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Home » Thus, the area of the larger square is \(\boxed50\) square cm. - Databee Business Systems

Thus, the area of the larger square is \(\boxed50\) square cm. - Databee Business Systems

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 A circle has a circumference of 31.4 meters. What is the radius of the circle? (Use \( \pi \approx 3.14 \))

📌 Circumference \( C = 2\pi r \).

📌 \( r = \frac{31.4}{6.28} = 5 \).

📌 If \( \log_b(64) = 3 \), what is \( b \)?

📌 This implies \( b^3 = 64 \).

📌 Solving, \( b = \sqrt[3]{64} = 4 \).

📌 The function \( f(x) = x^3 - 6x^2 + 11x - 6 \) has roots \( r_1, r_2, r_3 \). Find \( r_1 + r_2 + r_3 \).

📌 By Vieta's formulas, \( r_1 + r_2 + r_3 = -\frac{-6}{1} = 6 \).

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< 5n^2 + 5
< 5n^2
< n^2
n > \sqrt{19} \approx 4.358
The smallest integer greater than 4.358 is \(n = 5\).
Check:
\[ S(4) = \frac{100}{16 + 1} = \frac{100}{17} \approx 5.882 > 5 \]
\[ S(5) = \frac{100}{25 + 1} = \frac{100}{26} \approx 3.846 < 5 \]
So, the sensitivity first drops below 5 at \(n = 5\).
\boxed{5}

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