Thales of Miletus (ca 624 - 546 BC) Greek domain Thales was the Chief of the Seven Sages of ancient Greece‚ and has been called the "Father of Science‚" the "Founder of Abstract Geometry‚" and the "First Philosopher." Thales is believed to have studied mathematics under Egyptians‚ who in turn were aware of much older mathematics from Mesopotamia. Thales may have invented the notion of compass-and-straightedge construction. Several fundamental theorems about triangles are attributed to Thales‚ including
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Math Review for the Quantitative Reasoning Measure of the GRE® revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important to understand in order to solve problems and to reason quantitatively on the Quantitative Reasoning measure of the GRE revised General Test. The following material includes many definitions‚ properties‚ and examples‚ as well as a set of exercises (with answers) at the end of each review
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Math Review for the Quantitative Reasoning Measure of the GRE® revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important to understand in order to solve problems and to reason quantitatively on the Quantitative Reasoning measure of the GRE revised General Test. The following material includes many definitions‚ properties‚ and examples‚ as well as a set of exercises (with answers) at the end of each
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take for the solid metal to hit the ground? Ignore the air resistance. | Correct Answer: The solid metal will hit the ground in about 2 seconds. | Which of the following functions shows the graph below? | f(x) = x2 + 2x | Find the quadratic equation whose roots are 1/2 and 6. | 2x2 - 13x + 6 = 0 | The curve y = -2x2 is shifted so that its axis of symmetry is the line x = -2 and its orthogonal axis is y = 8. Find the equation of the new curve. | Correct Answer: Answer: y
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Math Exam Notes Unit 1 The Method of Substitution -Solving a linear system by substituting for one variable from one equation into the other equation -To solve a linear system by substitution: Step 1: Solve one of the equations for one variable in terms of the other variable Step 2: Substitute the expression from step 1 into the other equation and solve for the remaining variable Step 3: Substitute back into one of the original equations to find the value of the other variable Step
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is continuous because it is associated with a measurement and its possible to have the same y value for different x values. And since the data is measuring height a decimal answer is possible. A function that would fit most of the data would be a quadratic function. The
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x-axis y-axis Foci ( ±c‚ 0) (0‚ ±c) Vertices (±a‚ 0) (0‚ ±a) Semitransverse axis a a Semiconjugate axis b b Pythagorean relation Asymptotes Hyperbolas with Center (h‚ k) Standard Equation Focal Axis y=k x=h Foci ( h ± c‚ k) (h‚ k ± c) Vertices (h ± a‚ k) (h‚ k ± a) Semitransverse axis a a Semiconjugate axis b b Pythagorean relation Asymptotes See pg. 656-658 in textbook for drawings.
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com 1. Find a quadratic polynomial‚ the sum and product of whose zeroes are 0 and √5 respectively. 2. Find the quadratic polynomial‚ the sum and product of whose zeroes are 4 and 1‚ respectively 3. If a and b are the zeros of the quadratic polynomial f(x)= x2-5x+4‚ find the value of 1/a + 1/b-2a b 4. Find the zeroes of the quadratic polynomial 4√3 x2+ 5 x - 2 √3 and verify the relationship between the zeroes and the coefficients. 5. Find the zeroes of the quadratic polynomial 4u2+ 8u
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Lesson 1: Trigonometric Functions of an Acute Angle c a b C A B The ratios of the lengths of the sides of a right triangle are called the trigonometric ratios. For convenience‚ we will name the three sides and three vertices of the right triangle as‚ a‚ b‚ and c for sides and the A‚ B‚ and C for the vertices as shown in the figure: Sine (sin) Function of an acute angle of a right triangle is equal to the ratio of the length of the opposite leg to the length of the hypotenuse. Cosine (cos)
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Section 1.2: Quadratic Equations Learning Objectives: 1. Solve a quadratic equation by (a) factoring‚ (b) completing the square‚ (c) the quadratic formula 2. Solve applied problems involving quadratic equations Examples: 1. Find the real solutions by factoring: [pic] 2. Find the real solutions by using the square root method: [pic] 3. Find the real solutions by completing the square: [pic] 4. Find the real solutions by using the quadratic formula: [pic]
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