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Home » Thus, the length is \( \sqrt169 = 13 \) meters. - Simpleprint

Thus, the length is \( \sqrt169 = 13 \) meters. - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Simplify by combining like terms:

📌 = 2\sin^2 x + 2\cos^2 x = 2(\sin^2 x + \cos^2 x)

📌 Using the Pythagorean identity \(\sin^2 x + \cos^2 x = 1\):

📌 = 2 \times 1 = 2

📌 Therefore, the maximum value is \(\boxed{2}\).

📌 Find the value of \(x\) such that the vectors \(\begin{pmatrix} \sin x \\ \cos x \end{pmatrix}\) and \(\begin{pmatrix} \cos x \\ -\sin x \end{pmatrix}\) are orthogonal.

📌 Two vectors are orthogonal if their dot product is zero. Let’s compute the dot product:

📌 \begin{pmatrix} \sin x \\ \cos x \end{pmatrix} \cdot \begin{pmatrix} \cos x \\ -\sin x \end{pmatrix} = \sin x \cos x + \cos x (-\sin x) = \sin x \cos x - \sin x \cos x = 0

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If \( x \) and \( y \) are positive numbers such that \( x + y = 10 \)...
Use the identity: \( x^2 + y^2 = (x + y)^2 - 2xy \)
Substitute \( x + y = 10 \) and \( xy = 21 \):
\( x^2 + y^2 = 10^2 - 2 \times 21 = 100 - 42 = 58 \)
A triangle has sides of length 7 cm, 24 cm, and 25 cm. Is it a right t...
Check if it satisfies the Pythagorean theorem:
\( 7^2 + 24^2 = 49 + 576 = 625 = 25^2 \)
Yes, it is a right triangle.
Area of a right triangle is \( \frac{1}{2} \times \text{base} \times \...
Take 7 cm and 24 cm as base and height:

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