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Home » Determine the maximum value of \((\sin x + \cos x)^2 + (\sin x - \cos x)^2\). - Dyverse

Determine the maximum value of \((\sin x + \cos x)^2 + (\sin x - \cos x)^2\). - Dyverse

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 This is \( 25 + 144 = c^2 \).

📌 Thus, \( c^2 = 169 \).

📌 Therefore, \( c = \sqrt{169} = 13 \).

📌 A rectangle's diagonal is 10 cm, and one side is 6 cm. What is the area of the rectangle?

📌 Let the sides be \( a = 6 \) and \( b \).

📌 Using the Pythagorean theorem: \( 6^2 + b^2 = 10^2 \).

📌 So, \( 36 + b^2 = 100 \).

📌 Subtract 36: \( b^2 = 64 \).

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#### 52.50
A cylindrical tank has a radius of 3 meters and a height of 10 meters....
The volume \( V \) of a cylinder is given by \( V = \pi r^2 h \).
Here, \( r = 3 \) meters and \( h = 10 \) meters.
So, \( V = \pi \times 3^2 \times 10 = 90\pi \) cubic meters.
Using \( \pi \approx 3.14159 \), the volume is approximately \( 90 \ti...
A solution is made by mixing 20% alcohol with 80% water. If 15 liters...
Let the total volume of the solution be \( x \) liters.
Since 20% of the solution is alcohol, \( 0.2x = 15 \) liters.
Solve for \( x \):

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