Question:An architect designs two houses that are shaped and positioned like a part of the branches of the hyperbola whose equation is 625y^2 - 400x^2=250‚000‚ where x and y are in yards. How far apart are the houses at their closeset point? Answers:625y^2 - 400x^2=250‚000 y^2 / 20^2 - x^2 / 25^2 = 1 The closest two points on separate branches are the vertices‚ and their separation is 2 * 20 = 40yd. I find the question a little confusing‚ though. Question:LORAN (long distance radio navigation)
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Polynomial Functions Function Center and Vertices‚ Foci‚ Major and Minor Axes‚ Standard Equation for an Conic Sections - Ellipse Ellipse Center and Vertices‚ Foci‚ Transverse and Conic Sections Conjugate Axes‚ Asymptotes‚ Standard Hyperbola Equation for a Hyperbola Solving a Rational Expression Using Exponents‚ Solving a Rational Expression Rational Functions from a Graph Binomial Theorem Expansion Binomial Theorem Combinations and Combinations‚ Permutation Permutations Points 3
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EXERCISE 2STRAIGHT LINES Question 1: Write the equations for the x and y-axes. Answer : The y-coordinate of every point on the x-axis is 0. Therefore‚ the equation of the x-axis is y = 0. The x-coordinate of every point on the y-axis is 0. Therefore‚ the equation of the y-axis is x = 0. Question 2: Find the equation of the line which passes through the point (–4‚ 3) with slope . Answer : We know that the equation of the line passing through point ‚ whose slope is m‚ is . Thus‚ the equation
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The black hyperbolas ($E=A/\protect\angle^{LAB}\left(\gamma1‚\gamma2\right)$) plotted on this histogram represent different neutral split off cuts used for the systematic studies. The parameter $A$ for each hyperbola is written in the legend of the histogram. } \label{Fspltsys} \end{figure} % The hyperbolas shown in the split-off plot (Fig.~\ref{Fspltsys}) represent the different neutral split-off cuts used for the systematic studies. The definition of hyperbolas is given in Equation~\ref{sdspltsyshyp}
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www.Vidyarthiplus.com UNIT-I PART-B −2 2 −3 1. Find all the eigenvalues and eigenvectors of the matrix 2 1 −6 −1 −2 0 7 −2 0 2. Find all the eigenvalues and eigenvectors of the matrix −2 6 −2 0 −2 5 3. Find all the eigenvalues and eigenvectors of the matrix 2 2 1 1 3 1 1 2 2 2 −1 2 4. Using Cayley Hamilton theorem find A when A= −1 2 −1 1 −1 2 4 1 2 −2 5. Using Cayley Hamilton theorem find A When A = −1 3 0 0 −2 1 −1 1 0 3 6. Using Cayley Hamilton theorem find A find A = 2 1 −1 1 −1 1 −1 −1 0
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Mathematical modelling of a hyperboloid container Mathematical model is a method of simulating real-life situations with mathematical equations to forecast their future behaviour. Eykhoff (1974) defined a mathematical model as ’a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form’. Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics‚ biology
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10.6 SURFACES IN SPACE EXAMPLE 6.1 Sketching a Surface © The McGraw-Hill Companies‚ Inc. Permission required for reproduction or display. Slide 1 10.6 SURFACES IN SPACE EXAMPLE 6.1 Sketching a Surface Solution Since there are no x’s in the equation‚ the trace of the graph in the plane x = k is the same for every k. This is then a cylinder whose trace in every plane parallel to the yz-plane is the parabola z = y2. © The McGraw-Hill Companies‚ Inc. Permission required for
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------------------------------------------------- History Predecessors The Babylonians sometime in 2000–1600 BC may have invented the quarter square multiplication algorithm to multiply two numbers using only addition‚ subtraction and a table of squares. However it could not be used for division without an additional table of reciprocals. Large tables of quarter squares were used to simplify the accurate multiplication of large numbers from 1817 onwards until this was superseded by the use of
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coordinate plane positions of billiard ball A with coordinates (xA‚ yA) and billiard ball B with coordinates (xB‚ yB)‚ and also the radius of the circle‚ the solution points are at any of the points of intersection of the circular table with the hyperbola‚ x 2 @ y 2 P + r 2 ` yp @ xm a + xy2M ”‚ where P b c b c b c = y A A xB + yB A x A ‚ M = y A A yB @ x A A xB ‚ p = x A + xB ‚ m = b c ` a b c b y A + y B and r is the c radius. The solution was verified by considering specific
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Many people fail to realize the importance of physics in athletics. People who are untrained in the scientific field may believe that an athlete’s performance level is solely based on their skill-set‚ such as strength and training. However‚ one’s ability to employ physics concepts is the true determinant for success. This is imperative to dancers; most movement and technique can be improved dramatically by following Newton’s laws accordingly. By utilizing key physics concepts‚ a dancer can improve
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