Examples for secondary school students - page 15
What must be the elevation of an observer in order that he may be able to see an object on the earth 782 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
Find the cuboid that has the same surface area as the volume.
- Triangle and its heights
Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
- Circular sector
I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector?
How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km).
In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
Mother bought 5 boxes of milk and 7 kg of potatoes and paid a total CZK 147. Aunt bought 7 boxes of milk and 3 kg of potatoes and paid 131 CZK. What is the price of one carton of milk and 1 kg of potatoes? How CZK together would have saved if bought at the
A cyclist is moving at 35 km/h and follow pedestrian who is walking at speed 4 km/h. Walker has an advantage 19 km. How long take cyclist to catch up with him?
Cinema auditorium is built for 3300 people. The first row is planned for 36 seats and each next gradually 4 more. How many rows of seats will have auditorium?
We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
- Electronics: Resistors in parallel
From relation for calculating the resistance of parallel combination of resistors: ? Calculate the R, if R1 = 2Ω a R2 = 15Ω
How many diagonals has convex 11-gon?
- Car factory
Carmaker now produce 4 cars a day more than last year, so the production of 388128 cars will save just one full working day. How many working days needed to manufacture 388128 cars last year?
- Triangular prism
The base perpendicular triangular prism is a right triangle whose hypotenuse measures 5 cm and one cathetus 2 cm. Height of the prism is equal to 7/9 of the perimeter of the base. Calculate the surface area of prism.
Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
- Lord Ram
When lord Ram founded the breed white sheep was 8 more than black. Currently white sheep are four times higher than at the beginning and black three times more than at the beginning. White sheep is now 42 more than the black. How many white and black sh
- MO circles
Juro built the ABCD square with a 12 cm side. In this square, he scattered a quarter circle that had a center at point B passing through point A and a semicircle l that had a center at the center of the BC side and passed point B. He would still build a ci
- Event probability
The probability of event P in 8 independent experiments is 0.33. What is the probability that the event P occurs in one experiment (probability is same)?
- Triangle KLB
It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area o
The rod are 1.9 m long hanging weights 4 kg and 1 kg on ends. Where are centre of rod (distance from weight 4 kg) to be in balance?