Calculating Distance and Function of a Horse on a Merry Go Round

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In summary, the conversation discusses a scenario involving a horse on a merry go round and a ticket booth outside of it. The function D(t) is given to describe the distance between the horse and ticket booth after t seconds. The conversation then poses four questions: a) the distance between the booth and nearest point on the merry go round, b) the diameter of the merry go round, c) the number of revolutions in two minutes, and d) the largest interval of time for which D(t) is invertible. The person being addressed is asked to show their attempted solution and where they are having trouble.
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CrossFit415
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Homework Statement


Imagine a horse located on the outer edge of a merry go round, and a ticket booth located outside the merry go round, as pictured below. The function D(t) describes the distance D (in feet) between the horse and the ticket booth t seconds after the merry go round starts;

D(t) = 40 - 15 cos (Pi (t) / 10)

a. How far is the ticket booth from the nearest point on the merry go round?

b. What is the diameter of the circular deck of the merry go round?

c. How many revolutions will the merry go round complete in two minutes?

d.) D is not an invertible function. However, give the largest interval of time containing t - 2 on which the function D(t) is invertible?
 
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  • #2
Hi CrossFit415! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 

1. What is a function?

A function is a mathematical concept that describes the relationship between two variables, where for every input there is a unique output. It can be thought of as a machine that takes in an input and produces an output.

2. How do you determine the distance between two points?

The distance between two points can be determined using the Pythagorean theorem, which states that the distance (d) is equal to the square root of the sum of the squares of the differences between the coordinates of the two points. This can also be calculated using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2).

3. What is the difference between distance and displacement?

Distance is a scalar quantity that measures the length of the path taken from one point to another, while displacement is a vector quantity that measures the shortest distance between the initial and final positions, taking into account the direction of motion.

4. How do you find the average rate of change of a function over a given interval?

The average rate of change of a function over a given interval can be calculated by finding the slope of the secant line between the two points on the graph corresponding to the interval. This can be found using the slope formula: m = (y2 - y1) / (x2 - x1).

5. What is the relationship between function and distance?

The relationship between function and distance depends on the specific context. In mathematics, a function can represent the distance traveled over time, while in physics, distance is often represented by a function that describes the motion of an object. In general, a function can be used to represent the relationship between any two quantities, including distance and another variable.

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