# Grade - examples - page 54

1. Work
First paver pave pavement for 27 hours. Second for 27 hours. Started first paver and after 4 hours, join the second. How long will they finish pavement?
2. Diamond
Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal.
3. Triangle
Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
4. Vector sum
The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
5. Saving
Mom said that Suzan save about 120 EUR (rounded to tens). How many euros she could at least save (minimum)?
6. Painters
First painter painted fence himself for 4 hours, the second painter 1.2 hours sooner than first, and the third painters slowest up to 16 hours. How long took them paint fence if worked together?
7. Jan
Jan is 13 years and Peter 21 years old. For how many years will their ages in the ratio of 7:9?
8. Isosceles triangle
The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.
9. Paul and Honza
Honza went to chat on a bike without a break 4.0 hours. Paul the same way without breaks 50 minutes longer. The difference between the speeds of the two boys was the one kilometer per hour. How fast was Paul, if you know that the speed of the boys did not.
10. Square
If we increase side of the square, increase its area of 63%. What is the percentage we increase side of the square?
11. Arc
The length of the circle is 41 amd arc length of the circle 9. What is the magnitude of the angle of this arc?
12. Examination
The class is 21 students. How many ways can choose two to examination?
13. Resistors
Two resistors connected in series give the resulting resistance 216Ω and 48Ω in parallel. Determine the resistance of this resistors.
14. Center traverse
It is true that the middle traverse bisects the triangle?
15. Work
Workers works 5 days a week and has 21 days of vacation a year. Calculate how many days is out of work and express it as a percentage. Consider that a year has 52 weeks.
16. Juice box
The juice box has a volume of 200ml with its base is an isosceles triangle with sides a = 4,5cm and a height of 3,4cm. How tall is the box?
17. Angles 1
It is true neighboring angles have not common arm?
18. Enterprise and wages
The enterprise operates a total 162 workers and their average salary is M dollars. If the company has hire an additional 18 employees whose average wage would be the S dollars, would reduce the overall average salary in the company of 3.6%. Calculate the
19. Euclidean distance
Calculate the Euclidean distance between shops A, B and C, where: A 45 0.05 B 60 0.05 C 52 0.09 Wherein the first figure is the weight in grams of bread and second figure is price in USD.
20. Tourist
Tourist walk at 4.1 km/h. Every 5 km have 20-minute break. How many kilometers passed, when started at 4:40 and finished at 10:30?

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.