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Home » We will compute the terms of the sequence step-by-step using the recursive relation: - jntua results

We will compute the terms of the sequence step-by-step using the recursive relation: - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Amount after 3 years: \(1102.50 \times 1.05 = 1157.625\)

📌 A loan of $2000 is taken at an annual interest rate of 6% compounded monthly. Calculate the total amount to be paid after 2 years.

📌 Monthly interest rate: \(0.06/12 = 0.005\)

📌 Number of months: \(2 \times 12 = 24\)

📌 Total amount: \(2000 \times (1 + 0.005)^{24} = 2000 \times 1.12716 = 2254.32\)

📌 #### 2254.32

📌 A projectile is launched at an initial velocity of 50 m/s at an angle of 30° above the horizontal. Calculate the horizontal range of the projectile (assuming no air resistance and using \(g = 9.8 \, \text{m/s}^2\)).

📌 Horizontal velocity: \(50 \times \cos(30^\circ) = 50 \times \frac{\sqrt{3}}{2} \approx 43.3\) m/s

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The volume of the cylinder is $ V_{\text{cyl}} = \pi r^2 h = \pi r^2 (...
The total volume is:
V_{\text{total}} = V_{\text{hemisphere}} + V_{\text{cyl}} = \frac{2}{3...
Thus, the total volume is $ \boxed{\frac{8}{3} \pi r^3} $.
Question: A right triangle has legs of lengths $ 5 $ and $ 12 $. What...
Solution: The area of the triangle is:
A = \frac{1}{2} \cdot 5 \cdot 12 = 30
The hypotenuse is:
c = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13
Altitude to leg 5: $ h_5 = \frac{2A}{5} = \frac{60}{5} = 12 $

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