he level of water over time.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Understanding Sinusoidal Functions: Tsunami Example
A tsunami is approaching the San Francisco Bay! Here's a detailed breakdown of how the water level changes:
- The water first dips below its normal level.
- Then, it rises to a height equal to that below the normal level on the other side.
- Finally, it returns to its normal level after 20 seconds.
The key information we have:
- **Normal water depth:** 15 meters
- **Maximum water depth:** 26 meters
Let's write a sinusoidal function to represent the water level over time.
#### Step-by-Step Solution:
1. **Identify the amplitude:**
The amplitude (\(A\)) is the difference between the maximum and the midpoint (normal level) of the wave.
\[
A = 26 \, \text{meters} - 15 \, \text{meters} = 11 \, \text{meters}
\]
2. **Determine the period:**
The period (\(T\)) is the time it takes for the wave to complete one full cycle. Given that the water returns to its normal level after 20 seconds:
\[
T = 20 \, \text{seconds}
\]
3. **Calculate the frequency:**
The frequency (\(f\)) is the reciprocal of the period.
\[
f = \frac{1}{T} = \frac{1}{20 \, \text{seconds}}
\]
4. **Find the angular frequency:**
The angular frequency (\(\omega\)) is calculated using:
\[
\omega = \frac{2\pi}{T} = \frac{2\pi}{20 \, \text{seconds}} = \frac{\pi}{10} \, \text{radians per second}
\]
5. **Determine the vertical shift:**
The vertical shift (\(D\)) is the normal water level.
\[
D = 15 \, \text{meters}
\]
6. **Capture the phase shift:**
We can use either sine or cosine as our base function. If we use cosine, which starts at the maximum value, our function does not need a phase shift.
#### Final Sinusoidal Function:
Using cosine (since it starts at the maximum):
\[
y(t) = A \cdot \cos(\omega t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc89c18a2-afd8-4314-b625-35ad42cf4ebf%2F2effbce7-864c-42d5-b934-49e31ec58a8c%2Fjr43mbv_processed.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps with 4 images
