Arc Length The definition of radian measure s = rθ The unit circle An angle of 1 radian Proof of the theorem IT IS CONVENTIONAL to let the letter s symbolize the length of an arc‚ which is called arc length. We say in geometry that an arc "subtends" an angle θ; literally‚ "stretches under." Now the circumference of a circle is an arc length. And the ratio of the circumference to the diameter is the basis of radian measure. That ratio is the definition of π. π | = | C D | . |
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was to learn more about freely falling objects. Unfortunately‚ his timing devices were not precise enough to allow him to study free fall directly. Therefore‚ he decided to limit the acceleration by using fluids‚ inclined planes‚ and pendulums. In this lab exercise‚ you will see how the acceleration of a rolling ball or cart depends on the ramp angle. Then‚ you will use your data to extrapolate to the acceleration on a vertical “ramp;” that is‚ the acceleration of a ball in free fall. If the angle
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Trenerry §5 Graph Theory Loosely speaking‚ a graph is a set of dots and dot-connecting lines. The dots are called vertices and the lines are called edges. Formally‚ a (finite) graph G consists of A finite set V whose elements are called the vertices of G; A finite set E whose elements are called the edges of G; A function that assigns to each edge e ∈ E an unordered pair of vertices called the endpoints of e. This function is called the edge-endpoint function. Note that these graphs are not related
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The edge of the cliff is 8 feet above the level of the water. The tip of his fishing rod is directly above the edge of the cliff and is 7 feet above the cliff. He lowers his fishing line so that it enters the water at the base of the cliff. The length of his fishing line‚ l‚ which is measured from the tip of his fishing rod to the place his line enters the water‚ and the angle between his line and the water‚ θ‚ are changing as the river carries his line downstream. The horizontal distance‚ r‚
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NAME_________________________________ STAMP________________ PERIOD____ PICTURES & GRAPHS A. The Atom 1. Calculate the average atomic mass using the spectrum below. 2. Answer the questions regarding the energy level diagram shown. a) The emission lines for the series above are in the IR‚ Vis and UV regions. Match the series with the region and justify your choice (FYI – AP you do not need to memorize the names of the series. IB will need to know then for next year). b) Would the wavelength
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right edge of the oscilloscope. 3. Click the Stimulate button once‚ and allow the tracing to complete. 4. When you measure the length of the latent period from a printed graph‚ you measure the time between the application of the stimulus and the beginning of the first observable response(increase in force). The computer can’t “look ahead‚” anticipating the change in active force. To measure the length of the latent period using the computer‚ click the Measure button. Then click the right arrow button
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1. Introduction 1. Why do you want to write about this topic? What are the new things we can learn by reading your paper? 2. What are the main objectives? 3. How are you going to support your ideas (i.e.‚ the theory or method)? 4. Structure of your paper 2. Present the major concepts or real world problems you want to address 3. Present the theories and models that you want to use to analyze the concepts or problems based on your real world experiences 4. Analyze the concepts or problems by using these theories and models
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relationship between equity and debt. This is carried out numerically via a simplified financial statement‚ which takes us through the methodology that leads to the ROE‚ WACC and firm’s value‚ all plotted against leverage. Introduction The Modigliani and Miller (M&M) theorems on capital structuring have‚ inarguably‚ laid down the foundations for modern corporate finance. There are several principles that underlie these theorems and two of these‚ which are most relevant to this paper‚ may‚ very simply‚ be
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JavaArray An array is a container object that holds a fixed number of values of a single type. The length of an array is established when the array is created. After creation‚ its length is fixed. You have seen an example of arrays already‚ in the main method of the "Hello World!" application. This section discusses arrays in greater detail. An array of 10 elements. Each item in an array is called an element‚ and each element is accessed by its numerical index. As shown in the preceding
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There have been reported quite a lot of cases in which muscle building programs have led to serious side effects‚ causing people who followed these programs to end up in the hospital with severe health problems. However one can not have problems only by following a normal muscle building program. That is if one follows the strict rules these programs imply. One of the most common side effects when trying to build muscle is overtraining. People don’t seem to understand that these programs are serious
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