The path traveled by a roller coaster is modeled by the equation `y=27sin13x+30` where y is measured in meters. What is the number of meters in the maximum altitude of the roller coaster?

Options

A. `13`
B. `27`
C. `30`
D. `57`

Answer

To find the maximum altitude of the roller coaster modeled by the equation \( y = 27 \sin(13x) + 30 \), we can follow these steps:

### Step 1: Identify the components of the equation
The equation is given as:
\[ y = 27 \sin(13x) + 30 \]
Here, \( 27 \) is the amplitude of the sine function, and \( 30 \) is a vertical shift.

### Step 2: Determine the maximum value of the sine function
The sine function, \( \sin(13x) \), varies between -1 and 1. Therefore, the maximum value of \( \sin(13x) \) is \( 1 \).

### Step 3: Substitute the maximum value into the equation
To find the maximum altitude, we substitute the maximum value of the sine function into the equation:
\[ y = 27 \cdot 1 + 30 \]

### Step 4: Calculate the maximum altitude
Now, calculate the value:
\[ y = 27 + 30 = 57 \]

### Step 5: State the maximum altitude
Thus, the maximum altitude of the roller coaster is:
\[ \text{Maximum altitude} = 57 \text{ meters} \]

### Summary
The maximum altitude of the roller coaster is \( 57 \) meters.

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