gpt-oss-20.3b-specialized-math-pruned-moe-only-31-experts

<|channel|>analysis<|message|>Just solve linear equation.<|end|><|start|>assistant<|channel|>final<|message|>**Equation to solve**

\[
2x + 5 = 17
\]

---

### Step 1: Isolate the term with \(x\)

Subtract \(5\) from both sides of the equation to get the variable term alone on the left:

\[
\begin{aligned}
2x + 5 - 5 &= 17 - 5 \\
2x &= 12
\end{aligned}
\]

---

### Step 2: Solve for \(x\)

Divide both sides by the coefficient of \(x\), which is \(2\):

\[
\begin{aligned}
\frac{2x}{2} &= \frac{12}{2} \\
x &= 6
\end{aligned}
\]

---

### Step 3: Verify the solution

Plug \(x = 6\) back into the original equation:

\[
2(6) + 5 = 12 + 5 = 17
\]

The left‑hand side equals the right‑hand side, so the solution is correct.

---

\[
\boxed{x = 6}
\]<|return|>

<|channel|>analysis<|message|>Need explain theorem and usage.<|end|><|start|>assistant<|channel|>final<|message|>**Pythagorean Theorem**

> In a right‑angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides.

Mathematically:

\[
c^{2}=a^{2}+b^{2}
\]

where  
- \(c\) = length of the hypotenuse,  
- \(a\) and \(b\) = lengths of the two legs.

---

### How It’s Used

| Context | What you do | Example |
|---------|-------------|---------|
| **Finding a missing side** | Rearrange the formula to solve for the unknown side. | Triangle with legs 3 m and 4 m → \(c=\sqrt{3^{2}+4^{2}}=\sqrt{9+16}=5\) m. |
| **Checking if a triangle is right‑angled** | Verify if \(c^{2}=a^{2}+b^{2}\). | Triangle sides 5, 12, 13 → \(5^{2}+12^{2}=25+144=169=13^{2}\). |
| **Distance between two points** | Treat the coordinate differences as legs. | Points (2, 3) and (5, 11): Δx=3, Δy=8 → distance \(=\sqrt{3^{2}+8^{2}}=\sqrt{9+64}=√73\). |
| **Engineering & construction** | Design right‑angled structures, calculate beam lengths, etc. | Determining the length of a diagonal support in a rectangular frame. |
| **Computer graphics** | Compute pixel distances, collision detection, etc. | Finding the Euclidean distance between two vertices in a 2‑D or 3‑D space. |
| **Navigation & GPS** | Approximate straight‑line distances over small areas. | Estimating the shortest path between two geographic coordinates. |
| **Physics** | Resolve vectors into perpendicular components. | Decomposing a force into horizontal and vertical components. |

---

### Quick Tips

- **Always label the hypotenuse** as the side opposite the right angle; it’s the longest side.
- For **non‑right triangles**, use the Law of Cosines: \(c^{2}=a^{2}+b^{2}-2ab\cos

<|channel|>analysis<|message|>Need area πr^2 = π*49 = 49π ≈ 153.938.<|end|><|start|>assistant<|channel|>final<|message|>The area \(A\) of a circle is given by

\[
A = \pi r^{2}
\]

where \(r\) is the radius.

For a radius of \(7\) m:

\[
A = \pi (7\,\text{m})^{2}
  = \pi \times 49\,\text{m}^2
  = 49\pi \,\text{m}^2
\]

If you want a numerical value using \(\pi \approx 3.14159\):

\[
A \approx 49 \times 3.14159 \approx 153.938 \,\text{m}^2
\]

So the area is **\(49\pi\) square meters** (about **153.94 m²**).<|return|>