Examples for 9th grade - page 22
At the pharmacy are in one container 20% solution in the second 50% solution of disinfectant. They need to prepare 24 L of 36-percent solution. What amount of solution from each container is needed to mix?
In a circle with radius r=11 cm is chord 4× longer than its distance from the center. What is the length of the chord?
- Two workers
The first worker completed the task by himself in 9 hours, the second in 18 hours. After two hours of joint work left first worker to a doctor and the second finished the job himself. How many hours worked second worker himself?
- Ladislav in Amsterdam
Ladislav was reward and went to conference in Amsterdam. Conferense fee was € 2184. Calculate how many books Ladislav could buy at the price of 42 and 28 euros if he don't want fill whole home library and he can buy only 63 books?
In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
- Rhombus base
Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u1 = 22 cm and u2 = 15 cm. Prism height is twice base edge length.
- Hexagon 5
The distance of parallel sides of regular hexagonal is 81 cm. Calculate the length of the radius of the circle described to this hexagon.
- Train from Prague
First train from Prague started at 8:00 hour at 40 kilometers per hour. Train from Ostrava started at 9:20 at 80 km per hour. In how many hours and how far from cities with trains meet if the distance of cities is 400 km.
- Tank and water
Cylindrical tank were poured with 3.5 liters of water. If tank base diameter is 3 dm, how height is water level in?
- Triangle SAA
The triangle has one side long 34 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
- Circle arc
Calculate the area of the circular arc in m2 where the diameter is 206 dm and a central angle is 150°. Result round to three decimal places.
If the segment of the line y = -8x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
9.A to attend more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, the ninth to mark 3. No one gets mark 4. How many students of class 9.A wrote a test to mark 5?
- Isosceles trapezoid
Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.
From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 390 tiles.
Suppose the length of the hair is affected by only the α-keratin synthesis, which is the major component. This synthesis takes place in the epithelial cells of the hair bulb. The structure of α-keratin is made up of α-helix, wherein in one revolution it is
- Pine wood
From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lum
- Volume from surface area
What is the volume of the cube whose surface area is 96 cm2?
- Triangular prism
Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm.
- Right triangle
Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.