0.75 -0.7421 = 0.7707-0.7421 0.85-0-8 2= z = 0.8144 . (z - 0.8)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
How did you put these in the calculator to get the answers. I keep trying and I keep getting different numbers.
![The equation presented is:
\[
0.75 - 0.7421 = \frac{0.7707 - 0.7421}{0.85 - 0.8} \cdot (z - 0.8)
\]
Followed by the solution:
\[
z = 0.8144
\]
### Explanation:
This equation involves solving for \( z \) using a form of interpolation. Here's a step-by-step breakdown:
1. **Initial Equation:**
- The left side of the equation calculates the difference between 0.75 and 0.7421.
- The right side involves dividing the difference between 0.7707 and 0.7421 by the difference between 0.85 and 0.8, then multiplying the result by \( (z - 0.8) \).
2. **Solving for \( z \):**
- You equate both sides and solve for \( z \) to find that \( z = 0.8144 \).
This technique is often used in linear interpolation problems, which predict or estimate unknown values by using known data points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F070e8b65-931e-44e7-bfb4-6d69e5ced655%2F43bd5316-83a6-4b52-bd38-531577e34483%2F8k5zgq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The equation presented is:
\[
0.75 - 0.7421 = \frac{0.7707 - 0.7421}{0.85 - 0.8} \cdot (z - 0.8)
\]
Followed by the solution:
\[
z = 0.8144
\]
### Explanation:
This equation involves solving for \( z \) using a form of interpolation. Here's a step-by-step breakdown:
1. **Initial Equation:**
- The left side of the equation calculates the difference between 0.75 and 0.7421.
- The right side involves dividing the difference between 0.7707 and 0.7421 by the difference between 0.85 and 0.8, then multiplying the result by \( (z - 0.8) \).
2. **Solving for \( z \):**
- You equate both sides and solve for \( z \) to find that \( z = 0.8144 \).
This technique is often used in linear interpolation problems, which predict or estimate unknown values by using known data points.
![The given text involves a mathematical expression, specifically a calculation involving an exponential function. Here's the transcription for educational purposes:
1. The expression starts with an equation:
\[
= 0.23 \cdot \exp\left(\frac{-32900}{1.987 \cdot (273 + 1100)}\right)
\]
- The equation contains an exponential function, denoted as \(\exp\), which is the base of natural logarithms, \(e\), raised to a power.
- The numerator inside the exponential is \(-32900\).
- The denominator contains two parts: a constant \(1.987\) and a sum in the parentheses \((273 + 1100)\).
2. The second part of the text shows the evaluated result of the calculation:
\[
= 1.33 \cdot 10^{-6} \, \text{cm}^2/\text{s}
\]
- This indicates a final result expressed in scientific notation.
- The unit for the result is \(\text{cm}^2/\text{s}\), which could be a measure of diffusion or area change per unit time, typically used in physics or chemistry contexts.
There are no graphs or diagrams in the image, just mathematical expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F070e8b65-931e-44e7-bfb4-6d69e5ced655%2F43bd5316-83a6-4b52-bd38-531577e34483%2F0epn44r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The given text involves a mathematical expression, specifically a calculation involving an exponential function. Here's the transcription for educational purposes:
1. The expression starts with an equation:
\[
= 0.23 \cdot \exp\left(\frac{-32900}{1.987 \cdot (273 + 1100)}\right)
\]
- The equation contains an exponential function, denoted as \(\exp\), which is the base of natural logarithms, \(e\), raised to a power.
- The numerator inside the exponential is \(-32900\).
- The denominator contains two parts: a constant \(1.987\) and a sum in the parentheses \((273 + 1100)\).
2. The second part of the text shows the evaluated result of the calculation:
\[
= 1.33 \cdot 10^{-6} \, \text{cm}^2/\text{s}
\]
- This indicates a final result expressed in scientific notation.
- The unit for the result is \(\text{cm}^2/\text{s}\), which could be a measure of diffusion or area change per unit time, typically used in physics or chemistry contexts.
There are no graphs or diagrams in the image, just mathematical expressions.
Expert Solution
Step 1: Introduction
given equation to find the values
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Solved in 3 steps with 2 images
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