Weekly Contest #104

(Ended)

Standings

Q1.

Define an operation $\star$ for positive real numbers as $a\star b=\frac{ab}{a+b}$. Then $4 \star (4 \star 4)$ equals:

 

Answer must be a floating-point or integer value and precision error less than 10^-6 is allowed.


Editorial
Tags: Algebra

Q2.

A straight line passing through the point $(0,4)$ is perpendicular to the line $x-3y-7=0$. Its equation is:

 

Answer must be a floating-point or integer value and precision error less than 10^-6 is allowed.


Editorial
Tags: Geometry

Q3.

If $S=1!+2!+3!+\cdots +99!$, then the units' digit in the value of S is:

 

Answer must be a floating-point or integer value and precision error less than 10^-6 is allowed.


Editorial
Tags: Number Theory

Q4.

A triangle has angles of $30^\circ$ and $45^\circ$. If the side opposite the $45^\circ$ angle has length $8$, then the side opposite the $30^\circ$ angle has length

 

Answer must be a floating-point or integer value and precision error less than 10^-6 is allowed.


Editorial
Tags: Trigonometry