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Home » Difference: \( 20 - 12 = 8 \) - ClickBalance

Difference: \( 20 - 12 = 8 \) - ClickBalance

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Altitude to 12: $\frac{108}{12} = 9$

📌 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.

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x + y = \pm 10
Now compute \( x^2 - y^2 = (x - y)(x + y) \):
If \( x + y = 10 \), then \( x^2 - y^2 = 4 \cdot 10 = 40 \)
If \( x + y = -10 \), then \( x^2 - y^2 = 4 \cdot (-10) = -40 \)
But from \( x - y = 4 \) and \( x^2 + y^2 = 58 \), suppose \( x + y =...
Then solving \( x - y = 4 \), \( x + y = 10 \), add: \( 2x = 14 \Right...
Check: \( x^2 + y^2 = 49 + 9 = 58 \) â
Then \( x^2 - y^2 = 49 - 9 = 40 \)
If \( x + y = -10 \), then \( x = 2 \), \( y = -8 \), check \( x - y =...
e 4 \) â

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