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Home » |2\sin x + 3\cos x + 4| - AMAZONAWS

|2\sin x + 3\cos x + 4| - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 A car accelerates uniformly from rest to a speed of 30 m/s in 10 seconds. What is the acceleration of the car?

📌 Acceleration is defined as the change in velocity divided by the time taken:

📌 \[ a = \frac{v - u}{t} = \frac{30 \, \text{m/s} - 0 \, \text{m/s}}{10 \, \text{s}} = 3 \, \text{m/s}^2 \]

📌 A rectangle has a length that is 3 times its width. If the perimeter is 64 meters, what is the area of the rectangle?

📌 Let the width be \( w \). Then the length is \( 3w \). The perimeter is given by:

📌 The length is \( 3 \times 8 = 24 \, \text{m} \). The area is:

📌 \[ \text{Area} = w \times \text{length} = 8 \times 24 = 192 \, \text{m}^2 \]

📌 A projectile is launched with an initial velocity of 50 m/s at an angle of 30 degrees to the horizontal. What is the horizontal range of the projectile? (Assume no air resistance and \( g = 9.8 \, \text{m/s}^2 \))

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Average speed = \( \frac{500}{7.5} \approx 66.67 \) mph.
If \( \log_2(x) + \log_2(8) = 5 \), what is the value of \( x \)?
Use the property: \( \log_2(x) + \log_2(8) = \log_2(8x) \).
So, \( \log_2(8x) = 5 \).
Convert to exponential form: \( 8x = 2^5 \).
Calculate \( 2^5 = 32 \).
Solve for \( x \): \( 8x = 32 \) implies \( x = 4 \).
A mixture contains 20% alcohol and the rest water. If 10 liters of wat...
Original alcohol = \( 0.2 \times 30 = 6 \) liters.
Original water = 30 - 6 = 24 liters.

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