Examples for secondary school students - page 19
The lottery is 60000 elk in which 6200 wins. What is the probability that the purchase of 12 elks won nothing?
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.
- Volume from surface area
What is the volume of the cube whose surface area is 96 cm2?
- 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.
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.
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
- Area codes
How many 6 digit area codes are possible if the first number can't be zero?
- Hockey players
After we cycle five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other?
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.
If the angle α is acute, and cotg α = 1/3. Determine the value of sin α, cos α, tg α.
- Father and son
Father is three times older than his son. 12 years ago father was nine times older than the son. How old are father and son?
- 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.
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.
- Angles in a triangle
The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=60°. What sizes have other angles in a triangle?
- 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)
- 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)?
Calculate the coordinates of the circle center: ?
- Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
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?
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].