Math Problem Statement

rewrite relation as the function of C

Solution

The equation in the image is:

S2+T=3STyS^2 + T = 3S - T - y

To rewrite this relation as a function of CC, we need to interpret CC as one of the variables involved in the equation. Since CC isn't explicitly present, I'll assume that you want to express yy (or another variable if CC represents it) as a function of the other variables.

Let's solve the equation for yy (assuming y=Cy = C):

  1. First, let's simplify the equation by isolating yy: S2+T+T=3SyS^2 + T + T = 3S - y S2+2T=3SyS^2 + 2T = 3S - y

  2. Now, let's solve for yy: y=3SS22Ty = 3S - S^2 - 2T

So, the relation expressed as a function of yy (which we'll assume is the same as CC) is:

y=3SS22Ty = 3S - S^2 - 2T

This equation shows yy (or CC) as a function of SS and TT.

Would you like any further details or have any questions?

Here are 5 related questions:

  1. How would the equation change if yy was isolated on the other side?
  2. What would the graph of this function look like in terms of SS and TT?
  3. Can we express SS as a function of yy and TT?
  4. What are the conditions for this function to be linear?
  5. How does the function behave as SS and TT approach certain limits?

Tip: When rewriting equations, always keep track of the variables you're isolating to ensure that your function is expressed correctly.

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Math Problem Analysis

Mathematical Concepts

Equations
Functions

Formulas

Quadratic equation rearrangement

Theorems

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Suitable Grade Level

Grades 10-12