Hello everyone, One of my Calculus students had an interesting Related Rates problem that I had to go home and think about for a while in order to figure out. The problem was set up as such: A 25 inch piece of rope needs to be cut into 2 pieces to form
a square and a circle. How should the rope be cut so that the combined surface area of the circle and square is as small as possible? Here's what we'll need to do: 1. We will have to form equations that relate the length of the perimeter and circumference to
the combined surface area. 2. We will then differentiate to create an equation with the derivative of the surface area with respect to lengths of rope. 3. Wherever this derivative equals 0 there will be a maxima or minima, and so we will set the derivative =
to 0 and determine which critical points are minima. Let's start by looking at the problem conceptually...
I was working with a student today, and as we worked through the section in his book dealing with Trigonometric Identities and Pythagorean Identities, we stumbled across a problem that gave us a bit of trouble. The solution is not so complicated, but it
sure had us stumped earlier.
The problem was presented as such:
Factor and simplify the following using Trigonometric and Pythagorean Identities:
sec3(x) - sec2(x) - sec(x) + 1
We tried a couple of different approaches, such as factoring sec(x) from each term:
sec(x) * [ sec2(x) - sec(x) - 1 + 1/sec(x) ]
and factoring sec2(x) from each term:
sec2(x) * [ sec(x) - 1 - 1/sec(x) + 1/sec2(x) ]
We followed these approaches through a few steps, but nothing we were attempting led to the solution. After doing some reading online, I found that the solution required a simple approach that I had overlooked.
Instead of attempting...
I greatly enjoyed the years I spent serving in the US Marine Corps and loved my job. I don't regret making the choice to enlist, choosing the Marine Corps, or choosing to be in the infantry as a rocket and missle gunner. I do however wish that I had maxed
out my retirement funds starting from the day I joined up. I'm currently employed as a civil service member and I enjoy the government matching 5% of my retirement investment. I could've saved tens of thousands more though if I had saved while I was enlisted.
You live and you learn though! I'm saving over 15% of my income, now, so I feel that I'm on the right track.
Hello! Skyler here, just wanted to say hello and that I look forward to meeting and working with some of you. I am currently attending Middle Georgia State College in Macon. My major is a Bachelor's of Science in Mathematics. I have taken the majority of
my math series including Calculus I. The Calculus series fascinates me and - you won't believe it what I'm about to say - I can't wait to take Calc III next semester! I am enrolled in Calculus II this semester and my average thus far is a 103. The three above
100 come from some of the bonus questions my professor has placed on her exams. I am pretty darn proficient in Calculus and the subjects leading up to it, and hope you'll utilize my tutoring services. No math problem too big or too small! :) Feel free to contact
me any time; I'll respond as soon I see the notification on my phone!