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Home » Current total = \( 85 + 90 + 78 + 92 = 345 \). - Get link 4share

Current total = \( 85 + 90 + 78 + 92 = 345 \). - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Divide \( x^4 \) by \( x^2 \) to get \( x^2 \).

📌 Multiply and subtract:

📌 Multiply \( x^2 \) by \( x^2 + 1 \) to get \( x^4 + x^2 \).

📌 Subtract from the original polynomial:

📌 Repeat the process:

📌 Divide \( 2x^2 \) by \( x^2 \) to get \( 2 \).

📌 Multiply \( 2 \) by \( x^2 + 1 \) to get \( 2x^2 + 2 \).

📌 The remainder is \(-1\). Therefore, the remainder when \( x^4 + 3x^2 + 1 \) is divided by \( x^2 + 1 \) is \(\boxed{-1}\).

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Substitute $v_3$ into the second equation:
3v_1 - (11 + 3v_1) = 5 \implies -11 = 5, \text{ which is a contradicti...
However, the condition $\mathbf{v} \cdot \mathbf{a} = 0$ implies $v_1...
v_1 + 2(6 + 2v_1) + 3(11 + 3v_1) = 0 \implies v_1 + 12 + 4v_1 + 33 + 9...
Then $v_2 = 6 + 2(-\frac{45}{14}) = \frac{84 - 90}{14} = -\frac{6}{14}...
Thus, $\mathbf{v} = \left\langle -\frac{45}{14}, -\frac{3}{7}, \frac{1...
Verification: Cross product and dot product conditions are satisfied.
\boxed{\left\langle -\dfrac{45}{14}, -\dfrac{3}{7}, \dfrac{19}{14} \ri...
Question: In spherical coordinates, describe the surface defined by $\...
Solution: Convert to Cartesian coordinates using $\rho = \sqrt{x^2 + y...

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