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a_n = S_n - S_n-1 - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \[ N(t) = 250 \times 2^{18/3} \]

📌 \[ 18/3 = 6 \]

📌 Calculate \( 2^6 \):

📌 \[ 2^6 = 64 \]

📌 \[ N(t) = 250 \times 64 = 16,000 \]

📌 An immunologist is studying the effectiveness of a new cancer treatment that decreases tumor volume by 15% each week. If the initial tumor volume is 200 cubic centimeters, what will the volume be after 10 weeks? Use the formula \( V(t) = V_0 \times (1 - r)^t \). Calculate \( V(t) \).

📌 Initial volume, \( V_0 = 200 \) cm\(^3\)

📌 Weekly decrease rate, \( r = 15\% = 0.15 \)

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We want to compute \(\frac{A}{r^2}\):
\frac{A}{r^2} = \frac{A}{\left(\frac{A}{s}\right)^2} = \frac{A \cdot s...
Now express \(A\) and \(s\) in terms of \(c\). For a right triangle:
A = \frac{1}{2}ab, \quad \text{and} \quad a^2 + b^2 = c^2
Also, the semiperimeter is:
A = r(a + b + c - c) = r(a + b - c) + rc? \quad \text{(Not helpful dir...
Instead, recall a known formula for a right triangle:
Also, area \(A = r s\), so:
\frac{A}{r^2} = \frac{s}{r} = \frac{\frac{a + b + c}{2}}{\frac{a + b -...
Now, write in terms of \(c\). Use the identity:

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