# Examples for 9th grade - page 43

1. Trees Loggers wanted to seed more than 700 and less than 800 trees. If they seed in rows of 37, left them 8 trees. If they seed in rows of 43, left the 11 trees. How many trees must seed ?
2. Machines 2 2 machines for 50 hours produces 2,000 products. How many machines need to buy to make in 30 hours 15,000 products?
3. Thales Calculate the length of the Thales' circle described to right triangle with hypotenuse 18.4 cm.
4. Rectangle The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to rectangle.
5. Chord MN Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle.
6. Total displacement Calculate total displacement of the 4-cylinder engine with the diameter of the piston bore B = 6.6 cm and stroke S=2.4 cm of the piston. Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and back.
7. Two pumps The first pump fills the tank in 24 hours second pump in another 40 hours. For how long will take fill the tank if operate both pumps at the same time?
8. Deposit 3 After a year had Martin on bank account € 2028. What was the interest rate when the initial deposit was € 1879?
9. Gravel - cone Mound of gravel has shape of regular circular cone with a height 3.3 meter and a base circumference of 18.85 meters. How many cubic meters of gravel are in the pile? Calculate the weight of gravel if its density is p = 640 kg / cubic m.
10. Clocks How long track travel the second hand in 46 hours, the end of which is 4 cm long.
11. Triangle SSA Construct a triangle ABC if |AB| = 5cm va = 3cm, CAB = 50 °. It is to create the analysis and construction steps.
12. Olympics In how many ways can be placed 6 athletes on the podium at the Olympics? Depend on the color of the metal.
13. Circular flowerbed Circular flowerbed with diameter 8 m we split by concentric circle to circle and annulus with the same area. Determine the radius of the circle.
14. Apples A 2 kg of apples cost a certain sum of money. This sum is equal to the amount of kilograms for which we pay 72 CZK. How much is 1 kg of apples?
15. Hexagonal pyramid Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
16. Bottle Bottle with wine costs 58 USD. Wine is 27 USD more expensive than the empty bottle. How much is the bottle itself?
17. Beer permille In the 5 kg of blood of adult human after three 10° beers consumed shortly after another is 6.6 g of the alcohol. How much is it as per mille?
18. Friends Some friends had to collect the sum 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends?
19. Algebrogram Solve algebrogram for sum of three numbers: BEK KEMR SOMR ________ HERCI
20. Rectangular trapezoid Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.

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