# Examples for 9th grade - page 36

1. Peleton
Cycling race was run at an average speed of 45 km/h. One cyclist lost with defect 8 minutes. How long and how far he must go at speed 51 km/h to catch peleton again?
2. Drunk and alcohol
One drunk measured 2.7 ‰ alcohol in the blood, another 1.75 ‰. How many grams of alcohol in the blood they had if they has 6 kg of blood?
3. Sports games
Pupils of same school participated district sports games. When dividing into teams found that in the case of the creation teams with 4 pupils remaining 1 pupil, in the case of a five-member teams remaining 2 pupils and in the case of six-members teams r
4. Cable car
Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
5. Tin with oil
Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm2. Calculate how many liters of oil is in the tin.
6. Simple interest
Peter put into bank 790 euros deposit. After 2 years on account overall was 974 euro. What was the interest rate if bank add simple interest?
7. Climb
For horizontal distance 4.9 km road rise by 6.1 m. Calculate the road pitch in ‰ (permille, parts per thousand).
8. Car rent
Rental cars are paid a fixed daily fee plus 16 cents for each kilometer traveled. Samuel want to rent a car for a day and worked out that will pay 175 euros. When paying he got a 20% discount on the daily fee, the cost per kilometer is unchanged. Samuel th
9. Annulus
Two concentric circles form an annulus of width 10 cm. The radius of the smaller circle is 20 cm. Calculate the content area of annulus.
10. Rhombus IV
Calculate the length of the diagonals of the rhombus, whose lengths are in the ratio 1: 2 and a rhombus side is 35 cm.
11. Father and son
Father is 48 years old, son 23. When will be the father twice older than a son?
12. Logs
The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it?
13. Bus stop
Determine at what time the bus leaves from the bus stop outside the village, if you know that when you leave home at 8:00 and go at speed 3 km/h, you come to a stop 9 minutes after the departure of the bus, and when you go speed at 4 km/h, you come to the
14. Rotary cylinder
The rotating cylinder has a surface area 69.08 cm2. The area of the shell is 62.8 cm 2. What is the diameter of the cylinder?
15. Chord - TS
The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
16. The hall
The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m2. What were the original dimensions of the hall?
17. Copiers
The new copier copying a folder of papers 5 min. faster than the old. The operator used new, but out of toner and exchange took 5 min. In that time copied on the old. The whole work has been done for 9 min. How long would the work done only by old copier?
18. Diagonal in rectangle
In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts.
19. Rectangle - sides
What is the perimeter of a rectangle with area 266 cm2 if length of the shorter side is 5 cm shorter than the length of the longer side?
20. Angles and sides of the triangle
Triangle ABC has a circumference of 26 cm. Lengths of the sides are as follows: a = 11.2 cm; b = 6.5 cm. Arrange the interior angles in order of its size. ?

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