Question

Convert 27 ft / min into m / sec
Answer should be 0.1372
Use these conversions below to help in your conversion
1 foot = 12 inches
3 Foot = 1 yards
5,280 Ft = I mile
1 inch = 2.54 cm
1 Km = 0. 62 miles
1000mm = 1 m
100 cm = 1 m
10 mm = 1 cm
1 Km = 1000 m
60 Sec = 1 min
60 min= 1 hr
24 hr = 1 day
365 days = 1 year
1 days = 1 week
52 weeks = 1 year

Answer 1

I got 0.12192? Why didn’t I get 0.1372 M/S?

Answer 2

Does this format work for Advanced Dimensional Analysis? For algebra 2?

Answer 3

To convert 27 feet per minute (ft/min) to meters per second (m/sec), we will follow these conversion steps:

1. **Convert feet to meters**:
- We know that 1 foot = 30.48 cm (since 1 ft = 12 in and 1 in = 2.54 cm, thus 1 ft = 12 * 2.54 = 30.48 cm).
- Therefore, to convert feet to meters:
\[
1 \text{ ft} = 30.48 \text{ cm} = 0.3048 \text{ m}
\]
- So, 27 ft is:
\[
27 \text{ ft} = 27 \times 0.3048 \text{ m} = 8.2296 \text{ m}
\]

2. **Convert minutes to seconds**:
- We know that 1 minute = 60 seconds.

Now, we can convert 27 ft/min to m/sec:
\[
27 \text{ ft/min} = \frac{8.2296 \text{ m}}{60 \text{ sec}} \approx 0.1371 \text{ m/sec}
\]

However, if we round that to four decimal places, we have:
\[
\approx 0.1372 \text{ m/sec}
\]

Thus, \(27 \text{ ft/min} \approx 0.1372 \text{ m/sec}\).

Answer 4

Let's double-check the conversion step-by-step to clarify how to properly convert 27 feet per minute (ft/min) to meters per second (m/sec).

### Step 1: Convert Feet to Meters
1. **Feet to Meters Conversion**:
- We know that \(1 \text{ foot} = 0.3048 \text{ meters}\).
- So, for \(27 \text{ feet}\):
\[
27 \text{ ft} = 27 \times 0.3048 \text{ m} = 8.2296 \text{ m}
\]

### Step 2: Convert Minutes to Seconds
2. **Minutes to Seconds Conversion**:
- Since \(1 \text{ minute} = 60 \text{ seconds}\):

### Step 3: Convert Feet Per Minute to Meters Per Second
3. **Putting It Together**:
- Now, we need to convert 27 ft/min to m/sec.
- We found that \(27 \text{ ft} = 8.2296 \text{ m}\).
- Since this measurement is per minute, we divide by the number of seconds in a minute:
\[
\text{Velocity in m/sec} = \frac{8.2296 \text{ m}}{60 \text{ sec}} \approx 0.13716 \text{ m/sec}
\]

When rounded to four decimal places, this value is approximately **0.1372 m/sec**.

### Resolving Your 0.12192 Value
If you calculated 27 feet/min and got 0.12192 m/sec, it could be due to:
- An incorrect conversion factor for feet to meters.
- A calculation error in multiplying or dividing.

To confirm your calculation, ensure:
- You multiplied \(27\) by \(0.3048\) correctly.
- You then divided the resulting meters by \(60\) to convert from minutes to seconds.

Please double-check your calculations following these steps!

Answer 5

Yes, the format of conversion we used can be adapted for advanced dimensional analysis and is applicable in Algebra 2 contexts, especially when dealing with word problems that involve unit conversions. Here’s how you can structure the approach for dimensional analysis:

### Advanced Dimensional Analysis Format:

1. **Identify Given Units and Required Units**:
- Start with the units you have (in this case, feet per minute: ft/min).
- Identify the units you want to convert to (in this case, meters per second: m/sec).

2. **Set Up Conversion Factors**:
- Write down the relevant conversion factors:
- \(1 \text{ ft} = 0.3048 \text{ m}\)
- \(1 \text{ min} = 60 \text{ sec}\)

3. **Multiply by Conversion Factors**:
- Arrange the conversion factors so that the units cancel out, leading from the original unit to the desired unit:
\[
27 \text{ ft/min} \times \left(\frac{0.3048 \text{ m}}{1 \text{ ft}}\right) \times \left(\frac{1 \text{ min}}{60 \text{ sec}}\right)
\]
- Here, feet (ft) will cancel out and minutes (min) will cancel out as well.

4. **Perform the Calculations**:
- Combine the multiplications:
\[
= 27 \times 0.3048 \text{ m} \times \frac{1}{60} \text{ sec}^{-1}
\]
- Calculate:
\[
= \frac{8.2296 \text{ m}}{60 \text{ sec}} \approx 0.1372 \text{ m/sec}
\]

5. **Check Units**:
- Always make sure that your final unit matches the desired units.

### Application in Algebra 2:
- Dimensional analysis and unit conversions are often included in algebra, particularly in problems involving rates, conversions, and real-life applications of mathematics.
- It helps in solving word problems that may relate to physics or chemistry, where unit consistency is crucial.

By following this structured approach, students can enhance their understanding of dimensional analysis and improve their ability to handle conversions, which is a critical skill in higher mathematics and science courses. Overall, using this format is effective in teaching and applying dimensional analysis concepts in Algebra 2.