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Home » x = rac{6 \pm 2\sqrt3}6 = 1 \pm rac{\sqrt3}3 - ToelettAPP

x = rac{6 \pm 2\sqrt3}6 = 1 \pm rac{\sqrt3}3 - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \boxed{\dfrac{3}{5}}

📌 Question: A geneticist analyzes a protein structure shaped like a regular octahedron with edge length 4 nm. What is the surface area in square nanometers?

📌 Solution: A regular octahedron has 8 equilateral triangular faces. The area of one face is $\frac{\sqrt{3}}{4} \times 4^2 = 4\sqrt{3}$. Total surface area: $8 \times 4\sqrt{3} = 32\sqrt{3}$ nm².

📌 \boxed{32\sqrt{3}}Question: What is the largest possible number of identical research grants that can be awarded using 2025 and 1515 units of funding, ensuring no funds remain unallocated?

📌 Solution: To determine the largest number of identical grants, compute $\gcd(2025, 1515)$.

📌 Factorize:

📌 $2025 = 3^4 \times 5^2$

📌 $1515 = 3 \times 5 \times 101$

🔥 Popular Posts

Solution: Let $\mathbf{v} = \langle v_1, v_2, v_3 \rangle$. The cross...
\begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
v_1 & v_2 & v_3 \\
& 2 & 3 \\
\end{vmatrix} = \langle 2v_3 - 3v_2, 3v_1 - v_3, v_2 - 2v_1 \rangle =...
This yields the system:
2v_3 - 3v_2 = 4, \quad 3v_1 - v_3 = 5, \quad v_2 - 2v_1 = 6.
From the third equation, $v_2 = 6 + 2v_1$. Substituting into the first...
2v_3 - 3(6 + 2v_1) = 4 \implies 2v_3 - 18 - 6v_1 = 4 \implies 2v_3 = 2...

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