In the adjacent image, the two circles on the map represent lines of position for the Sun and Moon at GMT on October 29, At this time, a navigator on a ship at sea measured the Moon to be 56 degrees above the horizon using a sextant. Ten minutes later, the Sun was observed to be 40 degrees above the horizon. Lines of position were then calculated and plotted for each of these observations. Since both the Sun and Moon were observed at their respective angles from the same location, the navigator would have to be located at one of the two locations where the circles cross. In most cases, determining which of the two intersections is the correct one is obvious to the observer because they are often thousands of miles apart.
Analog—digital hybrids[ edit ] Analog computing devices are fast, digital computing devices are more versatile and accurate, so the idea is to combine the two processes for the best efficiency. An example of such hybrid elementary device is the hybrid multiplier where one input is an analog signal, the other input is a digital signal and the output is analog. It acts as an analog potentiometer upgradable digitally.
This kind of hybrid technique is mainly used for fast dedicated real time computation when computing time is very critical as signal processing for radars and generally for controllers in embedded systems. In the early s analog computer manufacturers tried to tie together their analog computer with a digital computer to get the advantages of the two techniques.
In such systems, the digital computer controlled the analog computer, providing initial set-up, initiating multiple analog runs, and automatically feeding and collecting data.
The purpose of speed dating is to meet as many people in as short an amount of time as possible. In the few minutes you spend with the other person, you want to find something out about them and you want to trade information in case you decide to pursue things further in the future.
Construct viable arguments and critique the reasoning of others. Once students have submitted their responses I will review the answer with the class. Flipchart – solving exponenital equations with logs p. Speed Dating with Log and Exponential Equations 45 minutes Student tutors are the key to the success of this activity. Each student will need their own card. So I was going to just make a double set of copies of these 16 problems.
You may also want to have whiteboards and markers available for student work unless you want to collect and analyze their work. I just want them to have practice solving logarithmic and exponential equations. I am going to ask students to pick up a card as they enter class. I give the students 10 minutes to become an expert on solving and explaining their problem to someone else. They may ask others for help, if needed.
After 10 minutes, they will need to be the expert on the problem. The answers are copied on the back of the card so that students can check themselves. Once students are experts they will take a seat at a desk and will exchange problems with the person in front of them.
Q: What makes natural logarithms natural? What’s so special about the number e?
JEE Mathematics Syllabus Algebra Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations. Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots. Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.
Logarithms and their properties. Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.
Speed is the distance traveled divided by the time of travel. For example; if you were to travel a distance of 10 miles in 2 hours time, then your average speed equals 5 miles per hour. s=d/t (s=speed, d=distance, t=time, and the / means to divide). The word velocity is very similar to speed (except velocity also has a direction called a vector) and in most cases we will now use the letter “v.
History of Technology Heroes and Villains – A little light reading Here you will find a brief history of technology. Initially inspired by the development of batteries, it covers technology in general and includes some interesting little known, or long forgotten, facts as well as a few myths about the development of technology, the science behind it, the context in which it occurred and the deeds of the many personalities, eccentrics and charlatans involved.
You may find the Search Engine , the Technology Timeline or the Hall of Fame quicker if you are looking for something or somebody in particular. Scroll down and see what treasures you can discover. Background We think of a battery today as a source of portable power, but it is no exaggeration to say that the battery is one of the most important inventions in the history of mankind.
Volta’s pile was at first a technical curiosity but this new electrochemical phenomenon very quickly opened the door to new branches of both physics and chemistry and a myriad of discoveries, inventions and applications. The electronics, computers and communications industries, power engineering and much of the chemical industry of today were founded on discoveries made possible by the battery. Pioneers It is often overlooked that throughout the nineteenth century, most of the electrical experimenters, inventors and engineers who made these advances possible had to make their own batteries before they could start their investigations.
They did not have the benefit of cheap, off the shelf, mass produced batteries. For many years the telegraph, and later the telephone, industries were the only consumers of batteries in modest volumes and it wasn’t until the twentieth century that new applications created the demand that made the battery a commodity item. In recent years batteries have changed out of all recognition. No longer are they simple electrochemical cells.
Sunday, September 11, Significant Figures Speed Dating Activity My physical science students are currently working on determining the correct number of significant figures to use in different situations. The first step is for them to be able to recognize how many significant figures there are in a number. I made posters to hang up in my classroom for them and me! I decided this was the perfect topic to make into a speed dating activity.
You can find the files for my significant figures posters here.
Click here for the speed dating activity. A couple of equations were cut off when I converted to G Docs; however, I have a Microsoft Word copy if needed. A couple of equations were cut off when I converted to G Docs; however, I have a Microsoft Word copy if needed.
Student View Task Carbon 14 is a common form of carbon which decays over time. The half-life of Carbon 14, that is the amount of time it takes for half of the Carbon 14 to decay, is approximately years. If there is currently one microgram of Carbon 14 remaining in the preserved plant, approximately when did the plant die? IM Commentary The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places.
Note that the purpose of this task is algebraic in nature — closely related tasks exist which approach similar problems from numerical or graphical stances. The two solutions provided differ slightly in their approach in this regard. In either case, it is more appropriate to report the time since the plant has died as approximately 19, years since these measurements are never completely precise.
Alt version for sol’n 1 Since the half life of Carbon 14 is years, this means that after years there will only be 5 micrograms of Carbon 14 left in the fossilized plant:
Speed is the distance traveled divided by the time of travel. For example; if you were to travel a distance of 10 miles in 2 hours time, then your average speed equals 5 miles per hour. Most textbooks bold face the units that also contain direction information. All quantities that are not vectors are called scalars. Time is a scalar quantity. The WWW links on this site will take you directly to the various web site pages.
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I remember playing it with my sister soon after receiving it and really enjoying it. Years of living alone meant that it sat on the shelf and rarely got played. Now that there’s a husband in the picture, I decided it was time I taught him to play Farkle! The game of Farkle is not super-complicated. If you buy a copy, you will likely be shocked at just how simple it is.
The version I own features a cup for rolling dice that also doubles as game storage, six dice, and a set of rules in two different languages. If you have dice in your classroom, you don’t even need to buy the game! On your turn, you will roll all six dice. Any scoring dice are set aside. If you want to keep that score, you stop.
The second method uses a sliding linear L scale available on some models. Addition and subtraction are performed by sliding the cursor left for subtraction or right for addition then returning the slide to 0 to read the result. Standard linear rules[ change change source ] The length of the slide rule is quoted in terms of the nominal length of the scales. Models a couple of meters long were sold to be hung in classrooms for teaching purposes.
Get your students excited about logarithms with this math version of speed dating. Students start in two concentric circles facing one another. They “date” by working through each others condensing and expanding logarithm problems.4/5(35).
Some DCC locomotives feature on-board sound effects. A layout can be divided into blocks powered separately. Locomotives located by the power they use. Legendary railroad services, past and present. An exact value defining the ampere. The ratio of a photon’s energy to its frequency. Relating temperature to energy. The number of things per mole of stuff.
The ratio of the circumference of a circle to its diameter. The diagonal of a square of unit side. Diameter of a cube of unit side. The diagonal of a regular pentagon of unit side. Base of the exponential function which equals its own derivative.
Friday, July 29, Growth Mindset Mistakes Poster A continual focus in my classroom is helping my students build a growth mindset. One quote I’ve seen time and time again when it comes to mindset is “Mistakes are expected, respected, inspected, and corrected. This summer, I decided that I wanted to post this on the wall in my classroom as a reminder to students.
Heroes and Villains – A little light reading. Here you will find a brief history of technology. Initially inspired by the development of batteries, it covers technology in general and includes some interesting little known, or long forgotten, facts as well as a few myths about the development of technology, the science behind it, the context in which it occurred and the deeds of the many.
See Article History Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine sin , cosine cos , tangent tan , cotangent cot , secant sec , and cosecant csc. These six trigonometric functions in relation to a right triangle are displayed in the figure.
For example, the triangle contains an angle A, and the ratio of the side opposite to A and the side opposite to the right angle the hypotenuse is called the sine of A, or sin A; the other trigonometry functions are defined similarly. These functions are properties of the angle A independent of the size of the triangle, and calculated values were tabulated for many angles before computers made trigonometry tables obsolete.
Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures. Trigonometry developed from a need to compute angles and distances in such fields as astronomy , mapmaking , surveying , and artillery range finding. Problems involving angles and distances in one plane are covered in plane trigonometry.
Carbon 14 dating
Of course, you would require more than the energy in the whole known universe in order to attain c being massive. The only thing for certain is that the speed of light appears to be constant. In fact no one yet has been able to actually prove it. Einstein would have been better of saying he thinks the speed of light is the fastest thing in the universe.
Introduction Though perhaps best known throughout the world for his science fiction, Isaac Asimov was also regarded as one of the great explainers of science.
Sunday, January 12, Introducing Logarithms with Foldables, War, Bingo, and Speed Dating Missing three days of school due to the snow and ice really threw off my plans for Algebra 2. I had hoped to get through logarithms before Christmas Break. We did get started with logarithms. But, I had to spend the first four days of the new semester finishing up our logarithm unit. This might have had something to do with the fact that I chose to introduce them on a day that most students thought we should have been out of school.
Many of the schools around us had already closed due to the impending arrival of Cleon.