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Home » \[ p = \frac2q + 83 \] - ECD Germany

\[ p = \frac2q + 83 \] - ECD Germany

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 The ratio of the volume of the propeller to the volume of the drone is:

📌 \text{Ratio} = \frac{V_{\text{propeller}}}{V_{\text{drone}}} = \frac{\frac{4}{3} \pi}{\frac{500}{3} \pi}

📌 Simplify the ratio:

📌 \text{Ratio} = \frac{4}{500} = \frac{1}{125}

📌 Thus, the ratio of the volumes is \(\boxed{\frac{1}{125}}\).

📌 An urban planner is designing a new park with a circular pond. The pond has a diameter of 20 meters. A circular walking path is to be constructed around the pond, with a uniform width of 3 meters. What is the circumference of the outer edge of the walking path?

📌 First, find the radius of the pond. Since the diameter is 20 meters, the radius \( r_{\text{pond}} \) is:

📌 r_{\text{pond}} = \frac{20}{2} = 10 \text{ meters}

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Solve for x: \( 3x^2 - 12x + 9 = 0 \).
The quadratic formula is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).
Here, \( a = 3 \), \( b = -12 \), \( c = 9 \).
Calculate the discriminant: \( b^2 - 4ac = (-12)^2 - 4 \times 3 \times...
So, \( x = \frac{12 \pm \sqrt{36}}{6} = \frac{12 \pm 6}{6} \).
This gives \( x = \frac{18}{6} = 3 \) and \( x = \frac{6}{6} = 1 \).
The formula for the sum is \( S = \frac{n(n+1)}{2} \).
Set \( \frac{n(n+1)}{2} = 210 \). Multiply through by 2: \( n(n+1) = 4...
Solve the quadratic equation: \( n^2 + n - 420 = 0 \).
Using the quadratic formula: \( n = \frac{-1 \pm \sqrt{1 + 4 \times 42...

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