From the diagram above, what is the area of the shaded parts?
We can take the squares roll by roll, starting from roll 1 (the topmost):
Roll 1: The total area of roll 1 is 4 unit sq. (1 sq. unit x 4), But the half of the area is not shaded so ¹⁄₂ x 4 sq, unit = 2 sq. unit And also the first square as the bottom half not shaded = ¹⁄₂ x 1 sq. unit = ¹⁄₂ sq. unit
So, shaded part of roll 1 is = 2 sq. unit - ¹⁄₂ sq. unit = 1¹⁄₂ sq. unit
Roll 2: We have a whole square and half of a square shaded = 1¹⁄₂ sq. unit
Roll 3: We have only half of a square shaded = ¹⁄₂ sq. unit
Total area shaded = 1¹⁄₂ +1¹⁄₂ + ¹⁄₂ = 3¹⁄₂ sq. unit
From the diagram above, what is the area of the shaded parts?
We can take the squares roll by roll, starting from roll 1 (the topmost):
Roll 1: The total area of roll 1 is 4 unit sq. (1 sq. unit x 4), But the half of the area is not shaded so ¹⁄₂ x 4 sq, unit = 2 sq. unit And also the first square as the bottom half not shaded = ¹⁄₂ x 1 sq. unit = ¹⁄₂ sq. unit
So, shaded part of roll 1 is = 2 sq. unit - ¹⁄₂ sq. unit = 1¹⁄₂ sq. unit
Roll 2: We have a whole square and half of a square shaded = 1¹⁄₂ sq. unit
Roll 3: We have only half of a square shaded = ¹⁄₂ sq. unit
Total area shaded = 1¹⁄₂ +1¹⁄₂ + ¹⁄₂ = 3¹⁄₂ sq. unit
The S&P 500 slumped 1.8% on Monday and Tuesday, thanks to China Evergrande, the Chinese property company that looks like it is ready to default on its more-than $300 billion in debt. Cries of the next Lehman Brothers—or maybe the next Silverado?—echoed through the canyons of Wall Street as investors prepared for the worst.
Telegram auto-delete message, expiring invites, and more
elegram is updating its messaging app with options for auto-deleting messages, expiring invite links, and new unlimited groups, the company shared in a blog post. Much like Signal, Telegram received a burst of new users in the confusion over WhatsApp’s privacy policy and now the company is adopting features that were already part of its competitors’ apps, features which offer more security and privacy. Auto-deleting messages were already possible in Telegram’s encrypted Secret Chats, but this new update for iOS and Android adds the option to make messages disappear in any kind of chat. Auto-delete can be enabled inside of chats, and set to delete either 24 hours or seven days after messages are sent. Auto-delete won’t remove every message though; if a message was sent before the feature was turned on, it’ll stick around. Telegram’s competitors have had similar features: WhatsApp introduced a feature in 2020 and Signal has had disappearing messages since at least 2016.
