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Home » Find the smallest and largest such \( n \) in range: - Abu Waleed Tea

Find the smallest and largest such \( n \) in range: - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 v_y^2 = 2gh \Rightarrow h = \frac{v_y^2}{2g} = \frac{15^2}{2 \cdot 9.8} = \frac{225}{19.6} \approx 11.48 \, \text{m}

📌 #### 11.48

📌 A STEM student is modeling bacterial growth with the function \(N(t) = 500 \cdot e^{0.4t}\), where \(N\) is the number of bacteria after \(t\) hours. How many bacteria are present after 5 hours? Round to the nearest whole number.

📌 N(5) = 500 \cdot e^{0.4 \cdot 5} = 500 \cdot e^{2} \approx 500 \cdot 7.389 = 3694.5

📌 Round to nearest whole number: 3695

📌 Elena, a science administrator, is evaluating a climate study requesting $850,000. If 40% is allocated to data collection, 35% to modeling, and the rest to fieldwork, and fieldwork costs rise by 20%, how much more funding must be allocated to maintain the original fieldwork budget?

📌 Data collection: \(0.40 \times 850,000 = 340,000\)

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#### 0.75
A projectile is launched with an initial velocity of 50 m/s at an angl...
Use the formula: \(h = \frac{(v^2 \sin^2 \theta)}{2g}\).
Here, \(v = 50\), \(\theta = 30^\circ\), \(g = 9.8\).
\(\sin 30^\circ = 0.5\), so \(h = \frac{(50^2 \times 0.5^2)}{2 \times...
#### 31.89
Solve the system of equations: \(2x + 3y = 7\) and \(4x - y = 5\).
Solve the second equation for \(y\): \(y = 4x - 5\).
Substitute into the first equation: \(2x + 3(4x - 5) = 7\).
Simplify: \(2x + 12x - 15 = 7\), \(14x = 22\), \(x = \frac{22}{14} = \...

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