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Home » So \( x = 1 \) and \( x = 3 \) are critical points. - jntua results

So \( x = 1 \) and \( x = 3 \) are critical points. - jntua results

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Thus, the sequence has first term \( a_1 = 3^1 - 1 = 2 \) and common ratio \( r = 3 \).

📌 The nth term of a geometric sequence is \( a_n = a \cdot r^{n-1} = 2 \cdot 3^{n-1} \).

📌 So, the 5th term is \( a_5 = 2 \cdot 3^{4} = 2 \cdot 81 = 162 \).

📌 A committee of 4 people is to be chosen from 6 men and 5 women. What is the probability that the committee includes at least 2 women?

📌 Total ways to choose 4 from 11: \( \binom{11}{4} = 330 \).

📌 Favorable outcomes: committees with at least 2 women = (2W,2M) + (3W,1M) + (4W,0M).

📌 Total favorable = 150 + 60 + 5 = 215.

📌 Probability = \( \frac{215}{330} = \frac{43}{66} \).

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Overall percentage = (11,400 / 54,000) × 100 = <<(11400/54000)*100=21....
A geographer uses satellite imagery to monitor coastal erosion over th...
Assume the sequence of annual retreats is quadratic: aₙ = an² + bn + c
a₁ = 1.2 → a(1)² + b(1) + c = a + b + c = 1.2
a₂ = 1.8 → 4a + 2b + c = 1.8
a₃ = 2.5 → 9a + 3b + c = 2.5
Subtract first from second: (4a + 2b + c) − (a + b + c) = 1.8 − 1.2 →...
Subtract second from third: (9a + 3b + c) − (4a + 2b + c) = 2.5 − 1.8...
Now subtract: (5a + b) − (3a + b) = 0.7 − 0.6 → 2a = 0.1 → a = 0.05
Then 3(0.05) + b = 0.6 → 0.15 + b = 0.6 → b = 0.45

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