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Home » The volume \(V_\textsphere\) of a sphere with radius \(r\) is: - Carbonext

The volume \(V_\textsphere\) of a sphere with radius \(r\) is: - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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\( p(1)^2 + q(1) + r = 10 \implies p + q + r = 10 \)
\( p(2)^2 + q(2) + r = 18 \implies 4p + 2q + r = 18 \)
\( p(3)^2 + q(3) + r = 30 \implies 9p + 3q + r = 30 \)
System:
p + q + r &= 10 \quad \text{(1)}\\
4p + 2q + r &= 18 \quad \text{(2)}\\
9p + 3q + r &= 30 \quad \text{(3)}
Substitute \( p = 2 \) into (4):
3(2) + q = 8 \implies 6 + q = 8 \implies q = 2
Substitute \( p = 2 \), \( q = 2 \) into (1):

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To write a specific solution, choose \(a = -1\):
b = -rac{4(-1) + 5}{3} = -rac{-4 + 5}{3} = -rac{1}{3}
So one such vector is:
\mathbf{v} = egin{bmatrix} -1 \ -rac{1}{3} \end{bmatrix}
However, since the problem asks for *a* vector, the general solution i...
oxed{egin{bmatrix} -1 \ -rac{1}{3} \end{bmatrix}}
For a positive constant \(c\), a bioinformatician models cyclic gene e...
ho, heta, \phi)\), find the shape described by the equation \(
ho = c \cdot \sin(\phi)\).
We are given the equation in spherical coordinates:

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