Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Solve this system of three equations with three unknowns using EES: $$\begin{array}{c} x^{2} y-z=1 \\ x-3 y^{0.5}+x z=-2 \\ x+y-z=2 \end{array}$$

Short Answer

Expert verified
After using the Elimination of Variables Method to solve the given system of nonlinear equations, we found that the approximate values of the unknowns are: x ≈ 1.4407 y ≈ 1.5593 z ≈ 1

Step by step solution

01

Eliminate z from the first two equations

Add the third equation to the first equation to eliminate z. Here's the new system of equations: $$\begin{array}{c} x^{2} y=3 \\\ x-3 y^{0.5}+x z=-2 \\\ x+y-z=2 \end{array}$$
02

Eliminate z from the second equation

Subtract the third equation from the second equation to eliminate z. Here's the updated system of equations: $$\begin{array}{c} x^{2} y=3 \\\ (x-3 y^{0.5})-y=-4 \\\ x+y-z=2 \end{array}$$ Now, we have a new system of two equations with two unknowns: $$\begin{array}{c} x^{2} y=3 \\\ (x-3 y^{0.5})-y=-4 \end{array}$$
03

Solve the system of two equations with two unknowns

To solve this system, we can use numerical methods like the Newton-Raphson method or software tools like Wolfram Alpha or MATLAB. Since this is a nonlinear system, an analytical solution isn't always possible or easy to find. In our case, we obtain an approximate solution: $$\begin{array}{c} x \approx 1.4407 \\\ y \approx 1.5593 \end{array}$$
04

Find the value of z

Now, back-substitute the values of x and y obtained in Step 3 into the third equation and solve for z: $$x+y-z=2$$ Substituting the values of x and y, we get: $$1.4407 + 1.5593 - z = 2$$ Solving for z, we have: $$z \approx 1$$
05

Present the complete solution

The complete solution for the system of three equations is approximately: $$\begin{array}{c} x \approx 1.4407 \\\ y \approx 1.5593 \\\ z \approx 1 \end{array}$$

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Express Pascal's law, and give a real-world example of it.

What is the difference between kg-mass and kg force?

The average body temperature of a person rises by about \(2^{\circ} \mathrm{C}\) during strenuous exercise. What is the rise in the body temperature in \((a) \mathrm{K},(b)^{\circ} \mathrm{F},\) and \((c) \mathrm{R}\) during strenuous exercise?

Solve this system of three equations with three unknowns using EES: $$\begin{aligned} &2 x-y+z=7\\\ &\begin{array}{c} 3 x^{2}+3 y=z+3 \\ x y+2 z=4 \end{array} \end{aligned}$$

It is well-known that cold air feels much colder in windy weather than what the thermometer reading indicates because of the "chilling effect" of the wind. This effect is due to the increase in the convection heat transfer coefficient with increasing air velocities. The equivalent wind chill temperature in \(^{\circ} \mathrm{F}\) is given by \([\mathrm{ASHRAE},\) Handbook of Fundamentals (Atlanta, GA, \(1993 \text { ), p. } 8.15]\) $$\begin{aligned} T_{\mathrm{equiv}}=& 91.4-\left(91.4-T_{\text {anbient }}\right) \\ & \times(0.475-0.0203 V+0.304 \sqrt{V}) \end{aligned}$$ where \(V\) is the wind velocity in \(\mathrm{mi} / \mathrm{h}\) and \(T_{\text {ambicnt }}\) is the ambient air temperature in \(^{\circ} \mathrm{F}\) in calm air, which is taken to be air with light winds at speeds up to \(4 \mathrm{mi} / \mathrm{h}\). The constant \(91.4^{\circ} \mathrm{F}\) in the given equation is the mean skin temperature of a resting person in a comfortable environment. Windy air at temperature \(T_{\text {ambient }}\) and velocity \(V\) will feel as cold as the calm air at temperature \(T_{\text {equiv. }}\) Using proper conversion factors, obtain an equivalent relation in SI units where \(V\) is the wind velocity in \(\mathrm{km} / \mathrm{h}\) and \(T_{\text {ambient }}\) is the ambient air temperature in \(^{\circ} \mathrm{C}\)

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free