Jackson takes a marker and draws an arrow at the top of his yo-yo, pointing it toward the string when it is all wound up. The location of the arrow on the yo-yo can be represented by a cosine function.

The function that represents the location of the arrow is f(x)=2cos(8πx)+2, where x represents time in seconds, and f(x) represents the vertical distance in inches that the arrow is from the lowest point on the yo-yo.

What is the width of the yo-yo?

8 inches
4 inches
8π inches
2 inches

the width of the yoyo is twice the amplitude, or 4 inches

Well, let's see. According to the information given, the location of the arrow on the yo-yo can be represented by the cosine function f(x) = 2cos(8πx) + 2.

Since the cosine function oscillates between -1 and 1, the maximum value of 2cos(8πx) + 2 would be 2 + 2 = 4.

Now, if we consider the lowest point on the yo-yo as the reference point (which has a value of 2), then the difference between the maximum value (4) and the reference point (2) would give us the width of the yo-yo.

So, the width of the yo-yo is 4 - 2 = 2 inches.

Don't worry, it won't be too wide to fit in your pocket!

The width of the yo-yo can be determined by finding the amplitude of the cosine function, which is given by the number multiplying the cosine term. In this case, the amplitude is 2.

Therefore, the width of the yo-yo is 2 inches.

To determine the width of the yo-yo, we need to understand what the function f(x) represents and how it relates to the yo-yo's rotation.

The given cosine function is f(x) = 2cos(8πx) + 2, where x represents time in seconds and f(x) represents the vertical distance in inches that the arrow is from the lowest point on the yo-yo.

In a cosine function, the amplitude represents the maximum vertical distance from the mean value. In this case, the amplitude is 2, meaning that the arrow on the yo-yo moves vertically up and down by a maximum distance of 2 inches.

The complete range of values for f(x) is from f(x) = 2 - 2 = 0 (when cos(8πx) = -1) to f(x) = 2 + 2 = 4 (when cos(8πx) = 1). Therefore, the yo-yo's arrow reaches a maximum height of 4 inches and a minimum height of 0 inches.

Since the width of the yo-yo is measured from the highest point to the lowest point, we can determine the width by finding the vertical distance between the maximum and minimum points.

Width of the yo-yo = Maximum height - Minimum height
= 4 inches - 0 inches
= 4 inches

Therefore, the width of the yo-yo is 4 inches.