You are here:

Advanced Math/IMP 4 ( It's Algebra I think....)

Advertisement

Expert: - 11/10/2008


Question
The approximate number of hours between sunrise and sunset in Oregon varies throughout the year as a sine wave. On June 21st (the longest day of the year) there is 15 hours of sun. On March 21st (the spring equinox) there is 12 hours of sun.
a) Write an equation for the hours of sun with respect to day of the year. Also identify the period, amplitude, and midline.
b) Over the course of a year, during what period of time is the amount of daylight in Oregon at least 14 hours?
c) What percent of the year do we have at least 14 hours of daylight?

Answer
a) The equation would be a sin wave.  Compute when March 21st is (I believe its the 80th days of the year).  Take n = number of days.  The equation is 12 + 3*sin(π(n-80)/182.625, assuming the 80 is right.

The period is approximately a full year, which is 365.25 days (remember leap year every 4th year).  We want the full time of 2π radians to be equal to this value.

The amplitude involves the ±3 hours, which gives a total of 6 hours.

The midline is at the 80th day of the year and 253 days of the year.

b) To find when the daylight is at least 14 hours, solve to see when
3*sin(π(n-80)/182.625 = 2.  Note that this happens on two different days.

c)  To find out how many days there are with over 14 hours, take the difference between these two days plus one.  To find the perecentage, multiply by this many days and divide by 365.  Divide by 366 for leap year.  In the end, multiply by 100 to get a percentage from a fraction.  

Advanced Math

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scott A Wilson

Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

Experience

Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

©2012 About.com, a part of The New York Times Company. All rights reserved.