Examples for secondary school students - page 52
Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
From a set of 32 cards we randomly pull out three cards. What is the probability that it will be seven king and ace?
- Three numbers
What is three numbers which have the property: the sum of the reciprocals of the first and second numbers is 12/7, the first and third 11/24 and the second and the third 3/8.
- Roof 8
How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
- VCP equation
Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probabi
The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights.
- Angles in ratio
The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z.
- Water reservoir
The reservoir shape of a cylinder having a diameter 8 m and a height 2.8 m. The device indicates that the reservoir contains 800 hectoliters of water. Calculate how much % of volume is used.
- AP 6
Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38
- De Moivre's formula
There are two distinct complex numbers z such that z3 is equal to 1 and z is not equal 1. Calculate the sum of these two numbers.
How much is sum of square root of six and the square root of 225?
The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white?
- Axial cut
The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
- The city 3
The city has 22,000 residents. How long it is expected to have 25,000 residents if the average annual population growth is 1.4%?
Total remuneration for workers is 47 000 CZK. The second worker received 20% more than the first and third 4000 CZK less than a second employee. How many CZK each received?
- Equation with abs value
How many solutions has the equation ? in the real numbers?
- Krkonose CZ
Tourist's rod on the tourist route in the Krkonose was 1/5 of its length into the ground. Snow fell in winter and 1/3 of the length of the rod remained above the snow. Find the height of the snow if the length of the part above the snow is 32 cm greater t
- Cube in sphere
The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.