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Home » Multiply both sides by \( a \): - Appfinity Technologies

Multiply both sides by \( a \): - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 The ratio of the volume of the tetrahedron to the volume of the sphere is:

📌 \frac{V_{\text{tetrahedron}}}{V_{\text{sphere}}} = \frac{\frac{\sqrt{2}}{12} s^3}{\frac{\pi \sqrt{6}}{8} s^3} = \frac{\sqrt{2}}{12} \cdot \frac{8}{\pi \sqrt{6}} = \frac{2\sqrt{3}}{9\pi}

📌 Thus, the final answer is \(\boxed{\frac{2\sqrt{3}}{9\pi}}\).Question:

📌 A science journalist is writing an article and finds that two identical microscopes cost a total of \$120. What is the cost in dollars of five such microscopes?

📌 Let the cost of one microscope be \( x \). According to the problem, two microscopes cost \$120, so we can write the equation \( 2x = 120 \). To find the cost of one microscope, solve for \( x \) by dividing both sides by 2:

📌 x = \frac{120}{2} = 60

📌 Now, to find the cost of five microscopes, multiply the cost of one microscope by 5:

📌 5x = 5 \times 60 = 300

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\( \ln(81) = \ln(3^4) = 4\ln(3) \approx 4 \times 1.0986 = 4.3944 \)
< 0.2t \Rightarrow t > \frac{4.3944}{0.2} = 21.972
So the smallest integer \( t \
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