Examples for 9th grade - page 46
- ISO trapezoid v2
bases of Isosceles trapezoid measured 12 cm and 2 cm and its perimeter is 18 cm. What is the are of a trapezoid?
- Paul and Honza
Honza went to chat on a bike without a break 3.0 hours. Paul the same way without breaks 30 minutes longer. The difference between the speeds of the two boys was the one kilometer per hour. How fast was Paul, if you know that the speed of the boys did not.
- The body
The body on the figure consists of cubes with an edge length 10 cm. What surface has this body?
Jarek bought new trousers, but the trousers were too long. Their length was in the ratio 5: 8 to Jarek height. Mother his trousers cut by 4 cm, thus the original ratio decreased by 4%. Determine Jarek's high.
Determine the smallest integer p for which the equation 5 sin x = p has no solution.
- Pedestrian up-down hill
Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian?
Above the town hall tower flew the plane with constant speed 508 km/h and 15 minutes later the second plane at speed of 651 km/h. How long and how far from the town hall will be aircrafts caught up?
- Inscribed rectangle
The circle area is 184. Determine the area of inscribed rectangle with one side 10 long.
- 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.
- Circle section
Equilateral triangle with side 50 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector.
- Round table
Round table with diameter d = 95 cm is coated by square tablecloth with a side length 122 cm. About how many cm is higher center of tablecloth than its cornes?
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.
- n-gon II
What is the side length of the regular 9-gon circumscribed circle of radius 13 cm?
Calculate the volume of a cuboid ABCDEFGH if |AB| = 11 cm, |BC| = 8 cm and the angle ∠CDG = 29.4°
Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 5 cm has same volume as a cube with an edge length of 1 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube'
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.
In ▵ ABC, if sin(α)=0.5 and sin(β)=0.1 calculate sin(γ)
Between the two ports on the river is going steamship. The journey there and back takes 14:49. Downstream steamship traveling at 21 km/h, upstream 9 km/h. What is the distance between the ports?
- Triangle ABC
Calculate the sides of triangle ABC with area 1789 cm2 and if a: b: c = 6:16:11
The area of the regular 5-gon is 505 cm2. The area of similar 5-gon is 606 dm2. What is the coefficient of similarity.