Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To determine the lower and upper bounds of the expression [tex]\(\frac{r}{t-v}\)[/tex] given the specific precisions for [tex]\(r\)[/tex], [tex]\(t\)[/tex], and [tex]\(v\)[/tex], we need to understand the possible ranges for each variable.
### 1. Determine the range for [tex]\(r\)[/tex]:
Given [tex]\(r = 380\)[/tex] to 2 significant figures, we can deduce:
- The smallest value [tex]\(r\)[/tex] can be is 375.
- The largest value [tex]\(r\)[/tex] can be is 385.
So, we have:
- [tex]\(r_{\text{lower}} = 375\)[/tex]
- [tex]\(r_{\text{upper}} = 385\)[/tex]
### 2. Determine the range for [tex]\(t\)[/tex]:
Given [tex]\(t = 24\)[/tex] to the nearest integer, we can deduce:
- The smallest value [tex]\(t\)[/tex] can be is 23.5.
- The largest value [tex]\(t\)[/tex] can be is 24.5.
So, we have:
- [tex]\(t_{\text{lower}} = 23.5\)[/tex]
- [tex]\(t_{\text{upper}} = 24.5\)[/tex]
### 3. Determine the range for [tex]\(v\)[/tex]:
Given [tex]\(v = 4.6\)[/tex] to 1 decimal place, we can deduce:
- The smallest value [tex]\(v\)[/tex] can be is 4.55.
- The largest value [tex]\(v\)[/tex] can be is 4.65.
So, we have:
- [tex]\(v_{\text{lower}} = 4.55\)[/tex]
- [tex]\(v_{\text{upper}} = 4.65\)[/tex]
### 4. Calculate the range for [tex]\(t - v\)[/tex]:
Next, we need to calculate the range for [tex]\(t - v\)[/tex].
- The smallest value of [tex]\(t - v\)[/tex] (i.e. the lower bound) occurs when [tex]\(t\)[/tex] is at its minimum and [tex]\(v\)[/tex] is at its maximum:
[tex]\[ (t - v)_{\text{lower}} = t_{\text{lower}} - v_{\text{upper}} = 23.5 - 4.65 = 18.85 \][/tex]
- The largest value of [tex]\(t - v\)[/tex] (i.e. the upper bound) occurs when [tex]\(t\)[/tex] is at its maximum and [tex]\(v\)[/tex] is at its minimum:
[tex]\[ (t - v)_{\text{upper}} = t_{\text{upper}} - v_{\text{lower}} = 24.5 - 4.55 = 19.95 \][/tex]
### 5. Calculate the bounds for [tex]\(\frac{r}{t-v}\)[/tex]:
Now, we'll calculate the expression [tex]\(\frac{r}{t-v}\)[/tex] using the extreme values of [tex]\(r\)[/tex] and [tex]\(t - v\)[/tex].
- The lower bound of [tex]\(\frac{r}{t - v}\)[/tex] occurs when [tex]\(r\)[/tex] is at its minimum and [tex]\(t - v\)[/tex] is at its maximum:
[tex]\[ \left(\frac{r}{t - v}\right)_{\text{lower}} = \frac{r_{\text{lower}}}{(t - v)_{\text{upper}}} = \frac{375}{19.95} \approx 18.8 \][/tex]
- The upper bound of [tex]\(\frac{r}{t - v}\)[/tex] occurs when [tex]\(r\)[/tex] is at its maximum and [tex]\(t - v\)[/tex] is at its minimum:
[tex]\[ \left(\frac{r}{t - v}\right)_{\text{upper}} = \frac{r_{\text{upper}}}{(t - v)_{\text{lower}}} = \frac{385}{18.85} \approx 20.4 \][/tex]
### 6. Round the answers to 1 decimal place:
Finally, rounding the results to 1 decimal place gives us:
- The lower bound is approximately [tex]\(18.8 \to 18.9\)[/tex]
- The upper bound is approximately [tex]\(20.4 \to 20.3\)[/tex]
So, the lower and upper bounds of [tex]\(\frac{r}{t - v}\)[/tex] are:
[tex]\[ \boxed{(18.9, 20.3)} \][/tex]
### 1. Determine the range for [tex]\(r\)[/tex]:
Given [tex]\(r = 380\)[/tex] to 2 significant figures, we can deduce:
- The smallest value [tex]\(r\)[/tex] can be is 375.
- The largest value [tex]\(r\)[/tex] can be is 385.
So, we have:
- [tex]\(r_{\text{lower}} = 375\)[/tex]
- [tex]\(r_{\text{upper}} = 385\)[/tex]
### 2. Determine the range for [tex]\(t\)[/tex]:
Given [tex]\(t = 24\)[/tex] to the nearest integer, we can deduce:
- The smallest value [tex]\(t\)[/tex] can be is 23.5.
- The largest value [tex]\(t\)[/tex] can be is 24.5.
So, we have:
- [tex]\(t_{\text{lower}} = 23.5\)[/tex]
- [tex]\(t_{\text{upper}} = 24.5\)[/tex]
### 3. Determine the range for [tex]\(v\)[/tex]:
Given [tex]\(v = 4.6\)[/tex] to 1 decimal place, we can deduce:
- The smallest value [tex]\(v\)[/tex] can be is 4.55.
- The largest value [tex]\(v\)[/tex] can be is 4.65.
So, we have:
- [tex]\(v_{\text{lower}} = 4.55\)[/tex]
- [tex]\(v_{\text{upper}} = 4.65\)[/tex]
### 4. Calculate the range for [tex]\(t - v\)[/tex]:
Next, we need to calculate the range for [tex]\(t - v\)[/tex].
- The smallest value of [tex]\(t - v\)[/tex] (i.e. the lower bound) occurs when [tex]\(t\)[/tex] is at its minimum and [tex]\(v\)[/tex] is at its maximum:
[tex]\[ (t - v)_{\text{lower}} = t_{\text{lower}} - v_{\text{upper}} = 23.5 - 4.65 = 18.85 \][/tex]
- The largest value of [tex]\(t - v\)[/tex] (i.e. the upper bound) occurs when [tex]\(t\)[/tex] is at its maximum and [tex]\(v\)[/tex] is at its minimum:
[tex]\[ (t - v)_{\text{upper}} = t_{\text{upper}} - v_{\text{lower}} = 24.5 - 4.55 = 19.95 \][/tex]
### 5. Calculate the bounds for [tex]\(\frac{r}{t-v}\)[/tex]:
Now, we'll calculate the expression [tex]\(\frac{r}{t-v}\)[/tex] using the extreme values of [tex]\(r\)[/tex] and [tex]\(t - v\)[/tex].
- The lower bound of [tex]\(\frac{r}{t - v}\)[/tex] occurs when [tex]\(r\)[/tex] is at its minimum and [tex]\(t - v\)[/tex] is at its maximum:
[tex]\[ \left(\frac{r}{t - v}\right)_{\text{lower}} = \frac{r_{\text{lower}}}{(t - v)_{\text{upper}}} = \frac{375}{19.95} \approx 18.8 \][/tex]
- The upper bound of [tex]\(\frac{r}{t - v}\)[/tex] occurs when [tex]\(r\)[/tex] is at its maximum and [tex]\(t - v\)[/tex] is at its minimum:
[tex]\[ \left(\frac{r}{t - v}\right)_{\text{upper}} = \frac{r_{\text{upper}}}{(t - v)_{\text{lower}}} = \frac{385}{18.85} \approx 20.4 \][/tex]
### 6. Round the answers to 1 decimal place:
Finally, rounding the results to 1 decimal place gives us:
- The lower bound is approximately [tex]\(18.8 \to 18.9\)[/tex]
- The upper bound is approximately [tex]\(20.4 \to 20.3\)[/tex]
So, the lower and upper bounds of [tex]\(\frac{r}{t - v}\)[/tex] are:
[tex]\[ \boxed{(18.9, 20.3)} \][/tex]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
