# Examples for 7th grade (seventh) - page 13

1. The bridge
Across the circle lakepasses through its center bridge over the lake. At three different locations on the lake shore are three fishermen A, B, C. Which of fishermen see the bridge under the largest angle?
2. Box
Calculate the angle between box base 9 x 14 and body diagonal length 18.
3. Do you solve this?
Determine area S of rectangle and length of its sides if its perimeter is 102 cm.
4. Opposite numbers
Calculate opposite numbers (additive inverse) to given ones:
5. Workers
Workers digging a jump pit in the school yard. Pit has a cuboid shape with a length 12 m, a width 20 dm and depth 36 cm. They excavate 0.4 cubic meters of soil an hour. How much time (hours and minutes) is need to the excavate this pit?
6. Balance
The rod are 1.9 m long hanging weights 4 kg and 1 kg on ends. Where are centre of rod (distance from weight 4 kg) to be in balance?
7. Weight of air
What is the weight of air in the living room measuring width 5 m length 2 m and height 2.8 m? Air density is ρ = 1.2 kg/m3.
8. Rectangle A2dim
Calculate the side of the rectangle, if you know that its area is of 2590 m2 and one side is 74 m.
9. Car
Car travels 1/3 of the trip on the first day, second day 2/5 of the trip and left even 340 km for next days. How long is the trip?
10. Potatoes
Potatoes contain 78.6% starch. How many potatoes need to obtain 27 kg of starch?
11. Map
Forest has an area of ​​36 ha. How much area is occupied by forest on the map at scale 1:500?
12. School books
At the beginning of the school year, the teacher gave out 480 books and 220 textbooks. How many students were in the class?
Students of canoeists trip traveled in three days 102 km. Second day traveled 15% more than first day and at the third day 9 km over the second day. How many kilometers traveled each day?
14. 3-bracket
May be the largest angle in the triangle less than 20°?
15. Count of roots
How many solutions has equation x. y = 7757 with two unknowns on the set of natural numbers?
16. Water container
Container with water weighs 1.48 kg. When we cast 75% of water container of water weight 0.73 kg. How heavy is an empty container?
17. Company
After increasing the number of employees by 15% company has 253 employees. How many employees take?
18. Intersections
How many intersections have circles with radius 16 mm and 15 mm, if the distance of their centers is 16 mm.
19. 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?
20. Segments
Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?

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