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Home » Thus, the cost of five microscopes is \(\boxed300\). - Midis

Thus, the cost of five microscopes is \(\boxed300\). - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Take natural logarithm of both sides:

📌 \ln(2) = 0.08t

📌 t = \frac{\ln(2)}{0.08} \approx \frac{0.6931}{0.08} \approx 8.66 \text{ years}

📌 A conical tank with height 12 meters and base radius 4 meters is being drained at a rate of 3 m³/min. How fast is the water level decreasing when the water is 6 meters deep?

📌 V = \frac{1}{3}\pi r^2 h

📌 By similar triangles, \( \frac{r}{h} = \frac{4}{12} = \frac{1}{3} \), so \( r = \frac{h}{3} \).

📌 Substitute into volume:

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Subtract (6) from (7):
Now subtract (8) from (9):
Substitute into (8):
6\left(-\frac{4}{3}\right) + b = \frac{9}{2} \Rightarrow -8 + b = \fra...
Now use (5):
7\left(-\frac{4}{3}\right) + 3\left(\frac{25}{2}\right) + c = -4 \Righ...
Find common denominator (6):
-\frac{56}{6} + \frac{225}{6} + c = -4 \Rightarrow \frac{169}{6} + c =...
a + b + c + d = 3 \Rightarrow -\frac{4}{3} + \frac{25}{2} - \frac{193}...
Common denominator 6:

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