1 The given parabola 
doesn't intersect the 
-axis and passes from the points 
and 
. Find all the possible values of the 
coordinates of the vertex of this parabola.
doesn't intersect the -axis and passes from the points and . Find all the possible values of the coordinates of the vertex of this parabola. 2 The area and the perimeter of the triangle with sides 
are equal. Find all the triangles with integral sides whose area and perimeter are equal.
are equal. Find all the triangles with integral sides whose area and perimeter are equal. 3 In the acute angle triangle 
the point 
is the center of the circumscribed circle and the lines 
intersect sides 
respectively in points 
such that 
.
the point is the center of the circumscribed circle and the lines intersect sides respectively in points such that .(a) Find the ratios 
,
.
,.(b) If any of the angles of the triangle is 
, find the two other angles.
is , find the two other angles. 4 Find all prime numbers p such that 
is also a prime number.
is also a prime number. 5 The sweeties shop called "Olympiad" sells boxes of 
or 
chocolates. Groups of students from a school that is near the shop collect money to buy a chocolate for each student; to make this they buy a box and than give to everybody a chocolate. Like this students can create groups of 
students, 
students, etc. The seller has promised to the students that he can satisfy any group of students, and if he will need to open a new box of chocolate for any group (like groups of 
or 
students) than he will give all the chocolates for free to this group. Can there be constructed the biggest group that profits free chocolates, and if so, how many students are there in this group?
or chocolates. Groups of students from a school that is near the shop collect money to buy a chocolate for each student; to make this they buy a box and than give to everybody a chocolate. Like this students can create groups of students, students, etc. The seller has promised to the students that he can satisfy any group of students, and if he will need to open a new box of chocolate for any group (like groups of or students) than he will give all the chocolates for free to this group. Can there be constructed the biggest group that profits free chocolates, and if so, how many students are there in this group? 
Δεν υπάρχουν σχόλια:
Δημοσίευση σχολίου