File
... reason we think of sine being the y value, cosine being the x value, and tangent being sine divided by cosine is to determine whether the value of a trigonometric function is positive or negative. This of course all depends on where the terminal side of the angle lies. The following questions will r ...
... reason we think of sine being the y value, cosine being the x value, and tangent being sine divided by cosine is to determine whether the value of a trigonometric function is positive or negative. This of course all depends on where the terminal side of the angle lies. The following questions will r ...
CHAPTER I: The Origins of the Problem Section 1: Pierre Fermat
... methods more closely resemble our current method, and even though Descartes was reluctant at first to acknowledge Fermat’s work, eventually he did. Fermat also made significant progress on problems that led to the development of the calculus. Around this same time, he worked with Blaise Pascal in fo ...
... methods more closely resemble our current method, and even though Descartes was reluctant at first to acknowledge Fermat’s work, eventually he did. Fermat also made significant progress on problems that led to the development of the calculus. Around this same time, he worked with Blaise Pascal in fo ...
Notes on the Periodically Forced Harmonic Oscillator
... equation. In this case, we multiply the guess by t to obtain yp (t) = At cos(ω0 t) + Bt sin(ω0 t). This means that the particular solution is an oscillation whose amplitude grows linearly with t. This phenomenon is known as resonance. When we substitute yp into (2) and simplify, we obtain −2mω0 A si ...
... equation. In this case, we multiply the guess by t to obtain yp (t) = At cos(ω0 t) + Bt sin(ω0 t). This means that the particular solution is an oscillation whose amplitude grows linearly with t. This phenomenon is known as resonance. When we substitute yp into (2) and simplify, we obtain −2mω0 A si ...
linear program
... valid. Otherwise, all points on other side are instead valid. Equality constraints have no valid side. The solution must be on the line itself. Some constraint lines are horizontal or vertical. These involve only one variable and one intercept. ...
... valid. Otherwise, all points on other side are instead valid. Equality constraints have no valid side. The solution must be on the line itself. Some constraint lines are horizontal or vertical. These involve only one variable and one intercept. ...
Chapter 4, Section 4-8, Solving Problems with Trigonometry File
... Example A: Rows of parade volunteers pull a huge, helium-filled Sponge Bob Square Pants balloon around Central Park using guide wires. The angle of depression of the first set of guide wires from the base of Sponge Bob Square Pants to the handlers’ hands, about four feet in the air, is 71 degrees. F ...
... Example A: Rows of parade volunteers pull a huge, helium-filled Sponge Bob Square Pants balloon around Central Park using guide wires. The angle of depression of the first set of guide wires from the base of Sponge Bob Square Pants to the handlers’ hands, about four feet in the air, is 71 degrees. F ...
Pascal
... 52 rows of Pascal’s triangle, and then start at the left end of the 52nd row and count to 13 (starting at 0). But that just might be a lot of work (truly!). Is there a better way? The answer is yes––yes there is. There is a wonderful argument which produces a simple formula. For example, suppose you ...
... 52 rows of Pascal’s triangle, and then start at the left end of the 52nd row and count to 13 (starting at 0). But that just might be a lot of work (truly!). Is there a better way? The answer is yes––yes there is. There is a wonderful argument which produces a simple formula. For example, suppose you ...
Weber problem
In geometry, the Weber problem, named after Alfred Weber, is one of the most famous problems in location theory. It requires finding a point in the plane that minimizes the sum of the transportation costs from this point to n destination points, where different destination points are associated with different costs per unit distance.The Weber problem generalizes the geometric median, which assumes transportation costs per unit distance are the same for all destination points, and the problem of computing the Fermat point, the geometric median of three points. For this reason it is sometimes called the Fermat–Weber problem, although the same name has also been used for the unweighted geometric median problem. The Weber problem is in turn generalized by the attraction–repulsion problem, which allows some of the costs to be negative, so that greater distance from some points is better.