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When a cannon is on the ground, the cannonball lands the farthest from the cannon if it's shot at a $45^\circ$ angle.
Now, when the cannon is on a cliff, what shooting angle $\theta$ makes the cannonball land the farthest?
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Can $\sqrt2, \sqrt3, \sqrt5$ all be numbers in an arithmetic progression?
Note: The three numbers do not need to be consecutive in the progression.
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A cube with side length 1 is sliced such that the cut is a regular hexagon (in red).
What is the side length of this regular hexagon (to 4 decimal places)?
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$\large \sqrt[3]{x+\sqrt[3]{x+\sqrt[3]{x+\cdots}}}\ =\ \sqrt[3]{x\ \sqrt[3]{x\ \sqrt[3]{x\ldots}}}$
The non-zero solution $x$ of the equation above can be written as $\frac{\sqrt{a}+\sqrt{b}}{2},$ where $a$ and $b$ are positive integers.
What is $a+b?$
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The infinite Atwood’s machine shown has a string passing over each pulley, with one end attached to a mass and the other end attached to another pulley.
The masses are held fixed and then released simultaneously, and the acceleration of the top mass is $\lambda g.$
What is $\lambda?$
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