Refer to page 20 for solving a separable differential equation. Instructions: ⚫ Separate the variables explicitly. • Integrate both sides carefully, showing intermediate steps. • Simplify the final result and provide the explicit or implicit solution as required. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]

The winning time in the Olympic men's 500-meter speed skating race over the years 1924 to 2006 can be described by the following regression equation. winning time = 272.63 − 0.1184(year In 2010, the actual winning time for the gold medal was 34.91 seconds. Use the regression equation to predict the winning time (in seconds) for 2010. sec Compare the prediction to what actually happened. The actual 2010 winning time of 34.91 seconds is seconds slower than the prediction. (c) Explain what the slope of −0.1184 indicates in terms of how winning times change from one set of Olympic games to the next. Olympic games occur every 4 years. Winning times decrease, on average, by seconds from one set of Olympic games to the next. (d) Why should we not use this regression equation to predict the winning time for the men's 500-meter speed skating race in the 2080 Winter Olympics? The predicted winning time for the year 2080 is not possible.We would only be able to predict the winning time…

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The line of best fit through a set of data is ý = 14.714 – 3.985x According to this equation, what is the predicted value of the dependent variable when the independent variable has value 180? Round to 1 decimal place.