$Math Studyset Vaia Explanations$ Math

5 Edition

Applied Mathematics: For the Managerial, Life, and Social Sciences

Soo T. Tan

Chapter 12: Chapter 12

Problem 10

Next question

Let $g(u, v, w)=\left(u e^{v w}+v e^{w w}+w e^{u t}\right) /\left(u^{2}+v^{2}+w^{2}\right)$. Compute $g(1,2,3)$ and $g(3,2,1)$.

Short Answer

Expert verified

$g(1,2,3)=\frac{1\cdot e^{6} + 2\cdot e^{9} + 3\cdot e^{t}}{14}$ and $g(3,2,1)=\frac{3\cdot e^{2} + 2\cdot e^{1} + 1\cdot e^{3t}}{14}$.

See the step by step solution

Step by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Understanding the function g(u, v, w)

The function $g(u, v, w)$ is given as: $$g(u, v, w)=\frac{ue^{vw} + ve^{ww} + we^{ut}}{u^2+v^2+w^2}$$ Let's break down the expression. The numerator is the sum of three product terms containing exponentials, and the denominator is the sum of squares of $u$, $v$, and $w$.

Step 2: Compute g(1,2,3)

We are asked to find $g(1,2,3)$. That means substituting $u=1$, $v=2$, and $w=3$ in the function: $$g(1,2,3)=\frac{1\cdot e^{(2)(3)} + 2\cdot e^{(3)(3)} + 3\cdot e^{(1)(t)}}{1^2+2^2+3^2}$$ Now we will simplify the expression: 1. Calculate exponentials: $$g(1,2,3)=\frac{1\cdot e^{6} + 2\cdot e^{9} + 3\cdot e^{t}}{1^2+2^2+3^2}$$ 2. Simplify denominator: $$g(1,2,3)=\frac{1\cdot e^{6} + 2\cdot e^{9} + 3\cdot e^{t}}{1+4+9}$$ 3. Final simplification: $$g(1,2,3)=\frac{1\cdot e^{6} + 2\cdot e^{9} + 3\cdot e^{t}}{14}$$ So, $g(1,2,3)=\frac{1\cdot e^{6} + 2\cdot e^{9} + 3\cdot e^{t}}{14}$.

Step 3: Compute g(3,2,1)

Now, we are asked to find $g(3,2,1)$. That means substituting $u=3$, $v=2$, and $w=1$ in the function: $$g(3,2,1)=\frac{3\cdot e^{(2)(1)} + 2\cdot e^{(1)(1)} + 1\cdot e^{(3)(t)}}{3^2+2^2+1^2}$$ Now we will simplify the expression: 1. Calculate exponentials: $$g(3,2,1)=\frac{3\cdot e^{2} + 2\cdot e^{1} + 1\cdot e^{3t}}{3^2+2^2+1^2}$$ 2. Simplify denominator: $$g(3,2,1)=\frac{3\cdot e^{2} + 2\cdot e^{1} + 1\cdot e^{3t}}{9+4+1}$$ 3. Final simplification: $$g(3,2,1)=\frac{3\cdot e^{2} + 2\cdot e^{1} + 1\cdot e^{3t}}{14}$$ So, $g(3,2,1)=\frac{3\cdot e^{2} + 2\cdot e^{1} + 1\cdot e^{3t}}{14}$. To summarize our results: - $g(1,2,3)=\frac{1\cdot e^{6} + 2\cdot e^{9} + 3\cdot e^{t}}{14}$ - $g(3,2,1)=\frac{3\cdot e^{2} + 2\cdot e^{1} + 1\cdot e^{3t}}{14}$

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Recommended explanations on Math Textbooks

Find Study Materials for

Create Study Materials

Select your language

Chapter 12: Chapter 12

Let $g(u, v, w)=\left(u e^{v w}+v e^{w w}+w e^{u t}\right) /\left(u^{2}+v^{2}+w^{2}\right)$. Compute \(g(1,2,3)\) and \(g(3,2,1)\).

Short Answer

Step by step solution

Unlock all solutions

Step 1: Understanding the function g(u, v, w)

Step 2: Compute g(1,2,3)

Step 3: Compute g(3,2,1)

Access millions of textbook solutions in one place

Most popular questions from this chapter

More chapters from the book ‘Applied Mathematics: For the Managerial, Life, and Social Sciences’

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Statistics

Geometry

Pure Maths

Decision Maths

Mechanics Maths

Probability and Statistics