Prasun in the Valley (inside joke)

Algebra Level 5

Prasun is walking along a mountain defined by the function \(y\leq \frac{1}{4} (x^3-2x^2-19x+20)\) where \(-10\leq x \leq 10\)

The sun, fixed at the point \((-5,21)\), is shining light in all directions. However, its light cannot shine through the mountain. After walking into the valley for a little while, the Prasun, being the genius he is, realizes that he can no longer see the sun when he looks over his shoulder. The point at which Prasun will once again be able to see the sun has the coordinates \((t,s)\). Find \(t\cdot s\).

This is part of the set Trevor's Ten

Details and Assumptions

  • The sun does not move.

  • Think of Prasun as a particle travelling along the function. Meaning his height is negligible.

  • Prasun walks from \(x=-10\) to \(x=10\). Or in other words, he walks in the positive direction.

  • No Prasun, you don't have X-Ray vision and you can't see through the mountain.

  • If you do this using Algebra, (It can be done by calc or Alg) you may run into a system of equations that you may want to use wolfram for. But it's not necessary as most of this problem deals with integers.


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