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Microsoft Email Recall Now: Hackers Stole Your Inbox—Act Before Its Too Late! - Decision Point

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 An anthropologist recorded that a community gathers 18% more food during harvest season than in non-harvest months. If they gather 410 kg during harvest, how much do they gather monthly in non-harvest?

📌 Let x be the non-harvest harvest. Then x + 0.18x = 1.18x = 410 kg.

📌 A science communicators video on quantum physics received 4.8 million views. If 65% of viewers watched at least 75% of the video, how many viewers did that?

📌 A research grant of $225,000 was split among 4 scientists. Two received equal shares of $50,000 each, and one received 20% of the total. The remaining amount went to the last scientist. How much did the last scientist receive?

📌 Total distributed so far: $100,000 + $45,000 = $145,000.

📌 A science communicators YouTube channel gained 15% more subscribers in the second quarter than in the first, reaching 46,000 subscribers at quarter-end. How many subscribers did they have at the start of the second quarter?

📌 A science administrator distributed $180,000 among three labs. Lab A received 40% of the funds, Lab B received $30,000 less than Lab A, and Lab C got the remainder. How much did Lab C receive?

📌 Total to A and B: $72,000 + $42,000 = $114,000.

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Solution: Consider the polynomial:
z^6 - z^4 + z^2 - 1 = 0
So the roots satisfy either $ z^2 - 1 = 0 $ or $ z^4 + 1 = 0 $.
Roots from $ z^2 - 1 = 0 $:
$ z = \pm 1 $, both real, so imaginary part is 0.
Roots from $ z^4 = -1 $:
Write $ -1 = e^{i\pi} $, so:
z = e^{i(\pi + 2k\pi)/4} = e^{i\pi(2k+1)/4}, \quad k = 0, 1, 2, 3
So the roots are:
$ k=0 $: $ e^{i\pi/4} = \frac{\sqrt{2}}{2} + i\frac{\sqrt{2}}{2} $

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