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Home » Dimensions are 6 cm (width) and 12 cm (length). - Upplift

Dimensions are 6 cm (width) and 12 cm (length). - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Altitude to 9: $\frac{108}{9} = 12$

📌 The shortest altitude is $\boxed{7.2}$.

📌 Question: A micropaleontologist studies a microfossil shaped like a hemisphere with radius $3x$ and a spherical fossil with radius $x$. What is the ratio of their volumes?

📌 Solution: Volume of hemisphere: $\frac{2}{3}\pi (3x)^3 = \frac{2}{3}\pi \cdot 27x^3 = 18\pi x^3$.

📌 Volume of sphere: $\frac{4}{3}\pi x^3$.

📌 Ratio: $\frac{18\pi x^3}{\frac{4}{3}\pi x^3} = \frac{18}{\frac{4}{3}} = \frac{54}{4} = \frac{27}{2}$. $\boxed{\dfrac{27}{2}}$**Question:

📌 A hydrologist is studying the flow of groundwater and models the rate of flow through a porous medium using the equations \(y = 2x + 3\) and \(y = -x + 5\). Find the intersection point of these two lines.

📌 To find the intersection point of the lines \(y = 2x + 3\) and \(y = -x + 5\), we set the equations equal to each other:

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