Question

The path of a seat on a new Ferris wheel is modeled by: What is the maximum height a rider will experience?

Answer 1

B.  55 feet

For your question: "The path of a seat on a new Ferris wheel is modeled by: What is the maximum height a rider will experience?"

The answer is B. 55 feet.

I got this through working this on my own. Let me know if you have any other questions down below.

Answer 2

The path of a seat on a new Ferris wheel is modeled by the function. the maximum height a rider will experience is 55 feet.

How to obtain the maximum value of a function?

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

Putting those values of x in the second rate of function,

if results in negative output, then at that point, there is maxima.

If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.

The path of a seat on a new Ferris wheel is modeled by

$x = -25sin( \dfrac{ \pi} {30}t)\\\\y= -25cos( \dfrac{ \pi} {30}t)+ 30,$

To find its maximum, we will derivate this function and equalize it to 0.

$y'(t)= \dfrac{5}{6}\pi cos( \dfrac{ \pi} {30}t)\\\\y''(t)= \dfrac{1}{36}\pi^2 cos( \dfrac{ \pi} {30}t)$

Now given that we have an arbitrary critical point,

If   $y''(t) > 0$ then we will have a minimum at tn.

If  $y''(t) < 0$ then we will have a maximum at tn.

by replacing the equation with the critical points.

y(30) = 55

y(-30) = 55

We found out that the maximum height a rider will experience is 55 feet.

The answer is B. 55 feet.

Learn more about maxima and minima of a function here:

https://brainly.com/question/13333267

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