# Grade - examples - page 37

- Degrees to radians

Convert magnitude of the angle α = 9°39'15" to radians: - Party

At the party everyone clink with everyone. Together, they clink 406 times. How many people were at the party? - Horizon

The top of a lighthouse is 17 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.] - Quadrant II

Calculate the radius of the quadrant, which area is equal to area of circle with radius r = 15 cm. - Boat

A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight? - Cone in cylinder

The cylinder is inscribed cone. Determine the ratio of the volume of cone and cylinder. The ratio express as a decimal number and as percentage. - Kids

How many different ways can sit 8 boys and 3 girls in line, if girls want to sit on the edge? - Similarity n-gon

9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S_{1}=190 dm^{2}and the diagonal length GD is 32 dm. Calculate area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm. - Perpendicular

What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]? - Rhombus HP

Calculate area of the rhombus with height 24 dm and perimeter 12 dm. - Geometric mean

Calculate the geometric mean of numbers a=15.2 and b=25.6. Determine the mean by construction where a and b are the length of the lines. - Rectangle

The perimeter of the rectangle is 22 cm and content area 30 cm^{2}. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers. - Oil rig

Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes? - Two runners

Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 mi - Tiles

From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles. - Supermarket cashiers

When at the supermarket are opened only 2 cash people waiting in the front approximately 12 minutes. How many will shorten the average waiting time in a front where supermarket open another three cashiers? - Trains for people

It is said that the train is synonymous to delay. Calculate the average speed of travel by train long 85 km, with regular train leave at 7:00 and arrive at 8:18, but train is late and has departure at 8:10 and arrive at 9:27. - Baker

The baker makes from 10 kg of flour 12 kg dough. How much flour he need to make a 100 kg dough? - Icerink

Rectangular rink with dimensions of 68.7 m and 561 dm must be covered with a layer of ice 4.2 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 9.7% greater than the volume of water. - Aircraft

The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.

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