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Difference between revisions of "AMC 12C 2020 Problems"

(→‎Problem 2)
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==Problem 3==
 
==Problem 3==
  
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A field in the shape of a circle on the real <math>xy</math> plane is centered at <math>(5, 6)</math> and has a radius of <math>8</math>. The entire field is planted except for the part that is under the line <math>y = 0</math>. What fraction of the circular field is planted?
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A lamb is tied to a post at the origin <math>(0, 0)</math> on the real <math>xy</math> plane with a rope that measures <math>5</math> units. <math>2</math> wolves are tied with ropes of length <math>5</math> as well, both of them being at points <math>(5, 5)</math>, and <math>(-5, -5)</math>. What is the area that the lamb can run around without being in the range of the wolves?

Revision as of 13:56, 21 April 2020

Problem 1

What is the sum of the solutions of the equation $(x + 4)(x - 5)(x + 6) = 0$?


$\textbf{(A)}\ -5 \qquad\textbf{(B)}\ 0 \qquad\textbf{(C)}\ 5 \qquad\textbf{(D)}\ 12 \qquad\textbf{(E)}\ 14$


Problem 2

What is the numerical value of the sum $\sum_{k = 1}^{11}(i^{3} + i^{2})$


$\textbf{(A)}\ 4000 \qquad\textbf{(B)}\ 4608 \qquad\textbf{(C)}\ 4862 \qquad\textbf{(D)}\ 5792 \qquad\textbf{(E)}\ 6100$


Problem 3

A lamb is tied to a post at the origin $(0, 0)$ on the real $xy$ plane with a rope that measures $5$ units. $2$ wolves are tied with ropes of length $5$ as well, both of them being at points $(5, 5)$, and $(-5, -5)$. What is the area that the lamb can run around without being in the range of the wolves?

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