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Home » Thus, the area increases by \(\boxed13\sqrt3\) square centimeters. - Crosslake

Thus, the area increases by \(\boxed13\sqrt3\) square centimeters. - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: A science policy analyst is modeling the efficiency of a new energy policy using the expression

📌 Find the minimum value of this expression for $ x \in (0, \frac{\pi}{2}) $.

📌 We expand both terms:

📌 \sin^2 x + \cos^2 x + \sec^2 x + \csc^2 x + 2(\tan x + \cot x)

📌 Use identity $ \sin^2 x + \cos^2 x = 1 $, and:

📌 + (1 + \tan^2 x) + (1 + \cot^2 x) + 2(\tan x + \cot x) = 3 + \tan^2 x + \cot^2 x + 2(\tan x + \cot x)

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D) False — area is $ \frac{1}{2}ab $, and $ r s = r \cdot \frac{a+b+c}...
E) $ r s = \frac{ab}{2} $ — true
But best choice:
D) False — although $ r s = \frac{ab}{2} $, the statement area equals...
Best:
C) False — the identity $ A = r s $ is valid only if $ r $ is the inra...
Wait: $ A = r s $ is always true for inradius $ r $. So area is $ r s...
So the statement the area of the circle over the area of the triangle...
So correct claim is proven. Best choice:
A) True, by definition — correct.

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Substituting the values of \(a = 7\), \(b = 24\), \(c = 25\), we have:
A = \sqrt{28 \times (28-7) \times (28-24) \times (28-25)}
A = \sqrt{28 \times 21 \times 4 \times 3}
A = \sqrt{28 \times 252}
A = \sqrt{7056} = 84
Thus, the area of the triangle is \(\boxed{84}\).
Question:** A transportation engineer designs a roundabout with a circ...
Solution:** The area \(A\) of a circle is given by the formula:
A = \pi r^2
where \(r\) is the radius. Since the diameter is \(20\) units, the rad...

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