above the water respectively. How high is the diving board? 3. A ball is thrown into the air. Its height above the ground‚ h (measured in feet)‚ at any given time after the ball is thrown‚ t (measured in seconds)‚ can be modelled using the quadratic function h(t) = -16t2 + 16t + 32. From what height above the ground was the ball thrown? Solutions: 1. C = 0 Using point (-6‚ 4 ) and (6‚ 4) 4 = a (-6)^2 + (-6)b + c 4 = 36 a -6b + c
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Pre-Socratic Philosophers Stanford Encyclopedia of Philosophy 1. Who Were the Presocratic Philosophers? Our understanding of the Presocratics is complicated by the incomplete nature of our evidence. Most of them wrote at least one “book” (short pieces of prose writing‚ it seems‚ or‚ in some cases‚ poems of not great length)‚ but no complete work survives. Instead‚ we are dependent on later philosophers‚ historians‚ and compilers of collections of ancient wisdom for disconnected quotations (fragments)
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Relative Velocity and Riverboat Problems On occasion objects move within a medium that is moving with respect to an observer. For example‚ an airplane usually encounters a wind - air that is moving with respect to an observer on the ground below. As another example‚ a motorboat in a river is moving amidst a river current - water that is moving with respect to an observer on dry land. In such instances as this‚ the magnitude of the velocity of the moving object (whether it be a plane or a motorboat)
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Submitted By: Ma. Karla Rachelle Ulibas Student Submitted To: Mr. Ray-ann Buenafe Instructor HISTORY OF TRIGONOMETRIC FUNCTIONS Trigonometric functions seem to have had their origins with the Greek’s investigation of the indirect measurement of distances and angles in the “celestial sphere”. (The ancient Egyptians had used some elementary geometry to build the pyramids and remeasure lands flooded by the Nile‚ but neither they nor the ancient Babylonians had developed the concept of
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SD Statistical Calculations REG Population Standard Deviation (σn) = 1.316956719 Arithmetic Mean (o) = 53.375 Number of Data (n) = 8 SD Standard Deviation Sum of Values (Σx) = 427 Sum of Squares of Values (Σx 2 ) = 22805 Use the F key to enter the SD Mode when you want to perform statistical calculations using standard deviation. SD .................................... F 2 (fx-95MS) F F 1 (Other Models) • Always start data input with A B 1 (Scl) = to clear statistical
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MAPÚA INSTITUTE OF TECHNOLOGY Department of Mathematics VISION The Mapua Institute of Technology shall be a global center of excellence in education by providing instructions that are current in content and state-of-the-art in delivery; by engaging in cutting-edge‚ high impact research; and by aggressively taking on present-day global concerns. MISSION a. The Mapua Institute of Technology disseminates‚ generates‚ preserves and applies knowledge in various fields of study. b. The Institute
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Al-Khwarizmi: The Father of Algebra Muhammed Ibn Musa al-Khwarizmi‚ was a mathematical pioneer‚ and is considered by many to be the greatest mathematician of the Islamic world‚ as well as the founder algebra. His book entitled Kitâb al-Mukhtasar fî Hisâb al-Jabr wa ’l-Muqâbala‚ which means “The Compendious Book on Calculation by Completion and Balancing‚” established algebra as an independent discipline. While his arithmetic work‚ possibly entitled Kitāb al-Jamʿ wa-l-tafrīq bi-ḥisāb al-Hind
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di a + bi : Multiply top and bottom by the conjugate of the denominator‚ c − di. c + di Quadratic Equations Solve by Factoring Solve by completing the square 1. Divide every term by the leading coefficient. 2. Isolate the x2 and the x terms. coeff of x 2 3. Add to both sides . 2 4. Rewrite the LHS as a square. 5. Solve using square root property. 1 2 Solve by quadratic formula Quadratic formula: Discriminant: x= −b ± b2 − 4ac = 0 b2 − 4ac > 0 b2 − 4ac < 0 √ −→
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Trigonometric Identities I. Pythagorean Identities A. [pic] B. [pic] C. [pic] II. Sum and Difference of Angles Identities A. [pic] B. [pic] C. [pic] D. [pic] E. [pic] F. [pic] III. Double Angle Identities A. [pic] B. [pic] =[pic] =[pic] C. [pic] IV. Half Angle Identities A. [pic] B. [pic] C. [pic] 6-1 Inverse Trig Functions p. 468: 1-31 odd I. Inverse Trig Functions A. [pic]
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asked to find any one of the three variable quantities‚ provided the other two. A square root function that models tsunami velocity as a function of water depth is v = (gD)1/2‚ where g = 9.8m/s2 and D = water depth. Alternatively‚ this can be a quadratic model to find the depth of water if the wave velocity is known: D = v2 / g (Abbott‚ 2004‚ Banks‚ 1998). The energy of a water wave‚ particularly a tsunami‚ can be modeled as a function of wave height
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