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This star has five spokes that are each $1$ unit long, and the angles between adjacent spokes are all the same.
How many copies of this star would you need to completely cover a bigger star with spokes of length $1.1?$
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Pierre in Paris $(48.9 ^\circ \text{ N}, 2.3 ^\circ \text{ E})$ and Sadie in Sydney $(33.9 ^\circ \text{ S}, 151.2 ^\circ \text{ E})$ each perform the following experiment:
- Set a pendulum swinging exactly along the East-West direction.
- As Earth rotates about its axis, the plane of oscillation of the pendulum slowly rotates. Eventually, the pendulum will be momentarily swinging along the North-South direction.
- Measure the amount of time it takes for this to happen for the first time.
Whose pendulum will take a greater amount of time?
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A stuntman falls from the top of a building of height $H$. On his way down, he bounces off of an awning at a height of $h$ in a perfectly elastic collision. Immediately after the bounce, the stuntman moves horizontally.
For what value of $\frac hH$ will the man hit the safety cushion (at ground level) the farthest from the building?
Assume that air resistance is negligible.
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$\begin{aligned} 144 &= 12^2 \\ 1444 &= 38^2 \end{aligned}$
Are there any other numbers $144 \ldots 44$ (starting with 1 and followed by all 4s) that are perfect squares?
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The function $f(x)$ is defined for real constants $a,$ $b,$ $c,$ and $d:$
$f(x)=x^4+ax^3+bx^2+cx+d.$
The graph of the function is shown below.
Given that the tangent lines at $\big(1,f(1)\big)$ and at $\big(5,f(5)\big)$ coincide, what is the value of $a+b?$
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