# Examples for 9th grade - page 61

1. Sinus Determine the smallest integer p for which the equation 4 sin x = p has no solution.
2. Target Peter, Martin and Jirka were fire in a special target, which had only three fields with values of 12, 18 and 30 points. All boys were firing with the same number of arrows and all the arrows hit the target, and the results of every two boys differed in one
3. Three days During the three days sold in stationery 1490 workbooks. The first day sold about workbooks more than third day. The second day 190 workbooks sold less than third day. How many workbooks sold during each day?
4. Apprentice Worker and apprentice execute the work for 6 hours. Worker performs himself in 10 hours. How long do the work of an apprentice?
5. Sequence Write the first 6 members of these sequence: a1 = 5 a2 = 7 an+2 = an+1 +2 an
6. Coffee shop To the coffee shop brought 2 types of coffee totally 50 kg. The first type was CZK 220 per kilogram, coffee second type 300 CZK per 1 kg. For all the coffee trader earned CZK 12,000. How many kilograms of coffee of first type and how many kilograms of cof
7. Square garden On the plan with a scale of 1:1500 is drawn as a square garden with area 81 cm2. How many meters is long garden fence? Determine the actual acreage gardens.
8. Grandmother Grandmother wants to give the candies to grandchildren that when she gives 5 candy everyone 3 missing and when she gives 4 candies 3 is surplus. How many grandchildren has grandmother and how many candies has?
9. Vector - basic operations There are given points A [-9; -2] B [2; 16] C [16; -2] and D [12; 18] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w.
10. Painters 4 One painter will do the job for 12 days. After a 4 1/3 day he comes second to help him and complete work together for 8 days. How long would work the second painter himself?
11. School School attend 792 children, boys and girls ratio is 4:5. How many more girls go to school (than boys)?
12. Quadrilateral 2 Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
13. Interst on savings The bank offers 1.6% interest. How many euros have to insert at the beginning if we received € 15 on the interest?
14. Car Car goes some distance in 3 hours and 20 minutes. If it increase speed by 10 km/h, i goes this distance in 2.5 hours. Calculate the distance.
15. Broken tree The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top but does not fall off it refuted on the ground. How far from the base of the tree lay its peak?
16. Saving Paul save 155Kč in 46 2 Kc and 5Kc coins. How much saved 2Kc and 5Kc coins?
17. Mushrooms For five days, we have collected 410 mushrooms. Interestingly every day we have collected 10 mushrooms more than the preceding day. How many mushrooms we have collected during 4th day?
18. Loan If you take a bank loan \$ 10000 and we want to repay after the year, we have to pay the total amount \$ 10320/ What is the annual interest rate on this loan?
19. Sines In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
20. Cube Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm2.

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