# Algebra - problems - page 5

1. Cuboid
Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
2. Rectangular cuboid
The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
3. Clock
How many times a day hands on a clock overlap?
4. Server
Calculate how many average minutes a year is the web server is unavailable, the availability is 99.99%.
5. Z9-I-4
Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Fi
6. Bus vs. train
Bus started from point A 10 minutes before the train started from the same place. The bus went an average speed of 49 km/h, train 77 km/h. To point B train and bus arrived simultaneously. Calculate time of train journey, if train and bus travelled the.
7. Chickens and rabbits
In the yard were chickens and rabbits. They had 28 heads and 82 legs. How many chickens and how many rabbits was in the yard?
8. Inflation
What is better for people (employees)? ?
9. Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
10. Short cut
Imagine that you are going to the friend. That path has a length 270 meters. Then turn left and go another 1810 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
11. Discount
Ladies sweater was twice discounted. First by 17%, then by 17% of the new price. Its final price was 70 USD. Determine the original price of sweater.
12. River
From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
13. Tereza
The cube has area of base 225 mm2. Calculate the edge length, volume and area of its surface.
14. Right triangle Alef
The area of a right triangle is 294 cm2, the hypotenuse is 35 cm long. Determine the lengths of the legs.
15. No. of divisors
How many different divisors has number ??
16. Motion2
Cyclist started out of town at 19 km/h. After 0.7 hours car started behind him in the same direction and caught up with him for 23 minutes. How fast and how long went car from the city to caught cyclist?
17. Observer
The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence?
18. Proof PT
Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
19. Textbooks
After check of textbooks found that every 10-th textbook should be withdrawn. Together 58 textbooks were withdrawn. How many textbooks were in stock before withdrawn and how many after withdrawn?
20. Vinegar 2
How many percentage of getvinegar solution, if we mix to 2 liters of 5.9% and 2 liters of 3.5% vinegar?

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