Examples for 9th grade - page 20
- Oil rig
Oil drilling rig is 23 meters height and fix the ropes which ends are 8 meters away from the foot of the tower. How long are these ropes?
Area of circle inscribed in a square is 6. What is the area of a circle circumscribed around a square?
Rectangular rink with dimensions of 79.5 m and 529 dm must be covered with a layer of ice 4.5 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 10.9% greater than the volume of water.
- Geometric mean
Calculate the geometric mean of numbers a=23.4 and b=16.8. Determine the mean by construction where a and b are the length of the lines.
Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees).
- Triangle TBC
TBC is isosceles triangle with base TB with base angle 52° and legs length |TC| = |BC| = 30. How long is the base TB?
- Tetrahedral prism
Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm.
The plane flies at altitude 6800 m. At the time of first measurement was to see the elevation angle of 20° and second measurement of the elevation angle of 34°. Calculate the distance the plane flew between the two measurements.
Calculate distance between two points T[2; -10] and X[-6; 8].
- Circumferential angle
Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 5:5:3. Determine the size of the angles of the triangle ΔABC.
- Two workers
Two workers together execute some work in 10 days. The first worker would have done himself in 20 days. How many days would have done himself a second worker?
How many is subsets of set ??
- ISO trapezium
Calculate area of isosceles trapezoid with base 53 long, leg 43 long and with the angle between the base and leg 70 degrees.
A school survey found that 9 out of 16 students like pizza. If 5 students are chosen at random, what is the probability that all 5 students like pizza?
Apartment on the first floor was 10% more expensive than the same apartment on the second floor. The difference was 105 Kc annually. Calculate the annual rent of the apartment in the first floor and from apartment on the second floor.
- Trains for people
It is said that the train is synonymous to delay. Calculate the average speed of travel by train long 50 km, with regular train leave at 6:05 and arrive at 7:20, but train is late and has departure at 9:52 and arrive at 11:05.
The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
- Two runners
Two runners ran simultaneously towards each other from locations distant 21 km. The average speed of the first runner was 1/7 higher than the average speed of the second runner. How long should each ran a 21 km, if you know that they meet after 77 minute
- Map - climb
On the map of High Tatras in scale 1:25000 are cable car stations in the Tatranska Lomnica and in the Skalnate Pleso with distance 156 mm. Altitude of this stations are 944 m and 1755 m. What is average angle of climb of this cable car track?
Calculate height of the equilateral triangle if its perimeter is 54?