |w|=3 and the angle between and is pi/3, find |2v −w| Homework Equations ##cosθ=\frac {v dot w} {|v||w|} ##The Attempt at a Solution ## 6= v dot w ## This is as far as I got. How would I find the separate values of v and w for the equation?

Homework Statement In an equilateral triangle with sides u, v, w, where they are all unit vectors, find u dot w. Homework Equations u dot w = |u||w|cosθ The Attempt at a Solution The answer is ##\frac {-1} {2} ## cos(120) = -1/2 Elsewhere, I read the statement that since these are...

I haven't seen symmetric equations used for anything but finding intercepts, but they can be found using the parametric equations as well. I was wondering in what other instances would it be helpful/necessary to use this form. E.g. a linear equation is helpful when there are certain terms vs...

It seems that the only applicable use I've seen is in finding intercepts on various axes. Are there any other instances where this form would used? What else can this be used for?