Directions: Answer each of the following questions algebraically. You may sketch the graph of the parabola to help you visualize the flight of the ball. 1. A water balloon is tossed into the air with an upward velocity of 25ft/s. Its height h(t) in ft after t seconds is given by the function h(t) = -16t2 + 25t + 3. a) After how many seconds will the balloon hit the ground? b) What will the height be at t = 1 second? 2. A football is passed through the air and caught at ground level for
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PERSONAL FINANCIAL INVESTMENT STRATEGY ANALYSIS [pic] PROBLEM: Bob and Pina Ing‚ 31 and 28‚ a newly-wed couple found themselves in the midst of an interesting decision making problem. It appeared that their fortune had turned overnight when they won a mega lottery and received one million dollars after tax in price money. They were confused about how to invest their money‚ such that it gives them the maximum return on their investment. The couple consulted Jayhawks Financial Services LLC
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QUADRATIC FUNCTIONS (WORD PROBLEMS) 1. The area of a rectangle is 560 square inches. The length is 3 more than twice the width. Find the length and the width. Representation: Let L be the length and let W be the width. The length is 3 more than twice the width‚ so The area is 560‚ so Equation: Plug in and solve for W: Solution: Use the Quadratic Formula: Since the width can’t be negative‚ I get . The length is 2. The hypotenuse of a right triangle is 4 times the smallest side. The third
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Cost Formula Word Problem The cost formula for a manufacturer’s product is C = 5000 + 2 x ‚ where C is the cost (in dollars) and x is the number of units manufactured. (a) If no units are produced‚ what is the cost? (b) If the manufacturer produces 3000 units‚ what is the cost? (c) If the manufacturer has spent $16‚000 on production‚ how many units were manufactured? Answer these questions by substituting the numbers into the formula. (a) If no units are produced‚ then x = 0‚ and C = 5000 +
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PARTIAL DIFFERENTIAL EQUATIONS I YEAR B.Tech By Mr. Y. Prabhaker Reddy Asst. Professor of Mathematics Guru Nanak Engineering College Ibrahimpatnam‚ Hyderabad. SYLLABUS OF MATHEMATICAL METHODS (as per JNTU Hyderabad) Name of the Unit Unit-I Solution of Linear systems Unit-II Eigen values and Eigen vectors Name of the Topic Matrices and Linear system of equations: Elementary row transformations – Rank – Echelon form‚ Normal form – Solution of Linear Systems – Direct Methods
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Linear Functions There are three different ways to write linear functions. They are slope-intercept‚ point-slope‚ and standard form. There are certain situations where it is better to use one way than another to solve a problem. It is important to understand and comprehend the mechanics of these three forms so that you know what form to use when solving a problem. The first form‚ point-slope‚ is written as y-y1=m(x-x1). M is the slope and x1 and y1 correspond to a point on the line. It’s good to
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Balancing Equations Balancing equations is a fundamental skill in Chemistry. Solving a system of linear equations is a fundamental skill in Algebra. Remarkably‚ these two field specialties are intrinsically and inherently linked. 2 + O2 ----> H2OA. This is not a difficult task and can easily be accomplished using some basic problem solving skills. In fact‚ what follows is a chemistry text’s explanation of the situation: Taken from: Chemistry Wilberham‚ Staley‚ Simpson‚ Matta Addison Wesley
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6 Systems Represented by Differential and Difference Equations Recommended Problems P6.1 Suppose that y 1(t) and y 2(t) both satisfy the homogeneous linear constant-coeffi cient differential equation (LCCDE) dy(t) + ay(t) = 0 dt Show that y 3 (t) = ayi(t) + 3y2 (t)‚ where a and # are any two constants‚ is also a solution to the homogeneous LCCDE. P6.2 In this problem‚ we consider the homogeneous LCCDE d 2yt + 3 dy(t) + 2y(t) = 0 dt 2 dt (P6.2-1) (a) Assume that a solution to
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Mathieu Equations by Nikola Mišković‚ dipl. ing. Postgraduate course Differential equations and dynamic systems Professor: prof. dr. sc. Vesna Županović The Mathieu Equation An interesting class of linear differential equations is the class with time variant parameters. One of the most common ones‚ due to its simplicity and straightforward analysis is the Mathieu equation. The Mathieu function is useful for treating a variety of interesting problems in applied
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MC-B TOPIC; LINEAR PROGRAMMING DATE; 5 JUNE‚ 14 UNIVERSITY OF CENTRAL PUNJAB INTRODUCTION TO LINEAR PROGRAMMING Linear programming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming
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