# Examples for 9th grade - page 22

- Pharmacy

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? - Chord

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? - Park

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 u_{1}= 22 cm and u_{2}= 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 m^{2}where the diameter is 206 dm and a central angle is 150°. Result round to three decimal places. - Cone

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

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. - Tiles

From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 390 tiles. - Hairs

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 cm^{2}? - 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.

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