To solve for \(x\) and \(y\) when \(t = 1\), using the given parametric equations:

1. \(y = 3t - t^2\)
2. \(x = 3t^2\)

Substitute \(t = 1\) into both equations:

### For \(y\):
\[
y = 3(1) - (1)^2 = 3 - 1 = 2
\]

### For \(x\):
\[
x = 3(1)^2 = 3(1) = 3
\]

Thus, at \(t = 1\), the values of \(x\) and \(y\) are:
\[
x = 3, \quad y = 2
\]

Would you like a more detailed explanation or have any questions?

Here are 5 related questions:
1. What are parametric equations, and how do they differ from standard equations?
2. How do you find the derivative of \(y = 3t - t^2\) with respect to \(t\)?
3. How would you graph the parametric curve defined by \(y = 3t - t^2\) and \(x = 3t^2\)?
4. What happens to \(x\) and \(y\) as \(t\) increases or decreases from 1?
5. How can you eliminate \(t\) to express \(y\) as a function of \(x\)?

**Tip**: Parametric equations are especially useful in describing the motion of objects, as both \(x\) and \(y\) depend on a third variable (often time, \(t\)).

Learn how to solve the parametric equations y = 3t - t^2 and x = 3t^2 at t = 1 with a detailed step-by-step solution. This problem introduces key concepts such as parametric equations, algebraic substitution, and how to compute values for specific parameters. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation