Math Problem Statement
Jawab kan
Solution
Let's go through the questions from the image one by one.
Question 21:
You are given a line equation and a series of matrix transformations. The first matrix transformation is:
2 & 1 \\ -1 & -2 \end{pmatrix}$$ This is followed by another transformation with the matrix: $$\begin{pmatrix} 1 & 0 \\ 1 & -2 \end{pmatrix}$$ You are asked to find the resulting equation after these transformations. **Steps**: 1. Rewrite the line equation in matrix form and apply each matrix transformation step by step. 2. After applying the matrices, convert the resulting points back to the line equation form. ### Question 22: You are asked to find the equation of the transformed circle after a series of matrix transformations. The original equation of the circle is: $$(x - 2)^2 + (y + 3)^2 = 25$$ It undergoes transformations by: $$\begin{pmatrix} 1 & 0 \\ 1 & 0 \end{pmatrix}$$ and then: $$\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$$ The task is to determine the equation of the resulting curve. ### Question 23: Given an exponential function $$y = 5^{-3x - 2}$$, you are asked to find the reflection of this function across the x-axis. ### Question 24: The function $$y = 3^{2x - 1}$$ is rotated 90° clockwise. You are required to find the resulting equation. ### Question 25: The curve $$y = x^2 + 3$$ undergoes dilation with respect to the point $$P(-1, 2)$$ by a factor of 3. Then, it is rotated $$\frac{\pi}{2}$$ radians around the origin. --- Let me know which specific question you'd like help solving in detail, and I can walk you through the steps!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix transformations
Linear equations
Circle equations
Exponential functions
Rotations
Dilation of curves
Formulas
y = mx + c for line equations
Circle equation: (x - h)^2 + (y - k)^2 = r^2
Exponential function reflection and rotation
Matrix transformation formula: A' = MA
Theorems
Transformation Theorem for Matrices
Exponential Function Reflection Theorem
Rotation Matrix Formula
Dilation Transformation Theorem
Suitable Grade Level
Grades 11-12
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