problem
stringlengths 18
2.25k
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stringlengths 1
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Find the [area](https://artofproblemsolving.com/wiki/index.php/Area) of the region enclosed by the [graph](https://artofproblemsolving.com/wiki/index.php/Graph) of $|x-60|+|y|=\left|\frac{x}{4}\right|.$
|
480
|
A4. The domain of the function $f(x)=\frac{3}{2-\cos x}$ is
(A) $[-1,1]$
(B) $\mathbb{R}^{+}$
(C) $\mathbb{R}-\{x ; x=2 k \pi, k \in \mathbb{Z}\}$
(D) $\mathbb{R}$
(E) None of the above.
|
D
|
6. If in the real number range there is
$$
x^{3}+p x+q=(x-a)(x-b)(x-c),
$$
and $q \neq 0$, then $\frac{a^{3}+b^{3}+c^{3}}{a b c}=$ $\qquad$
|
3
|
Let $ P(x) \in \mathbb{Z}[x]$ be a polynomial of degree $ \text{deg} P \equal{} n > 1$. Determine the largest number of consecutive integers to be found in $ P(\mathbb{Z})$.
[i]B. Berceanu[/i]
|
n
|
65. Can a quadrilateral have three acute angles?
|
Yes
|
3. Real numbers $a, b, c$ are pairwise distinct, and the coordinates of the three points are respectively: $A(a+b, c), B(b+c, a), C(c+a, b)$. Then the positional relationship of these three points is ( ).
(A) form an obtuse triangle
(B) form a right triangle
(C) form an equilateral triangle
(D) are collinear
|
D
|
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