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Monthly Archives: August 2010

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No. 25: Math Problem of the Day! (30.08.10)

30 August, 2010 6:13 PM / Leave a Comment / Gene Dan

Hey everyone,

Today’s problem uses four new commands: left(, right), approx, and %, which represent the left and right delimiters (parentheses), the approximation symbol, and the percent sign, respectively.

Problem 2:

Mr. Burns deposits $3000 in a five-year certificate of deposit. At maturity the balance is $4,264.28. Find the annual effective rate of interest governing the account.

Solution 2:

Let i be the annual effective rate of interest. We want to use the relationship:

$latex displaystyle 3000(1+i)^5=4264.28$

to solve for i. The term (1+i)5 means that the $3000 in the account grew at an annual effective rate of interest i for five years.

$latex displaystyle (1+i)^5=frac{4264.28}{3000}$

Divide both sides by 3000.

$latex displaystyle 1+i=left(frac{4264.28}{3000}right)^frac{1}{5}$

Raise both sides to the 1/5 power.

$latex displaystyle i=left(frac{4264.28}{3000}right)^frac{1}{5}-1approx 7.2864541%$

Subtract 1 from both sides to yield the result. A very high yield for a CD!

Note: I’ve noticed that the $latex LaTeX$ support in WordPress doesn’t like currency symbols so I won’t be able to use them in my equations. So, any further financial problems I write will have to do without them (unless I figure out how to incorporate the symbols).

Posted in: Logs

No. 24: Math Problem of the Day! (29.08.10)

30 August, 2010 12:14 AM / Leave a Comment / Gene Dan

Hey everyone,

I’ve decided to create a series of daily math problems in order to improve my computer skills. Specifically, these posts will improve my knowledge of gnuplot, HTML, LaTeX, and Maxima. I’ve chosen to write these posts directly with HTML, even though I could have let WordPress do the HTML automatically. Each daily post contains a few pieces of mathematical text that will require me to use LaTeX, a markup language that has an advantage over HTML due to the fact that it can incorporate mathematical formulae within text. These posts will also help me with my gnuplot and Maxima skills, because they will sometimes contain diagrams and graphs that will accompany the problems.

I started learning gnuplot, HTML, LateX, and Maxima about a week ago, so I will probably make many mistakes. So, feel free to point out all my errors, because I wish to learn from my mistakes!

At first, these problems will be extremely elementary, so I can focus more on using HTML and LaTeX rather than getting bogged down with complexities of the problems. As my HTML and LaTeX skills improve, I’ll incorporate harder math problems for your enjoyment. Now, I present to you Problem 1, from Appendix D: Trigonometry of Stewart’s Calculus, 5e:

Problem 1:

A circular arc of length 6 cm is subtended by a central angle of 3π/4. Find the length of the radius of the circle.

Solution 1:

In order for us to solve the problem, we will need to know the relationship:

$latex displaystyle theta=frac{a}{r}$

Where θ represents the central angle, a represents the length of the subtended arc, and r represents the length of the radius. We know this relationship holds due to the fact that the subtended arc is proportional to the size of the central angle. Using this relationship, we have θ = 3π/4, a = 6 cm, and:

$latex displaystyle frac{3pi}{4}=frac{6~text{cm}}{r}$

The use of algebra yields us the result:

$latex displaystyle r=frac{8}{pi}~text{cm}$

Posted in: Logs

No. 23 SCCCC Conference Championships: Race Report

17 August, 2010 10:13 PM / Leave a Comment / Gene Dan

Hey everyone,

The final race of the SCCCC 2010 season took place on home soil on the outskirts of Austin at Manda, and on the UT Pickle Research Center north of campus. It would have been nice to have the race directly on the main UT campus, but logistical problems like cost and scheduling prevented us from doing so. It would have been great publicity for the team if we could have had a campus crit around the Darrell K. Royal Stadium, so if any of the officers happen to stumble across this post, I would suggest that you do everything in your power to stage this race in a location visible to our fellow students!

The team met at the CPE parking lot.

Anyway, I got to wake up slightly later at 6:30 AM for today’s race since it was held in town. At 7:30, the team met up in the CPE parking lot and we headed out to the Manda area for the race. The course would be the exact same as the one at Ronde von Manda, so I knew we would have a lot of wind, just like at Manda. When we got to the course, we signed in, set up our bikes, and warmed up. When I was signing in, I tried to downgrade to the D category, but I wasn’t allowed to because of the Conference Championship rules. That would rule me out of the D category TTT, which I really wanted to do because I had been training with Marc and Chi-Che the whole season. Anyway, my registration would put me on reserve for the C category TTT, with Stephen Salazar, Matthew Stottlemyre, Trent Boyd, and Robbie Booth.

Jacob loads the bikes onto the trailer.

After warm-up, we lined up at the start line, along with teams from Texas Pan-American (a team I had not raced against before), Baylor, Rice, Texas A&M, MSU, UH, and an assortment of other minor teams. I didn’t have any lofty goals for this race, mainly because I knew I would get dropped eventually because of the strong crosswinds during that day. Thus, I had a simple goal in mind, to make it further than I had at Manda, at which I dropped after five minutes of racing.

Steve, me, and Chi-Che before the start.

Immediately after the start, Trent took a flyer but no one chased him because the race was still neutralized, and the headwind reeled him back in shortly afterward. I stayed near the front drafting behind Matt and the Texas Pan American team. At the fifth mile, things started heating up and there were some accelerations at the corners in attempt to drop the weaker riders. My cornering had improved slightly but I was still not brave enough to tilt my bike to the limit, so I ended up wasting energy at each corner when I had to accelerate after the apex. Anyway, as soon as we hit the tailwind section of the course, a rider from Rice rode the gutter too aggressively and crashed headfirst over his handlebars. I’m not sure if he finished the race. For those of you who are unaware of the term “riding the gutter,” riding the gutter is a tactic in which the rider riders close to the edge of the road in order to make it hard for others to draft behind him, or “suck his wheel.” Drafting behind a person riding the gutter is somewhat nerve-wracking, not only because you can’t see anything in front of you, but also because you have no place to maneuver if an obstacle emerges. Riding the gutter, although a useful tactic, carries risk because it’s harder for the rider to handle, and increases the risk of crashing. I was glad that I wasn’t behind the Rice rider when that happened, but I know a crash will happen to me eventually, given enough miles.

At the start…

After going 35 mph+ in the tailwind section, we made a right turn into a crosswind, with Rice leading the pack. The pace had slowed down considerably to around 16mph as we were all playing cat-and-mouse with each other. At this point, Trent attacked the pack and Robbie chased him down, as did the rest of the pack. I heard a rumor that Trent was a Cat 2 Track rider, but only a Cat 4 road rider, which allowed him to race in the C category. Thus, the viciousness of the attack was not surprising, and the pack broke apart into about five different groups. I happened to be in the second-to last group with another rider from Texas A&M, and after catching our breaths, we knew the race was over. However, I still had some other priorities, one of which was to finish higher than last, which had happened at DFW. I knew the UH guy who outkicked me last time was still behind me so I wanted to finish ahead of him.

The Texas A&M rider didn’t help very much, however. He didn’t pull or make any effort to keep us ahead of the guys who were trying to catch up to us, so I suppose he knew that our race was already over and he wanted to just take the rest of the way easy. Somewhere during the middle of the second lap, we saw a battered and bruised rider from Rice walking in the opposite direction – I suppose it was the Rice rider that had crashed, or maybe another rider with mechanical. During the tailwind section my legs started to cramp up from my former injuries, and they gradually got worse as the race went on. After completing the second lap, I saw Trent on the sidelines because he had dropped out of the race. I was somewhat upset because he was the one who broke up the pack and dropped his teammates, only to drop out of the race later because he wasted too much energy. If he had spent his efforts helping Robbie or Matt, we would’ve had a chance to win. On the third lap, or at about mile 36, the UH guy caught us, and another guy from Rice shortly afterward. At about 1k from the finish, I had cramped up so badly that I dropped behind, but I still managed to finish. My legs were cramping up so badly that I had to ask Chi-Che to catch me as I rolled in at the finish. The results showed that I still finished ahead of another rider, a slight improvement over my last C category race.

After the race, Matt asked me if I wanted to take his place in the TTT. Since I could barely walk, I declined. Before the TTT, the team went out to eat at subway where I talked to Marc and learned what had happened in the D race: Three Texas Tech riders broke away from the pack and Marc followed them, but they eventually dropped him. Marc found himself in no-man’s land with another rider from Baylor, and managed to finish fifth, a personal best for him.

Since I wasn’t racing in the TTT, I volunteered to be a corner marshall, making sure riders didn’t turn where they weren’t supposed to. The job wasn’t hard, I just had to stand at an intersection and point in the direction of the course. I felt kind of bad because Trent dropped out of the TTT race, leaving the C-team with only 3 riders, one short of the customary 4. Had I aggravated my injury, I would have been able to help. For those of you new to the TTT, or Team Time Trial, It’s an event similar to a regular time trial, but with each team starting together, but separately from other teams. You have 4 members in each team, and each teammate can draft off of each other. Teams are released 30 seconds apart. If one team should catch another, they cannot draft off the team they catch, and vice-versa. The team that gets caught must let the team that catches them pass them, or else face a penalty. The team with the least cumulative time wins. Anyway, while I was volunteering I managed to take some pictures of the race:

Texas Pan American D

Texas Tech

Texas A&M C

Texas C

MSU B

MSU Women A

MSU A

Today wasn’t really a good day for Texas, except for Marc, who finished 5th in the RR and 2nd in the TT. We were down on manpower in the A team, because a lot of the officers were on that team and had to host the race. And furthermore, Tokarski crashed out of the A race, and his injuries were so bad that he had to go to the hospital. He has since recovered, however. The Crit the next day wasn’t much better, but Marc again had good form and finished 5th in the D race. I had to stay home because my legs were inflamed, and I had to take a week off the bike to recover. On the bright side it’s been about three months since this race and I can say that I’ve improved a lot. I’ve been doing intervals and I’ve regularly had averages of 21mph over 60 miles and my highest average was 22 mph. I haven’t raced since the close of Collegiate season, but I’ve had my sights set on the Metro Park Crit next week and a few more late-season races next month.

Posted in: Cycling, Logs

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