A few Multiple function product rule refresher videos later...
I believe the 1st term should go from:
-r \frac{d\theta}{dt} \sin(\theta)
to:
- \left( \frac{dr}{dt} \frac{d\theta}{dt} \sin(\theta) + r \frac{d}{dt}(\frac{d\theta}{dt} \sin (\theta)) \right)
- \left( \frac{dr}{dt}...
Ah yes, it's been 5 years since I typed anything in LaTeX either, but I wrote it correctly on my paper. Now I need a refresher on getting the second derivative of the equation.
I have:
\vec{r} = r \cos(\theta) \hat{i} + r \sin(\theta) \hat{j}
\vec{v} = \left( -r \dot{\theta} \sin(\theta) +...
Ok, so I don't need to chain rule the 1st cosine factor, and adding the chain rule on the cosine factor on the left: \cos(\theta) \cdot \frac{d\theta}{dt}
gives:
\frac{dx}{dt} = \frac d {dt}\left(r\cos(\theta)) \right) = \frac {dr}{dt} \cos(\theta) + r \cdot \left(\cos(\theta) \cdot...
I get that r is the magnitude of \vec{r}
Both r and \theta are functions of time.
Let me start with only the x-side of the equation:
x = r \cos (\theta)
Applying the product rule to r and \cos(\theta) yields:
\dot{x} = r (-\sin)(\theta) + \dot{r} \cos (\theta)
And adding the...
Homework Statement
This is a problem from Dynamics but I'm mostly having trouble with the calculus.
Derive an expression for the position, velocity, and acceleration of a machine in terms of: r, \dot {r}, θ, \dot{θ}, \ddot{r}, \ddot{θ}, .
r = length of the arm
θ = angle of the arm to the...
So, i assume math 111 is College Algebra/ Pre-Calc, and 112 is Trig.
There are usually several General-Education classes that have to be taken as well as ME specific classes, you can always take those while you complete the math sequence. I do not know your specific course requirements (or...
Well, from a quick google search I think Math 65: Developmental elementary algebra, and Math 95: Developmental Intermediate Algebra, but I'm not sure if your school allows you to take Calculus 1 after that.
I do not know if you can finish a ME degree before your GI bill runs out, but it does...
I am 32 and married to my wife for almost 3 years and we are expecting twin boys due in October. I have been attending CC for 2 years part time getting my gen-ed requirements, and the first 2 years toward a mechanical engineering degree, out of the way. And I may be here another 2 years before...
Summer:
Work full time,
Gen Ed......Macroeconomics
Fall:
Continue working full time,
Linear Algebra
Calc-based Physics 1 (online, including lab)
Become Daddy of twin boys!
I understand your frustrations, and yes this does seem like a big sacrifice. I, too, hope it will be worth it in the end. I currently work 45hrs per week and attend community college part time (10hrs of online and night classes).
I finally have most of my gen-ed classes out of the way, but...
In this formula?(f^{-1})(a)=\frac{1}{f'((f^{-1})(a))}
(f^{-1})(a)=\frac{1}{f'(1)}
then
f'(1)=\frac{1}{2}(25)^{-\frac{1}{2}}(6)
equals 3/5, and the inverse is 5/3.
So, is this the way I should go about these kind of problems?