# Examples for secondary school students - page 19

1. Property
The length of the rectangle-shaped property is 8 meters less than three times of the width. If we increase the width 5% of a length and lendth reduce by 14% of the width it will increase the property perimeter by 13 meters. How much will the property cost
2. Average
What is the average speed of the car, where half of the distance covered passed at speed 66 km/h and the other half at 86 km/h.
3. Triangular pyramid
It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?
4. Volume from surface area
What is the volume of the cube whose surface area is 96 cm2?
5. Geometric sequence 3
In geometric sequence is a8 = 312500; a11= 39062500; sn=1953124. Calculate the first item a1, quotient q and n - number of members by their sum s_n.
6. Cubes
Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm2. Determine the length of the edges of this cubes.
7. Hexagonal pyramid
Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.
8. Carpet
The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diag
9. Area codes
How many 6 digit area codes are possible if the first number can't be zero?
10. Numbers
How many different 7 digit natural numbers in which no digit is repeated, can be composed from digits 0,1,2,3,4,5,6?
11. Center
In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
12. Cotangent
If the angle α is acute, and cotg α = 1/3. Determine the value of sin α, cos α, tg α.
13. Angles in a triangle
The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle?
14. Park
In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
15. School trip
Class has 17 students. What different ways students can be accommodated in the hostel, where available 3× 2-bed, 1× 3-bed and 2× 4-bed rooms. (Each room has its own unique number)
16. Center
Calculate the coordinates of the circle center: ?
17. Statue
On the pedestal high 4 m is statue 2.7 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.
18. Cone
If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
19. Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.