Examples for 9th grade - page 29
A child weighing 12 kg is sitting on a swing at a distance of 130 cm from the axis of rotation. How far away from the axis of rotation (center) must sit down his mother weighs 57 kg if she wants to be swing in balance?
- Exam average
Average of marks that have on the certificates students of 8.A class in mathematics is exactly 2.45. If we did not add 1 and 3 of sutdents Michael and Alena, who arrived a month ago, it would average exactly 2.5. Determine how many students have class 8.
- Mountain railway
Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track.
First painter painted fence himself for 12 hours, the second painter 3 hours sooner than first, and the third painters slowest up to 20 hours. How long took them paint fence if worked together?
The volume of the cuboid is 245 cm3. Each cuboid edge length can be expressed by a integer greater than 1 cm. What is the surface area of the cuboid?
- 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.
- Cuboids in cube
How many cuboids with dimensions of 6 cm, 8 cm and 12 cm can fit into a cube with side 96 centimeters?
Diagonal of the rectangle has length 14 cm. Angle between diagonal and londer sife of rectangle is 37°. Calculate area of the rectangle.
- Iron fence
One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m3.
The gasholder has spherical shape with a diameter 23 m. How many m3 can hold in?
- Complete construction
Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs.
At this point, the first skier lead 14 km before the second skier and travels at a constant speed 13 km/h. The second skier rides at 19 km/h. How long take him to catch up the first?
- The professor's birthday
Professor of mathematics had 48 birthdays. The director congratulated him. The professor asked the director: "And how old are you?" The director replied: "I'm exactly twice as many years than you were when I was old as to you today." How old is the direc
- Four-digit number
Find also a four-digit number, which quadrupled written backwards is the same number.
The voltage station is every day changing the master password, which consists of three letters. Code generation process does not change and is based on the following procedure: The following letters (A) to (I) correspond to different numbers from 1 to 9. I
- Circle sector
Circular sector with a central angle 10 ° has area 254 cm2. Calculate its radius r.
- 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?
The class is 22 students. How many ways can choose four to examination?
- Cross-country competition
Cross-country competition was attended by 76% of pupils of class 9.B. Class consis of 16 boys, two of whom did not run and 4 girls did not run. How many girls go to class 9.B?
- Katy MO
Kate draw triangle ABC. Middle of AB have mark as X and the center of the side AC as Y. On the side BC wants to find the point Z such that the content area of a 4gon AXZY was greatest. What part of the triangle ABC can maximally occupy 4-gon AXZY?