Material Selection HW

Homework 1 – Materials Selection You can utilize any software, such as Matlab or WolframAlpha, for generating the graphs. Calculate logarithms using base 10 for all values. Understand Linear and Logarithmic scales: 1. Define what a linear scale and a logarithmic scale are in your own words. [10 points] 2. Explain why logarithmic scales are used in various scientific and engineering contexts. [10 points] 3. Use the logarithmic properties to simplify the expression: log(8) + log (2). Also, calculate the base-10 logarithm of 1000. [10 points] 4. Inquire with ChatGPT about the purpose of taking the logarithm of an equation and then provide a concise summary of the insights gained from the explanation. [10 points] 5. Plot the line equations 𝑦 = 2𝑥 + 3, 𝑦 = 2𝑥 + 1, 𝑎𝑛𝑑 𝑦 = 2𝑥 on a linear scale graph. Any line can be graphed using two points. Select two 𝑥 values and plug them into the equation to find the corresponding 𝑦 values. What commonalities and distinctions can be identified among these equations for lines? Indicate the direction of movement or shift in the line equations based on the value of the constant in each equation. How do 𝑦 = 2𝑥 + 3 𝑎𝑛𝑑 𝑦 = 2𝑥 ! + 3 differ from each other? [10 points] 6. Plot the equation 𝑦 = 2𝑥 𝑎𝑛𝑑 𝑦 = 2𝑥 ! on a linear scale graph. How do 𝑦 = 2𝑥 𝑎𝑛𝑑 𝑦 = 2𝑥 ! differ from each other? [10 points] 7. Plot the equation 𝑦 = 2𝑥 ! using a logarithmic scale. Then, compare it with the graph you generated in question 6, which was on a linear scale. Describe the difference in the appearance of the two graphs. Explain why using a logarithmic scale might be advantageous when creating a graph. [10 points] 8. Use the Laws of Logarithms and take the log of both sides of the equation 𝑦 = 2𝑥 ! . Identify the slope and the y-intercept. Afterward, graph the equation using a linear scale and logarithmic scale. [10 points] 9. What is the difference between logarithmic scale and plotting logarithms? Just like in question 8, take the log of both sides of the equation 𝑦 = 2𝑥 ! and then plot logarithms. Share your insights on the scale. [10 points] Using Materials Selection Charts & Selection Lines: Please ensure that you demonstrate your problem-solving process comprehensively on the charts when responding to the questions. Failure to do so, even if your answer is correct, will result in a score of zero for that question. It is essential to consistently display your work on the charts, including drawing contour lines and clearly identifying your search area. Remember, points will only be awarded if you thoroughly show your work on the charts. ” $%& 10. Use the 𝐸 − 𝜌 chart to identify metals with both 𝐸 > 100 𝐺𝑃𝑎 𝑎𝑛𝑑 # > 0.02 ‘(⁄)! . Show your work on the chart. [10 points]

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