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What percentage of the square's area is colored blue?
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15 can be written as the difference between two positive perfect squares: $15 = 16-1= 4^2 - 1^2.$ Which of the following numbers cannot be written as the difference of two positive perfect squares?
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A factory manufactures wooden squares whose side length should be one meter. However, the side length of the squares is not always $\SI{1}{\meter}$ but varies uniformly between $\SI{1}{\meter}$ and $\SI{1.1}{\meter}.$ Note that the height and the breadth of each square piece remain equal to each other.
Two inspectors, Alice and Bob, want to calculate the average area of a square.
Who is correct?
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An accelerometer is made using tubular sections, as shown below. The accelerometer is placed in a rocket that travels in the $\vec{x}$ direction, and the liquid levels are steady at $\SI{20}{\centi\meter}$ and $\SI{10}{\centi\meter}.$
Find the magnitude of the rocket’s acceleration (in $\text{m/s}^2$). Submit your answer to 3 decimal places.
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A ladder is placed on a stairway (as shown). What is the length of the shorter leg?
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