Megoldani a matematikai problémákat

Lépésről lépésre

1. \pi r^{2} = 50

   Start from the equation as given.

2. \pi r^{2} - 50 = 0

   Bring everything to one side and collect like terms so the right-hand side is 0.

3. a = \pi,\quad b = 0,\quad c = -50

   Read off the coefficients of the standard form ax² + bx + c = 0.

4. \Delta = b^2 - 4ac = (0)^2 - 4(\pi)(-50) = 200 \pi

   It does not factor nicely, so use the discriminant Δ = b² − 4ac.

5. r = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{0 \pm \sqrt{200 \pi}}{2 \pi}

   Δ > 0, so there are two distinct real roots. Substitute into the quadratic formula.

6. r = \frac{5 \sqrt{2}}{\sqrt{\pi}} \approx 3.9894 \quad\text{or}\quad r = - \frac{5 \sqrt{2}}{\sqrt{\pi}} \approx -3.9894

   Simplify each root.