Start By Drawing A Diagram Of The Situation In Your Selectio

Start By Drawing A Diagram Of The Situation In Your Selected Word Prob

Start by drawing a diagram of the situation in your selected word problem. Clearly label which direction is north, south, east, and west in your diagram, and label the known sides and angles in your triangle. Then use the Law of Cosines or Law of Sines to solve the problem. A vehicle travels due west for 30 miles. Then it turns and goes 30 miles in the direction of S68°W. How far is it from the starting place? Can you take a look at this solution it wasn’t graded yet. My Professor want some on the drawing of the angle that you did. MATH 108 Fall 2016 Quiz 7 Problem 1. 3 pts. Evaluate the sum ∑ 2(‘›2 5 ‘›=1 ’ 2(‘›’ − 5 Problem 2. 5 pts. 2A. Find the explicit formula for the general term an of the sequence given below. That is, find the rule that will allow you to calculate each term directly, without a recursive formula. 2B. Use your general rule to find the 800th term of the sequence. $15.24, $14.82, $14.40, $13.98,… Problem 3. 4 pts. Write the sum using sigma notation: −2 9 + 4 8 − 6 7 + 8 6 – Problem 4. 6 pts. On Jan 1, 2015, there were 1000 deer living in a national park. On Jan 1, 2016 there were 10% more deer than the year before. On Jan 1 of each year, it is estimated that the deer population will be another 10% above the previous year’s count. A. Write the first 4 terms of the sequence of annual deer population counts. B. Find the general rule for the sequence of annual deer population counts. C. What is the deer population expected to be in Jan 1, 2030? Problem 5. 6 pts. Consider the sequence 144, 108, 81, 60.75, …. 5A. Find the formula for the general term an of the sequence. That is, find the rule that will allow you to calculate each term directly, without a recursive formula. 5B. Find the 14th term of the sequence. 5C. Find S∞, which is the sum of an infinite number of terms of the sequence. Problem 6. 6 pts. A book on each year’s Breakthroughs in Mathematics is published annually. The 2016 edition costs $22.00. Each year, the price will increase by $2.50 over the previous year’s price. A. Find the general rule for the sequence of the book prices. B. Determine what the price will be in 2040. C. If you buy a book each year from 2016 to 2040, how much will you have spent in total?

Paper For Above instruction

The problem presented involves analyzing a real-world scenario requiring the application of the Law of Cosines, a fundamental principle in trigonometry that relates the lengths of sides of a triangle to an angle between them. Augmenting this, the scenario requires the creation of an accurate diagram, complete with directional labels (north, south, east, west), known sides, and angles. This illustration serves as a vital visualization tool that assists in setting up the correct mathematical model for the problem.

The journey begins with a vehicle traveling due west for 30 miles. The next movement changes the direction toward S68°W, a bearing indicating the vehicle turns southward from west at an angle of 68°. First, a schematic diagram should be drawn with the initial position marked, pointing west for 30 miles, and then turning toward S68°W. It is essential to identify the points representing the start, turn, and final positions, as well as the angles at these points. The critical step involves labeling the interior angle between the two paths to apply the Law of Cosines.

In the diagram, a right triangle is constructed with the initial westward path as one side, and the second movement along S68°W, forming an interior angle with the initial path. The angle between the initial westward direction and the second path is 68°, but since the path is South of West, the actual interior angle at the vertex where the turn occurs is 112° (180° - 68°), a key concept in solving the problem. Accurate labeling ensures the correct application of the Law of Cosines:

c² = a² + b² - 2ab cos(C)

Where a and b are known sides (both 30 miles), and C is the included angle (112°). Substituting the known values allows calculating the distance from the starting point to the final position, which involves algebraic steps such as computing cosine of 112°, calculating products, and taking the square root of the resulting expression. This method ensures an exact measurement of the straight-line distance, fulfilling the problem's objective.

Adding the diagram to the work process clarifies the geometric relationship and demonstrates understanding of trigonometry principles. The labeled diagram not only visually supports the calculations but also aligns with the professor’s request for an annotated and well-structured visual aid. Properly representing the angles and directions in the diagram is crucial to developing a precise solution, emphasizing the importance of meticulous diagrammatic work in trigonometry problems.

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