### Transcription and ExplanationThis mathematical solution involves solving an equation for a variable, denoted as \( u \), by using an exponential expression. Below is a transcription and explanation.#### Given Equation:\[ 1.10 = 45 \left[ 1 (e^t)^{-0.33333} \right] - 15 \left[ 1 - 1 (e^t)^{-0.33333} \right]^{0.66666}\]#### Steps:1. **Substitution:** - Let \( e^t = u \).2. **Rewriting the Equation:** - Substitute \( u \) into the equation to get: \[ 1.10 = 45 \left[ u^{-0.33333} \right] - 15 \left[ 1 - u^{-0.33333} \right]^{0.66666} \]3. **Goal:** - Find the value of \( u \).4. **Solution Box:** - The solution gives: \[ u = 2158.54545 \] - Calculating \( t \) using the natural logarithm function: \[ t = \ln(2158.54545) \] - Resulting in: \[ t = 7.627 \]This transcription provides the step-by-step transformation and illustration of the calculus involved in finding \( u \) and further calculations to evaluate \( t \).

Given: 1.10=151-et-0.33333-151-et-0.33333·e0.66666 Let, et=u…

Answered: 0.666 66 - 033333 D.3335 1.40 O.666 b6…

Math

Algebra

0.666 66 - 033333 D.3335 1.40 O.666 b6 -0.33333 +0. 3'33 33 45 find u=? Ansaer: e=2158-so545

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Transcription and Explanation

This mathematical solution involves solving an equation for a variable, denoted as \( u \), by using an exponential expression. Below is a transcription and explanation.

#### Given Equation:
\[
1.10 = 45 \left[ 1 (e^t)^{-0.33333} \right] - 15 \left[ 1 - 1 (e^t)^{-0.33333} \right]^{0.66666}
\]

#### Steps:
1. **Substitution:**
- Let \( e^t = u \).

2. **Rewriting the Equation:**
- Substitute \( u \) into the equation to get:
\[
1.10 = 45 \left[ u^{-0.33333} \right] - 15 \left[ 1 - u^{-0.33333} \right]^{0.66666}
\]

3. **Goal:**
- Find the value of \( u \).

4. **Solution Box:**
- The solution gives:
\[
u = 2158.54545
\]
- Calculating \( t \) using the natural logarithm function:
\[
t = \ln(2158.54545)
\]
- Resulting in:
\[
t = 7.627
\]

This transcription provides the step-by-step transformation and illustration of the calculus involved in finding \( u \) and further calculations to evaluate \( t \).

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