Orthogonal polynomials

Answers are hi-lighted yellow. Company A's nationally advertised brand is Brand X. Contribution to profit with Brand X is $40 per case. Company A's re-proportioned formula is sold under a private label Brand Y. Contribution to profit with Brand Y is $30 per case. Company A's objective is to maximize the total contribution to profit. Three constraints limit the number of cases of Brand X and Brand Y that can be produced. Constraint 1: The available units of nutrient C (n) is 30. Constraint 2:

Appendix B – Mathematical Extrapolation Technique for Predicting and Assessing Production Performance In this section developments in graphical methods of assessing water drive performance are presented. An extensive number of graphical and mathematical extrapolation techniques is available in the literature. A number mathematical extrapolation methods were also assessed (not presented here). Mathematical extrapolation technique presented by Dake (1994) was found to be quite effective in predicting

Analytical Mathematics: Matrices Matrices Matrices are a grouping of numbers or symbols that represent numbers in a semi-rectangle that are placed into order through one or a series of vertical lines known as columns and one or a series of horizontal lines known as rows. Matrices come in many sizes, they can be as few as one number and could go all the way to infinity. Not just one number or letter can be placed in a space a whole equation with numbers and variables can be placed in a single

During Summer 2014, I took my first college course “Math 10: Elementary Algebra” also known as remedial math. However, ever since I can remember, I have always liked math and this seems to contradict how I started my college career. My interest in math goes back to second grade when I received a 100 on my report card. In Bangladesh, grades are believed to reflect one’s identity, so I took a greater interest in the subject thereafter. After moving to New York, I continued to enjoy the subject though

As I reflect on my first four week of algebra I recall being very skeptical that I could learn and complete a mathematics course with a passing grade. Thats because I had not taken a mathematics course since graduating high school in 1999. I struggled with match in high school and never really felt overly confident that I could learn and apply mathematics in real life. Over the past four weeks I have learned a great deal of information and how algebra can be applied in real world applications. The

x = (1, 1, 1, 1), y = (2, 2, 2, 2) cosine, correlation, Euclidean COSINE cos (x, y)= (x.y)/(||x|| ||y||) x.y = 1*2 + 1*2 + 1*2 + 1*2 = 8 ||x||= √(1*1 + 1*1 + 1*1 + 1*1) = √4 = 2 ||y||= √(2*2 + 2*2 + 2*2 + 2*2) = √16 = 4 Hence, cos (x,y) = 8/(2*4)  1 CORRELATION corr(x, y) = (covariance(x,y))/([standard deviation(x) * standard deviation(y)]) Mean of x = (1+1+1+1)/4 = 1 ; Mean of y = (2+2+2+2)/4 = 2 covariance(x,y) = 1/(4-1) * [(1-1)(2-2) + (1-1)(2-2) + (1-1)(2-2) + (1-1)(2-2)]

Complex Analysis: Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including algebraic geometry, number theory, applied mathematics; as well as in physics, including hydrodynamics and thermodynamics and also in engineering fields such as nuclear, aerospace, mechanical and electrical engineering. Murray R. Spiegel described complex

INTRODUCTION: The study of large deflection of cantilever beam comes from theory of elasticity. Theory of elasticity state that “solid material will deform under the application of an external force it will again regain their original position when external force is removed is referred to as elasticity”. We took beam made of nickel titanium alloy which regain their original shape after removing external force act on the beam. It’s a prismatic circular cross section

Completing the square is use to prove the quadratic formula. Given ax^2+bx+c=0 we first have to make the coefficient of x^2 to be one. We divided the original formula by a: x^2+b/c x+c/a=0/a since 0/a we still have our quadratic equation. Subtract that c/a in both sides: x^2+b/c x+c/a-c/a=-c/a remember that b/a is b/2(a) now we will have to add it to the root of two: x^2+b/a x+b^2/(4a^2 )=b^2/(4a^2 )-c/a next is to set up our denominators to be the same we should have (x+b/2a)^2=b^2/(4a^2 )-4ac/(4a^2

It is visible in Fig.~\ref{ededhe3c} that the missing mass distributions for two energies have a peak at the $\omega$ meson mass 0.7827~GeV/c$^2$, on top of a continuous background. The peak positions for two energies are at the correct $\omega$ mass, indicating that the energy reconstruction is done properly. The background of the missing mass distributions ends at different values because of the different phase space of the two energies. The two phase space distributions are useful for systematic