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Home » Crush the Competition: Learn How to Build a Roblox Game in Minutes! - Londonproperty

Crush the Competition: Learn How to Build a Roblox Game in Minutes! - Londonproperty

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 Time from A to B is \( \frac{d}{60} \) hours, and return time is \( \frac{d}{90} \) hours.

📌 Total time: \( \frac{d}{60} + \frac{d}{90} = 5 \).

📌 Solve: \( \frac{3d + 2d}{180} = 5 \) gives \( 5d = 900 \), so \( d = 180 \) km.

📌 The sum of the first \( n \) terms of an arithmetic sequence is given by \( S_n = \frac{n}{2}(2a + (n-1)d) \). If the first term is 3 and the common difference is 2, find \( n \) such that \( S_n = 210 \).

📌 Substitute: \( 210 = \frac{n}{2}(2 \times 3 + (n-1) \times 2) = \frac{n}{2}(6 + 2n - 2) = \frac{n}{2}(2n + 4) \).

📌 Simplify: \( 210 = n(n + 2) \) → \( n^2 + 2n - 210 = 0 \).

📌 Solve quadratic: \( n = \frac{-2 \pm \sqrt{4 + 840}}{2} = \frac{-2 \pm 29.02}{2} \).

📌 Positive root: \( n = \frac{27.02}{2} \approx 13.51 \), so \( n = 14 \) (next whole number).

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d^2 = 16
d = 4
Thus, the shortest distance from the center to the path is $ \boxed{4}...
Question: A robotics engineer is designing a triangular linkage mechan...
Let the triangle have side lengths $ a = 7 $, $ b = 10 $, $ c = 13 $....
s = \frac{a + b + c}{2} = \frac{7 + 10 + 13}{2} = \frac{30}{2} = 15
Now, use Heron’s formula to find the area $ A $:
A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{15(15 - 7)(15 - 10)(15 - 13)...
A = \sqrt{15 \cdot 8 \cdot 10} = \sqrt{1200} = \sqrt{400 \cdot 3} = 20...
r = \frac{A}{s} = \frac{20\sqrt{3}}{15} = \frac{4\sqrt{3}}{3}

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