Systems of Nonlinear Equations and Inequalities: Apply It 1

  • Solve equations with squared variables or other exponents using substitution and elimination
  • Graph curved inequalities and find where they overlap

Real-World Applications

Ready to tackle a real-world challenge using your math skills? Imagine you’re solving a practical problem that involves finding the dimensions or quantities for various objects under specific constraints. Let’s dive into how you can use nonlinear equations to find the solution!

You’re tasked with designing an inclusive community center that features a rectangular activity room and a circular meditation space. The center aims to be accessible and welcoming, providing a variety of activities and quiet spaces for reflection and relaxation.

  • The activity room needs to be large enough to host diverse group activities and should have an area of [latex]200[/latex] square meters.
  • The length of the activity room is [latex]5[/latex] meters more than its width.
  • The meditation space should have an area of [latex]50[/latex] square meters, providing a peaceful environment for mindfulness and relaxation.

Determine the optimal dimensions for these spaces while adhering to the stated requirements.