DMCA
Contact
Privacy Policy

Home » The sum of the first \(n\) positive integers is 5050. Find \(n\). - Abbey Badges

The sum of the first \(n\) positive integers is 5050. Find \(n\). - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

Content is being prepared. Please check back later.

📚 You May Also Like These Articles

📌 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."

📌 Reinterpreting: "cost per unit" is standard, and we must minimize \( P(x) = C(x)/x \). But if \( C(x) = 5000 + 120x - 0.5x^2 \), then for large \( x \), the \( -0.5x^2 \) dominates and cost per unit becomes negative — impossible.

🔥 Popular Posts

Average speed = \( \frac{40 + 68}{2} = 54 \) km/h
Daily flight time = 8 hours
Daily distance = \( 54 \times 8 = 432 \) km
Total distance over 12 days = \( 432 \times 12 = 5184 \) km
#### 5184
An online astrophysics student calculates that a distant star emits en...
First, convert 2.5 years to seconds:
Seconds in one year = \( 365.25 \times 24 \times 3600 = 31,557,600 \)...
So, 2.5 years = \( 2.5 \times 3.15576 \times 10^7 = 7.8894 \times 10^7...
Energy = Power × Time = \( 3.8 \times 10^{26} \times 7.889

📝 Recent Posts

Check powers: is it divisible by \( 16 \)? Try 1–5: product \( 120 \),...
Check 9: need two multiples of 3, but in five consecutive, only one mu...
Any five consecutive integers must include at least one multiple of 3?...
Thus, product always divisible by \( 2^3 = 8 \), \( 3 \), \( 5 \), so...
And since for the sequence 1,2,3,4,5: product is \( 120 \), which is e...
Therefore, the largest integer that must divide the product of any fiv...
Question: What is the sum of all positive divisors of \( 360 \) that a...
First, factor \( 360 \):
= 36 \times 10 = (2^2 \cdot 3^2) \cdot (2 \cdot 5) = 2^3 \cdot 3^2 \cd...
We seek divisors of \( 360 \) that are perfect squares. A divisor is a...

© 2026 Abbey Badges · Powered by WordPress

Disclaimer: This website operates exclusively as an informational archive. Content consists of publicly available international death records, condolence statements, and memorial information. The site does not provide real-time news coverage or entertainment content.