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📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 A museum curator is creating a virtual reality exhibit featuring a 19th-century telescope. The original lens has a diameter of 30 cm and is scaled up by a factor of 5 for display. What is the diameter of the scaled model in meters?

📌 Scaled diameter = 30 cm × 5 = 150 cm = 1.5 meters.

📌 A biomedical engineer is modeling drug release from an implantable capsule. If the capsule releases 0.4 mg of medication every hour and contains 96 mg total, how many days will the full dose last?

📌 Total hours = 96 mg ÷ 0.4 mg/hour = 240 hours.

📌 Total days = 240 hours ÷ 24 hours/day = 10 days.

📌 A science educator is demonstrating conservation of momentum. A 2 kg cart moving at 5 m/s collides and sticks to a stationary 3 kg cart. What is the final velocity of the combined carts?

📌 Total momentum before = 2 kg × 5 m/s = 10 kg·m/s.

📌 Total mass after = 2 kg + 3 kg = 5 kg.

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We apply the distributive property to expand the product:
2x(x^2 + 4xy - 5y^2) = 2x^3 + 8x^2y - 10xy^2
-3y(x^2 + 4xy - 5y^2) = -3x^2y - 12xy^2 + 15y^3
$2x^3$
$8x^2y - 3x^2y = 5x^2y$
$-10xy^2 - 12xy^2 = -22xy^2$
$15y^3$
So the expanded expression is:
2x^3 + 5x^2y - 22xy^2 + 15y^3
oxed{2x^3 + 5x^2y - 22xy^2 + 15y^3}

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