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
Spiking bond yields driving sharp losses in tech stocks
A spike in interest rates since the start of the year has accelerated a rotation out of high-growth technology stocks and into value stocks poised to benefit from a reopening of the economy. The Nasdaq has fallen more than 10% over the past month as the Dow has soared to record highs, with a spike in the 10-year US Treasury yield acting as the main catalyst. It recently surged to a cycle high of more than 1.60% after starting the year below 1%. But according to Jim Paulsen, the Leuthold Group's chief investment strategist, rising interest rates do not represent a long-term threat to the stock market. Paulsen expects the 10-year yield to cross 2% by the end of the year.
A spike in interest rates and its impact on the stock market depends on the economic backdrop, according to Paulsen. Rising interest rates amid a strengthening economy "may prove no challenge at all for stocks," Paulsen said.
