1982 年

In the figure, $OACB$ is a sector of a circle of radius $6\text{ cm}$. Arc $ACB$ is longer than the chord $AB$ by

In the figure, $x=$

In the figure, $ABCD$ is a square and $PAB$ is an equilateral triangle. $\angle CPD=$

In the figure, $AEC$ and $BED$ are two chords of the circle. $\angle CBD=$

In the figure, $PQ$ and $RS$ touch the circle at $A$ and $C$ respectively. $\angle ABC=$

$\log_{10}\left(x^{\log_{10}x}\right)=$

The graphs of $y=\dfrac{x^2}{2}$ and $y=x+2$ intersect at the points $(x_1,y_1)$ and $(x_2,y_2)$. Which of the following equations has roots $x_1$ and $x_2$?

Let $a>2$. The inequality $2x-2a<ax+5a$ is equivalent to

If $\begin{cases}x\ge0,\\ y\ge0,\\ x+y\le5,\\ 2x+y\ge4,\\ x\ge y,\end{cases}$ in which of the following shaded regions do all the points satisfy the above inequalities?

$a$, $b$ and $k$ are real numbers. If $k>0$ and $a>b$, which of the following must be true? I. $a^2>b^2$ II. $-a<-b$ III. $ka>kb$