# Examples for 9th grade - page 35

1. Against each other
From two points A, B distant 23 km at the same time started two cars against each other at speeds 41 km/h and 65 km/h. How long does cars meet and what distance passes each of them?
2. Words
How many 3 letter "words" are possible using 14 letters of the alphabet? a) n - without repetition b) m - with repetition
3. Circles
In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).
4. Aluminum wire
Aluminum wire of 3 mm diameter has a total weight of 1909 kg and a density of 2700 kg/m3. How long is the wire bundle?
5. Railways - golden parachutes
As often happens in Slovakia habit, the state's financial institution which takes from poverty and gorilas give. A hardworking punishing taxes. Let's look at a short work of director Railway Company ZSSK - Mgr . P. K. : 18 months 'work' as director .
6. Sphere fall
How many percent fall volume of sphere if diameter fall 10×?
7. Permill
How many permill is 978 from 84370?
8. Train 2
The train slowed down from 90 km/h to 72 km/h in 5 seconds. How long track travel?
9. Trigonometry
Is true equality? ?
10. The camp
At the end of the camp a 8 friends exchanged addresses. Any friend gave remaining 7 friends his card. How many addresses they exchanged?
11. Triangular pyramid
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
12. Pipeline
How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter?
13. Two cars
Car A1 goes at average speed of 106 km/h and the second car A2 goes at 103 km/h. How many second will it take car A1 to circulate car A2? Assume that both cars are 5 meters long and the safety gap between cars is 1.5 meters.
14. Ray
Light ray loses 1/19 of brightness passing through glass plate. What is the brightness of the ray after passing through 7 identical plates?
15. Cosine
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
16. Clock hands
The hands on the clock shows the time 12 hours and 2 minutes. Calculate the size of a sharp angle between clock hands three hours later.
17. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
18. Pedestrian and the cyclist
Pedestrian and cyclist went against each from the two cities that are distant 40 km. Pedestrian started 30 minutes before the cyclist and walk an average speed of 5 km/h. What speed went cyclist when met after 120 minutes from the start of the pedestrian?
19. Function
For linear function f(x) = ax + ​​b ‬ is f(14)=179; f(15)=154. Calculate m, if f(m) = 2019 .
20. Scale
Cylinder was drawn in scale 2:1. How many times is the volume of the cylinder smaller in reality?

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