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Home » Calculate the determinant: - Red Crowns

Calculate the determinant: - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 A mixture contains 20% alcohol and the rest water. If 10 liters of water are added to 30 liters of this mixture, what is the new percentage of alcohol?

📌 Original alcohol = \( 0.2 \times 30 = 6 \) liters.

📌 Original water = 30 - 6 = 24 liters.

📌 After adding 10 liters of water, total water = 24 + 10 = 34 liters.

📌 Total new mixture = 30 + 10 = 40 liters.

📌 New percentage of alcohol = \( \frac{6}{40} \times 100 = 15\% \).

📌 A right triangle has legs of length 9 cm and 12 cm. What is the length of the hypotenuse?

📌 Use the Pythagorean theorem: \( c^2 = a^2 + b^2 \).

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\mathbf{v} imes \mathbf{a} = egin{vmatrix}
\end{vmatrix} = \mathbf{i}(y \cdot 3 - z \cdot 2) - \mathbf{j}(x \cdot...
= egin{pmatrix} 3y - 2z \ - (3x - z) \ 2x - y \end{pmatrix} = egin{p...
Set equal to \(egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}\):
3y - 2z = 0 \
-3x + z = 0 \
2x - y = 5
From second equation: \(z = 3x\)
From first: \(3y = 2z = 2(3x) = 6x \Rightarrow y = 2x\)
Substitute into third:

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