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MATH / The intersection of the graphic solutions of all three inequalities listed below…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

The intersection of the graphic solutions of all three inequalities listed below form an enclosed region in the coordinate plane. What is the area of this region? Express your answer in terms of π\pi. \[ \left\{ \begin{array}{l} (x-4)^2+y^2\leq 16 \\ y \geq x-4 \\ y\geq -\frac{1}{3}x \end{array} \right. \]
Plain-text mathematical notation (without MathML)
The intersection of the graphic solutions of all three inequalities listed below form an enclosed region in the coordinate plane.  What is the area of this region?  Express your answer in terms of π. \[
\left\{
\begin{array}{l}
(x-4)^2+y^2\leq 16 \\
y \geq x-4 \\
y\geq -\frac{1}{3}x
\end{array}
\right.
\]
Original LaTeX notation
The intersection of the graphic solutions of all three inequalities listed below form an enclosed region in the coordinate plane.  What is the area of this region?  Express your answer in terms of $\pi$. \[
\left\{
\begin{array}{l}
(x-4)^2+y^2\leq 16 \\
y \geq x-4 \\
y\geq -\frac{1}{3}x
\end{array}
\right.
\]

level

Level 5

type

Geometry

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Source and history

task_id
9d7b64a1-d081-5c7b-a473-93970f5a8bff
task_key
geometry--test--9d7b64a1-d081-5c7b-a473-93970f5a8bff
task_revision_id
1
config / split
geometry / test

Official source

initial import