Question
8. High tide occurred 4 hours after midnight. The formula for the displacement is \( 4 \equiv \frac{\pi}{b} \), Use \( b \) and solve for \( c_{1} \)
Ask by Ball Summers. in Jordan
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To find \( c_1 \), first solve \( b = \frac{\pi}{4} \). Then, use the displacement formula to determine \( c_1 \) based on the given information.
Solution
To solve the problem, we need to extract the known conditions and understand the formula provided.
1. **Extract Known Conditions:**
- High tide occurs 4 hours after midnight.
- The formula given is \( 4 \equiv \frac{\pi}{b} \).
2. **Solve Step by Step:**
- First, we need to solve for \( b \) from the equation \( 4 = \frac{\pi}{b} \).
- Rearranging the equation gives us:
\[
b = \frac{\pi}{4}
\]
3. **Next, we need to find \( c_1 \).** However, the problem does not provide a direct relationship or formula for \( c_1 \). If \( c_1 \) is related to \( b \) or the displacement formula, we need that information to proceed.
Assuming \( c_1 \) is a constant related to the displacement function, we can express it in terms of \( b \) if we have a specific formula for displacement.
If you have additional information or a specific formula for displacement that includes \( c_1 \), please provide it so we can continue solving for \( c_1 \).
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Simplify this solution The Deep Dive
To find \( b \), we start from the equation \( 4 = \frac{\pi}{b} \). By rearranging it, we get \( b = \frac{\pi}{4} \). Now, if we assume \( c_{1} \) relates to the wave's cycle or amplitude, we can plug \( b \) into a standard displacement formula for a periodic function, such as \( A \sin(kx - c_{1}) \), where \( k = \frac{2\pi}{b} \). Using \( b = \frac{\pi}{4} \), we have \( k = \frac{2\pi}{\frac{\pi}{4}} = 8 \). If you want to solve for a specific value of \( c_{1} \), you may need additional context about its role in the sine function, such as specific time intervals or initial conditions related to the tides.
