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how to get rid of a headache in 2 minutes - AssociationVoting

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 Set to zero:

📌 No solution in reals — derivative never zero.

📌 But this suggests no critical point. However, for minimum, consider behavior.

📌 Wait — likely the model is \( C(x) = 5000 + 120x + 0.5x^2 \) for increasing marginal cost, but given is \( -0.5x^2 \), which causes average cost to eventually decrease — not realistic.

📌 But assuming the function is correct as stated, and the goal is to minimize \( P(x) = \frac{5000}{x} + 120 - 0.5x \), set:

📌 P'(x) = -\frac{5000}{x^2} - 0.5 = 0 \quad \text{has no solution}

📌 So no minimum — but this contradicts realistic models.

📌 Alternatively, perhaps the function is \( C(x) = 5000 + 120x - 0.5x^2 \), and we want to minimize **total cost**, not per unit. But the problem says "cost per unit."

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Finally, multiply by \(\pi\): \( 250 \pi pprox 785.398 \).
The volume of the tank is approximately 785.398 cubic meters.
#### 785.398
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\( 7^2 = 49 \) and \( 24^2 = 576 \), so \( 49 + 576 = 625 \).
Since both sides are equal, the triangle is a right triangle.
The sum of the first \( n \) positive integers is given by the formula...
Set up the equation: \( rac{n(n + 1)}{2} = 5050 \).
Multiply both sides by 2: \( n(n + 1) = 10100 \).
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