Use a variation model to solve for the unknown value. The body mass index (BMI) of an individual varies directly as the weight of the individual and inversely as the square of the height of the in- mass index for a 195-1b person who is 65 in. tall, js.32.45. Determine the BMI for an individual who is 68 in. tall and 131 lb. The BMI of an individual who is 68 in. tall and 131 lb is approximately (Round to 2 decimal places.)
Use a variation model to solve for the unknown value. The body mass index (BMI) of an individual varies directly as the weight of the individual and inversely as the square of the height of the in- mass index for a 195-1b person who is 65 in. tall, js.32.45. Determine the BMI for an individual who is 68 in. tall and 131 lb. The BMI of an individual who is 68 in. tall and 131 lb is approximately (Round to 2 decimal places.)
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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![**Variation Model to Determine Body Mass Index (BMI)**
**Introduction**
This educational exercise aims to teach how to utilize a variation model to solve for an unknown value, specifically the Body Mass Index (BMI) of an individual.
**Explanation:**
The Body Mass Index (BMI) of an individual varies directly as the weight of the individual and inversely as the square of the height of the individual. Given the BMI for a 195-lb person who is 65 inches tall is 32.45, the task is to determine the BMI for an individual who is 68 inches tall and weighs 131 lbs.
**Steps to Solve:**
1. **Identify the given information:**
- Height (h₁) = 65 inches
- Weight (w₁) = 195 lbs
- BMI₁ = 32.45
2. **Direct Variation**:
\[ \text{BMI} = \left( \frac{w}{h^2} \right) \cdot k \]
Where \( k \) is a constant proportionality.
For the given person:
\[ 32.45 = \left( \frac{195}{65^2} \right) \cdot k \]
3. **Solving for \( k \)**:
\[ k = \frac{32.45 \cdot 65^2}{195} \]
4. **Substitute the new values:**
- Height (h₂) = 68 inches
- Weight (w₂) = 131 lbs
So,
\[ \text{BMI}_2 = \left( \frac{131}{68^2} \right) \cdot k \]
5. **Round off the answer to 2 decimal places.**
**Calculate:**
- Using the given values:
\( k = \frac{32.45 \cdot 4225}{195} \approx 705.97 \)
- Calculate the new BMI with the height 68 inches and weight 131 lbs:
\[ \text{BMI} = \left( \frac{131}{68^2} \right) \cdot 705.97 \]
\[ \text{BMI} \approx \frac{131 \cdot 705.97}{4624} \]
\[ \text{BMI}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9a4113c-7e46-4999-90ad-a989e5f085c8%2F00ebd737-a09e-4bb6-b76d-2610ffdeec1e%2F07i0kln_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Variation Model to Determine Body Mass Index (BMI)**
**Introduction**
This educational exercise aims to teach how to utilize a variation model to solve for an unknown value, specifically the Body Mass Index (BMI) of an individual.
**Explanation:**
The Body Mass Index (BMI) of an individual varies directly as the weight of the individual and inversely as the square of the height of the individual. Given the BMI for a 195-lb person who is 65 inches tall is 32.45, the task is to determine the BMI for an individual who is 68 inches tall and weighs 131 lbs.
**Steps to Solve:**
1. **Identify the given information:**
- Height (h₁) = 65 inches
- Weight (w₁) = 195 lbs
- BMI₁ = 32.45
2. **Direct Variation**:
\[ \text{BMI} = \left( \frac{w}{h^2} \right) \cdot k \]
Where \( k \) is a constant proportionality.
For the given person:
\[ 32.45 = \left( \frac{195}{65^2} \right) \cdot k \]
3. **Solving for \( k \)**:
\[ k = \frac{32.45 \cdot 65^2}{195} \]
4. **Substitute the new values:**
- Height (h₂) = 68 inches
- Weight (w₂) = 131 lbs
So,
\[ \text{BMI}_2 = \left( \frac{131}{68^2} \right) \cdot k \]
5. **Round off the answer to 2 decimal places.**
**Calculate:**
- Using the given values:
\( k = \frac{32.45 \cdot 4225}{195} \approx 705.97 \)
- Calculate the new BMI with the height 68 inches and weight 131 lbs:
\[ \text{BMI} = \left( \frac{131}{68^2} \right) \cdot 705.97 \]
\[ \text{BMI} \approx \frac{131 \cdot 705.97}{4624} \]
\[ \text{BMI}
![**Problem Statement:**
Determine the Contextual Body Mass Index (BMI):
The BMI of an individual varies directly as the weight of the individual and inversely as the square of the height of the individual.
1. **Given Information:**
- The BMI of an individual who is 65 inches tall and weighs 131 pounds is 32.45.
2. **Question:**
- Determine the BMI for an individual who is 68 inches tall and weighs 131 pounds.
**Solution Approach:**
To solve for the unknown BMI value, we follow these steps:
1. **Direct Variation:**
- BMI = k * (Weight / Height²)
- Where k is a constant of proportionality.
2. **Find the Constant of Proportionality (k):**
- Given BMI = 32.45 for height = 65 inches and weight = 131 pounds.
- \( 32.45 = k \times \left(\frac{131}{65^2}\right) \)
3. **Calculate the Constant (k):**
- \( k = \frac{32.45 \times 65^2}{131} \)
4. **Determine the BMI for the New Height and Weight:**
- For height = 68 inches, weight = 131 pounds.
- Use the formula: BMI = k * (Weight / Height²)
5. **Substitute the Known Values:**
- Calculate the new BMI.
**Input Fields:**
- Provide the space to input the weight and height values to automatically compute the BMI.
**Answer Box:**
- The BMI for an individual who is 68 inches tall and 131 pounds is approximately: [Answer Box]
**Interactive Elements:**
- An input box for direct data entry.
- A refresh/recalculate button to reset the values.
**Note:**
A detailed understanding of the relationships between these variables is crucial for accurate health assessments and applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9a4113c-7e46-4999-90ad-a989e5f085c8%2F00ebd737-a09e-4bb6-b76d-2610ffdeec1e%2Fp09n1l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Determine the Contextual Body Mass Index (BMI):
The BMI of an individual varies directly as the weight of the individual and inversely as the square of the height of the individual.
1. **Given Information:**
- The BMI of an individual who is 65 inches tall and weighs 131 pounds is 32.45.
2. **Question:**
- Determine the BMI for an individual who is 68 inches tall and weighs 131 pounds.
**Solution Approach:**
To solve for the unknown BMI value, we follow these steps:
1. **Direct Variation:**
- BMI = k * (Weight / Height²)
- Where k is a constant of proportionality.
2. **Find the Constant of Proportionality (k):**
- Given BMI = 32.45 for height = 65 inches and weight = 131 pounds.
- \( 32.45 = k \times \left(\frac{131}{65^2}\right) \)
3. **Calculate the Constant (k):**
- \( k = \frac{32.45 \times 65^2}{131} \)
4. **Determine the BMI for the New Height and Weight:**
- For height = 68 inches, weight = 131 pounds.
- Use the formula: BMI = k * (Weight / Height²)
5. **Substitute the Known Values:**
- Calculate the new BMI.
**Input Fields:**
- Provide the space to input the weight and height values to automatically compute the BMI.
**Answer Box:**
- The BMI for an individual who is 68 inches tall and 131 pounds is approximately: [Answer Box]
**Interactive Elements:**
- An input box for direct data entry.
- A refresh/recalculate button to reset the values.
**Note:**
A detailed understanding of the relationships between these variables is crucial for accurate health assessments and applications.
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