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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one right angle If the sides are known instead of the angles‚ then L’Huiller’s Formula can be used to solve for the spherical excess 1 s s − a s − b s−c tan E = tan tan tan tan 2 2 2 2 2 a+b+c Where: s= 2 Solutions to Right Spherical Triangles (C = 90o) Sides a‚ b‚ c are based on the corresponding arc lengths S = rθ that is based on its corresponding interior angles S a = rθ BOC ; Sb = rθ AOC ; Sc = rθ AOB and that a + b + c < 360o Angles A‚ B‚ C of
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projectile launcher. Also‚ we verified the angle at which the projection of the ball would produce a maximum range. Lastly‚ we predicted the range that a ball would travel at a certain angle‚ theta. Projectile motion is the motion of objects that are initially launched‚ or projected‚ and then continue moving with only the force of gravity acting upon it. The forces involved in projectile motion are the initial velocity of the projected object at a certain angle and gravity acting downward on the object
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Experiment 3: Projectile Range Versus Angle EQUIPMENT NEEDED – Mini Launcher and steel ball – Plumb bob – Measuring tape or meter stick – Carbon paper – Graph paper – White paper Purpose The purpose of this experiment is to find how the range of the ball depends on the angle at which it is launched. The angle that gives the greatest range is determined for two cases: launching on level ground and launching off a table. Theory The range is the horizontal distance‚ x
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Lab Report Experiment Aim: To determine the acceleration of an object down an incline plane using various methods. Research Question: Is there a relationship between the angle θ of the incline and the acceleration down the plane? Equipment: * Ticker Timer (AC 50Hz ) * Incline (wood) * Meter ruler * Dynamic Trolley ( Mass: 380.55 ± 0.01g ) * Carbonated paper * Power Source (2W) * Data Logger * Motion Sensor * Tennis Ball Method
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default settings for angle‚ initial speed and mass. 80‚18‚2 Look at the top of the screen. Which variables are calculated by the program? Range(11.5)‚ height(-1.2)‚ time(3.7) What variables can be changed by the user? Angle‚ initial speed‚ mass‚ diameter‚ (air resistance) List the different objects that can be fired from the cannon. Tanker shell‚ golf ball‚ baseball‚ bowling ball‚ football‚ pumpkin‚ adult human‚ piano‚ buickLaunch the cannon ball at a speed of 10 m/s at an angle of 35o. Launch the
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CHAPTER 1 INTRODUCTION 1.1 Introduction Geometry is one of the most interesting fields of mathematics. From the ancient times of the Greeks up to now‚ it has held captive the imagination of many mathematicians‚ artists‚ scientists‚ engineers and architects. Its application to modernization and technological advancement cannot be denied. Thus‚ it must be given emphasis in educational institutions particularly in secondary schools. The low achievement test results in mathematics of high
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Sharqueze Skinner Professor Rogers HUM 160 9 October‚ 2012 In This Corner From the Man’s Soul Is Love. “Hate‚ it is with this hand that Cane iced his brother. Love‚ these five fingers go strait to the soul of man. The story of life is this; static‚ one hand is always fighting the other.” This is said by Radio Raheem in the film Do the Right Thing by Spike Lee. Radio Raheem goes on to explain that no matter how much hate seems to get the best of us‚ love will always come out on top. The Film
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Data and Computations 1. The following data (obtained from a preliminary survey) and assumed standards will be used to layout the desired curve-centerline in the field. Station at PI = 4 + 350 Deflection angle at PI‚ ( = 420 15’ (( central angle of curve) Degree of curve‚ D = 80 (subtending a 20 meter chord) 2. Before laying out the curve in the field‚ first compute the value of the following curve parameters: Length of Tangent‚ T = (= R * tan
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Problems for Angle of Elevation Problems: 1. A ladder with its foot on a horizontal flat surface rests against a wall. It makes an angle of 30° with the horizontal. The foot of the ladder is 41 ft from the base of the wall. Find the height of the point where the ladder touches the wall. Solution: Draw the figure for the given data. [Given] The distance from the foot of the ladder to the foot of the wall adjacent = 41 ft‚ and the angle of elevation is 30° Leto be the height of the side
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