I need helpo with this. I need step by step solutions for this and I cant figure it out. Wire to be used in buildings and homes in the United States is standardized according to the AWGsystem (American Wire Gauge). Wires are assigned a gauge number according to their diameter.The scale ranges from gauge 0000 to gauge 36 in 39 steps. The equation for the wire gauge interms of the wire diameter in millimeters is the picture.(a) What is the equation for the diameter in millimeters in terms of the wire gauge N?(b) You have two wires, one that has five times the diameter of the other. By how much do thewire gauges differ for the two wires? (Give your answer to the nearest integer.) **Formula Explanation for Educational Purposes**The formula presented is:\[ N = 36 - 39 \log_{92} \left( \frac{d}{0.127 \, \text{mm}} \right) \]**Components of the Formula:**- **N**: Represents the variable or quantity being calculated. This could be a specific property or characteristic being assessed.- **36**: A constant value used in the calculation.- **39 log\(_{92}\)**: This expression represents the logarithm of a value to the base 92, multiplied by 39. Logarithms are often used to scale numbers in a nonlinear manner. - **\(d\)**: A variable representing some dimension or measurement in the same units as the constant divisor. It could be related to length, diameter, or some other measurable property.- **0.127 mm**: A constant reference point for the dimension \(d\), with units in millimeters, which serves as a scaling factor.**Purpose and Use:**This formula could be used in various scientific or engineering applications, such as calculating required dimensions, assessing materials, or scaling measurements to derive a certain property or characteristic. The base of the logarithm (92 in this case) and constants such as 36 and 39 suggest parameters specific to a particular field or formula derivation.**Implications:**Adjustments in the variable \(d\) will impact the outcome \(N\), showing sensitivity to this dimension relative to the reference point of 0.127 mm. The use of logarithms implies that changes in \(d\) might have exponential effects on \(N\).

A: To calculate the expression of diameter of the wire, simple the expression of gauge number using…

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Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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I need helpo with this. I need step by step solutions for this and I cant figure it out.

Wire to be used in buildings and homes in the United States is standardized according to the AWG
system (American Wire Gauge). Wires are assigned a gauge number according to their diameter.
The scale ranges from gauge 0000 to gauge 36 in 39 steps. The equation for the wire gauge in
terms of the wire diameter in millimeters is the picture.

(a) What is the equation for the diameter in millimeters in terms of the wire gauge N?
(b) You have two wires, one that has five times the diameter of the other. By how much do the
wire gauges differ for the two wires? (Give your answer to the nearest integer.)

**Formula Explanation for Educational Purposes**

The formula presented is:

\[ N = 36 - 39 \log_{92} \left( \frac{d}{0.127 \, \text{mm}} \right) \]

**Components of the Formula:**

- **N**: Represents the variable or quantity being calculated. This could be a specific property or characteristic being assessed.
- **36**: A constant value used in the calculation.
- **39 log\(_{92}\)**: This expression represents the logarithm of a value to the base 92, multiplied by 39. Logarithms are often used to scale numbers in a nonlinear manner.
- **\(d\)**: A variable representing some dimension or measurement in the same units as the constant divisor. It could be related to length, diameter, or some other measurable property.
- **0.127 mm**: A constant reference point for the dimension \(d\), with units in millimeters, which serves as a scaling factor.

**Purpose and Use:**

This formula could be used in various scientific or engineering applications, such as calculating required dimensions, assessing materials, or scaling measurements to derive a certain property or characteristic. The base of the logarithm (92 in this case) and constants such as 36 and 39 suggest parameters specific to a particular field or formula derivation.

**Implications:**

Adjustments in the variable \(d\) will impact the outcome \(N\), showing sensitivity to this dimension relative to the reference point of 0.127 mm. The use of logarithms implies that changes in \(d\) might have exponential effects on \(N\).

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