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2nd gen cummins - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \( a = 3 \), \( r = 2 \), \( n = 6 \)

📌 \( a_n = ar^{n-1} = 3 \times 2^{5} = 3 \times 32 = 96 \)

📌 The volume of a sphere is given by \( V = \frac{4}{3} \pi r^3 \). What is the radius if the volume is \( 288\pi \) cubic units?

📌 \( \frac{4}{3} \pi r^3 = 288\pi \)

📌 \( r^3 = \frac{288 \times 3}{4} = 216 \)

📌 \( r = \sqrt[3]{216} = 6 \)

📌 A right circular cone has a base radius of 4 units and height of 9 units. What is the slant height?

📌 Use Pythagorean theorem:

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This gives two equations:
$ t - 8 = 4 $ → $ t = 12 $
$ t - 8 = -4 $ → $ t = 4 $
Both are integers, so there are 2 values.
Question: Two advanced polymer sensors cost a total of \$88. If the pr...
Solution: Original total cost for two sensors is \$88, so each sensor...
\frac{88}{2} = 44 \text{ dollars}
A 12.5% increase means the new price per sensor is:
+ 0.125 \times 44 = 44 + 5.5 = 49.5 \text{ dollars}
For six sensors:

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