gpt-oss-19.7b-specialized-math-pruned-moe-only-30-experts

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

\[
2x + 5 = 17
\]

---

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

Subtract \(5\) from both sides of the equation to get the \(x\)-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 of a right triangle. | Points (2, 3) and (5, 11): Δx=3, Δy=8 → distance \(=\sqrt{3^{2}+8^{2}}=\sqrt{9+64}= \sqrt{73}\). |
| **Engineering & construction** | Design right‑angled structures, calculate diagonal supports, etc. | Roof truss with side lengths 6 m and 8 m → diagonal \(=10\) m. |
| **Computer graphics** | Compute pixel distances, collision detection, etc. | Pixel at (x1, y1) to (x2, y2) → Euclidean distance. |
| **Navigation & surveying** | Determine straight‑line distances over a grid. | Surveyor measures 30 m east and 40 m north → straight‑line distance \(=50\) m. |
| **Physics** | Resolve vector components, calculate resultant forces. | Force components 3 N and 4 N → resultant \(=5\) N. |

---

### Quick “Rule of Three” Check

If the

<|channel|>analysis<|message|>Compute area πr^2 = π*49 ≈ 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:

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

Using \(\pi \approx 3.14159\):

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

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