Please only answer Q64. Thank you! ### Problem 63. Seasonal Sales**Context:**The average number of guests visiting the Magic Kingdom at Walt Disney World per day is modeled by the function:\[ n(x) = 30,000 + 20,000 \sin\left( \frac{\pi}{2} (x + 1) \right) \]where $ n $ is the number of guests and $ x $ is the month. **Question:**If January corresponds to $ x = 1 $, how many people on average are visiting the Magic Kingdom per day in February?**Solution:**To find the average number of guests in February, we substitute $ x = 2 $ into the given function.\[ n(2) = 30,000 + 20,000 \sin\left( \frac{\pi}{2} (2 + 1) \right) \]\[ n(2) = 30,000 + 20,000 \sin\left( \frac{3\pi}{2} \right) \]Since $\sin\left( \frac{3\pi}{2} \right)$ is -1:\[ n(2) = 30,000 + 20,000 (-1) \]\[ n(2) = 30,000 - 20,000 \]\[ n(2) = 10,000 \]Thus, on average, 10,000 guests are visiting the Magic Kingdom per day in February.### Problem 64. Seasonal Sales**Question:**How many guests are visiting the Magic Kingdom in Exercise 63 in December?**Solution:**To find the number of guests in December, we note that December corresponds to $ x = 12 $. Substituting $ x = 12 $ into the function:\[ n(12) = 30,000 + 20,000 \sin\left( \frac{\pi}{2} (12 + 1) \right) \]\[ n(12) = 30,000 + 20,000 \sin\left( \frac{13\pi}{2} \right) \]Since $\sin\left( \frac{13\pi}{2} \right)$ is 1:\[ n(12) = 30,000 + 20,000 (1) \]\[ n(12

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Description: Please only answer Q64. Thank you! ### Problem 63. Seasonal Sales**Context:**The average number of guests visiting the Magic Kingdom at Walt Disney World per day is modeled by the function:\[ n(x) = 30,000 + 20,000 \sin\left( \frac{\pi}{2} (x + 1) \r

Use the following trigonometric formula, while solving this problem. Where, n is an integer .

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Seasonal Sales. The average number of guests visiting the Magic Kingdom at Walt Disney World per day is given by TT n(x) = 30,000 + 20,000 sin(x + 1) where n is the %3D number of guests and x is the month. If January corresponds to x = 1, how many people on average are visiting the Magic Kingdom per day in February? Seasonal Sales. How many guests are visiting the Magic Kingdom in Exercise 63 in December?

Seasonal Sales. The average number of guests visiting the Magic Kingdom at Walt Disney World per day is given by TT n(x) = 30,000 + 20,000 sin(x + 1) where n is the %3D number of guests and x is the month. If January corresponds to x = 1, how many people on average are visiting the Magic Kingdom per day in February? Seasonal Sales. How many guests are visiting the Magic Kingdom in Exercise 63 in December?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

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A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.

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Question

Please only answer Q64. Thank you!

### Problem 63. Seasonal Sales

**Context:**
The average number of guests visiting the Magic Kingdom at Walt Disney World per day is modeled by the function:
\[ n(x) = 30,000 + 20,000 \sin\left( \frac{\pi}{2} (x + 1) \right) \]
where $ n $ is the number of guests and $ x $ is the month.

**Question:**
If January corresponds to $ x = 1 $, how many people on average are visiting the Magic Kingdom per day in February?

**Solution:**
To find the average number of guests in February, we substitute $ x = 2 $ into the given function.

\[ n(2) = 30,000 + 20,000 \sin\left( \frac{\pi}{2} (2 + 1) \right) \]
\[ n(2) = 30,000 + 20,000 \sin\left( \frac{3\pi}{2} \right) \]

Since $\sin\left( \frac{3\pi}{2} \right)$ is -1:

\[ n(2) = 30,000 + 20,000 (-1) \]
\[ n(2) = 30,000 - 20,000 \]
\[ n(2) = 10,000 \]

Thus, on average, 10,000 guests are visiting the Magic Kingdom per day in February.

### Problem 64. Seasonal Sales

**Question:**
How many guests are visiting the Magic Kingdom in Exercise 63 in December?

**Solution:**
To find the number of guests in December, we note that December corresponds to $ x = 12 $. Substituting $ x = 12 $ into the function:

\[ n(12) = 30,000 + 20,000 \sin\left( \frac{\pi}{2} (12 + 1) \right) \]
\[ n(12) = 30,000 + 20,000 \sin\left( \frac{13\pi}{2} \right) \]

Since $\sin\left( \frac{13\pi}{2} \right)$ is 1:

\[ n(12) = 30,000 + 20,000 (1) \]
\[ n(12

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