After a diver jumps off a diving board, the edge of the board oscillates with position given by s(t) = −5cos(t) cm at t seconds after the jump. Part I: Complete the following steps: Using the GeoGebra tool in Canvas, sketch one period of the position function for t ≥ 0. Find the velocity function. Using the GeoGebra tool in Canvas, sketch one period of the velocity function for t ≥ 0. Determine the times in the first period (or a single perio
After a diver jumps off a diving board, the edge of the board oscillates with position given by s(t) = −5cos(t) cm at t seconds after the jump. Part I: Complete the following steps: Using the GeoGebra tool in Canvas, sketch one period of the position function for t ≥ 0. Find the velocity function. Using the GeoGebra tool in Canvas, sketch one period of the velocity function for t ≥ 0. Determine the times in the first period (or a single perio
After a diver jumps off a diving board, the edge of the board oscillates with position given by s(t) = −5cos(t) cm at t seconds after the jump. Part I: Complete the following steps: Using the GeoGebra tool in Canvas, sketch one period of the position function for t ≥ 0. Find the velocity function. Using the GeoGebra tool in Canvas, sketch one period of the velocity function for t ≥ 0. Determine the times in the first period (or a single perio
After a diver jumps off a diving board, the edge of the board oscillates with position given by s(t) = −5cos(t) cm at t seconds after the jump.
Part I: Complete the following steps:
Using the GeoGebra tool in Canvas, sketch one period of the position function for t ≥ 0.
Find the velocity function.
Using the GeoGebra tool in Canvas, sketch one period of the velocity function for t ≥ 0.
Determine the times in the first period (or a single period) when the velocity is 0.
Find the acceleration function.
Using the GeoGebra tool in Canvas, sketch one period of the acceleration function for t ≥ 0.
Save your GeoGebra work as a .pdf file for submission.
Part II: Based on your work in Part I, discuss the following:
Discuss any observations you can make about the relationships between the graphs of the position, velocity, and acceleration functions. In particular, make sure to include the following:
The connections between critical points on each graph.
The similarities and differences among the characteristics of the three graphs (i.e. amplitude, midline, and period).
How fast is the edge of the board moving after 2 seconds?
Based on your graph, over what intervals is the edge of the diving board moving upward?
Discuss how your answers to Part I would be affected if:
The sign of the coefficient of cos(t) were opposite.
The coefficient of cos(t) were double.
Provide at least two other real-world situations that serve as applications to this concept and respond to the following:
What common characteristics do the real-world scenarios you chose share?
What did you look for in the way that the real-world scenario can be modeled?
Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.
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